Circle of friends ravena: Child Care in New York
Circle of Friends | Ravena NY Day Care Center
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About the Provider
Description: Circle of Friends offers classroom and community-based special education programs that bring special education and therapeutic services to children in the most appropriate, least restrictive, or natural environment. This can be the home (particularly for very young children) or a general education classroom setting. An important aspect of this program is the commitment to collaboration and communication between parents, therapists, and educators.
Services for children are determined through an evaluation process in either Early Intervention (birth to three years of age) or the Committee on Preschool Special Education (three to five years of age). When approved by the local county Early Intervention (EI) or local school district Committee on Preschool Special Education (CPSE), the services are then provided. Each child receives services that meet his or her specific needs.
Additional Information: This facility is authorized to administer medications;Initial License Date: 9/8/1993;
Program and Licensing Details
- License Number:
42005 - Capacity:
68 - Age Range:
Total Capacity: 68;Infants: 0;Toddlers: 0;Preschool: 68;School-Age: 0; - Enrolled in Subsidized Child Care Program:
No - Schools Served:
Ravena-Coeymans School District - Current License Issue Date:
Sep 08, 2019 - Current License Expiration Date:
Sep 07, 2023 - District Office:
Albany Regional Office - District Office Phone:
(518) 402-3038 (Note: This is not the facility phone number.)
Location Map
Inspection/Report History
Where possible, ChildcareCenter provides inspection reports as a service to families. This information is deemed reliable,
but is not guaranteed. We encourage families to contact the daycare provider directly with any questions or concerns,
as the provider may have already addressed some or all issues. Reports can also be verified with your local daycare licensing office.
Date | Type | Regulations | Status |
---|---|---|---|
2018-08-03 | 418-1.5(aa) | Corrected | |
Brief Description: The following items must be used and stored in such a manner that they are not accessible to children: handbags, backpacks or briefcases belonging to adults; plastic bags; and toys and objects small enough for young children to swallow. |
|||
2018-07-26 | 418-1.5(n)(2) | Corrected | |
Brief Description: Play equipment must be installed and used in accordance with the manufacturer’s specifications and instructions, be in good repair, and be placed in a safe location. |
If you are a provider and you believe any information is incorrect, please contact us. We will research your concern and make corrections accordingly.
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Preschool Tuition 2022-2023 – Circle of Friends Preschool, Framingham, MA
Tuition in preschool programs is based on a child to teacher ratio of 6:1 for children 2. 9 through 4 and 7:1 for Pre-Kindergarten. Please note that our prices in the 9 Month Morning Program reflect a 3.25 hour school day. Children are grouped in classes according to age. Tuition is non-refundable. Final decisions regarding schedules and pricing will depend on EEC mandates and the COVID climate as of 8/1/2022. These hours of operation and rates are subject to change.
9 Month Morning Program |
|
---|---|
(Morning Program 9AM-12PM; Program Ends 6/9/23) |
|
Program |
10 Monthly Payments (9/1-6/1) |
5 Day AM (M-F) |
$757 |
3 Day AM (M/W/F) |
$472 |
2 Day AM (T/TH) |
$314 |
12 Month and 10 Month Program |
||||
---|---|---|---|---|
(Available 7:30am to 6:00pm in 9 or 10. 5 hr options) |
||||
12 Month Program- Monthly Tuition |
10 Month Program- Monthly Tuition |
|||
Up to 9 hours |
Up to 10.5 hours |
Up to 9 hours |
Up to 10.5 hours |
|
5 Day (M-F) |
$1,761 |
$1,828 |
$1,937 |
$2011 |
3 Day (M/W/F) |
$1,362 |
$1,446 |
$1,496 |
$1,592 |
2 Day (T/TH) |
$ 1,039 |
$ 1,133 |
$ 1,142 |
$ 1,247 |
Registration Fee – An initial non-refundable registration fee of $100 per child is required at the time a registration form is submitted. Students must register for each school year and all outstanding fees and deposits must be paid in full prior to registration. Annual registration fees for the Children’s Center and Preschool are limited to a maximum of $200 per family per year.
Programming Options, Tuition Deposits and Payments
9 Month Morning Program – This program runs on a 9 month school year calendar from 9 AM-12 PM with vacations similar to the Framingham Public Schools. A copy of the preschool calendar is distributed during the summer and is available on request. A deposit equivalent to one tuition payment is due on or before June 1st. This deposit holds the child’s place in the program for the school year from early September through early June. Tuition payments are then due by the first of the month from September through June. This program is a 9 month commitment. Tuition is broken into 10 equal payments, September – June.
Extended Day Program – This program is only for children enrolled in the 9 Month Morning Program. This program is for families that would like to lengthen their child’s day on the 9 month schedule. Students enrolled in the 9 Month Morning Program can register for extended hours for the school year. This program starts on the first day of preschool and ends on the last day of preschool. Rates are on the backside of the preschool registration form. Drop in extended hours are also possible on an occasional basis as space is available. The Extended Day Program is closed when the morning preschool program is closed. See school calendar for details.
The 12 Month Program – This program operates on a year round calendar from 9/6-8/31. The 12 Month Program is closed on the following holidays: Labor Day, Columbus Day, Day before Thanksgiving (close at 1:00), Thanksgiving Day, Day after Thanksgiving, Christmas Eve, New Year’s Eve, Martin Luther King Jr. Day, Presidents’ Day, Patriots’ Day, Memorial Day, Independence Day, and two professional days, one in March and one in August. When preschool is not in session, children in the 12 Month Program participate in our vacation and summer programs at no additional cost. A deposit equivalent to one month’s tuition is due on or before August 10. This deposit holds the child’s place in the program for the full year from September 1st through August 31st of the following year. Tuition is due the first of each month beginning in September. A 12 month commitment is necessary for this program. This program includes care every day that a child is scheduled to attend and the center is open.
The 10 Month Program – This program operates from 9/6-6/30. Great Program for Educators! The 10 Month Program is closed on the following holidays: Labor Day, Columbus Day, Day before Thanksgiving (close at 1:00), Thanksgiving Day, Day after Thanksgiving, Christmas Eve, New Year’s Eve, Martin Luther King Jr. Day, Presidents’ Day, Patriots’ Day, Memorial Day and one professional day, in March. When preschool is not in session, children in the 10 Month Program participate in our vacation program at no additional cost. A deposit equivalent to one month’s tuition is due on or before June 1st. This deposit holds the child’s place in the program for the school year from September 1st through June 30th. Tuition payments are then due by the first of the month from September through June. This program is a 10 month commitment. Families have the option of a 9 or 10.5 hour day schedule. See school calendar for specific dates.
Tuition Deposits: All deposits are adjusted annually. For those students who will not return the next year, the deposit, less any outstanding fees, is returned at the end of the program. As preschool places are extremely difficult to fill in the summer or mid-year, deposits and tuition payments are forfeited for students who do not begin or complete the school year for which they registered. If you choose to withdraw or make changes to your registered program, permanently or temporarily, before the end of the year, all or a portion of your deposit will be forfeited. See the Deposit Policy for more detailed information.
Summer Program – This program complements the school year. Children enrolled in the 12 Month Program are automatically enrolled in our Summer Program for their regular hours. Other students may attend all or some days with regular hours from 9:00 AM to 1:00 PM. Extended hours are available. Information and sign-up sheets for the Summer Program are distributed in the children’s backpacks in March. See the Summer Program brochure for additional information. To be eligible for enrollment in our summer program, children must be currently enrolled for the upcoming school year.
Holidays – Holidays are taken into account when setting the yearly tuition. Tuition for those months containing holidays is charged at the regular rate and is not reduced.
Sibling Discount – A sibling discount of 5% is applied to the least expensive regular tuition charge. Sibling discounts do not apply to additional hours or special programs.
Illness and other Absences – Because of staff scheduling requirements, credit or refunds are not given for illness or other absences. Please call the office (508-877-2593) whenever your child will not attend school.
Emergency Building Closures – In the event of severe weather conditions, closing the school is up to the discretion of the Director. A detailed message will be left on the school answering machine by 6AM (508)-877-2593 and an email will be sent to parents no later than 6:30 AM. If the building has to close due to an internal building emergency or a state of emergency declared by the governor, parents will be notified immediately via email/phone. Full tuition is due for months in which emergency conditions require the Center to close.
Late Payment and Returned Check Fees – Monthly tuition payments are due on or before the first day of the month. A late payment fee of $20.00 will be assessed for each month in which the payment is more than 10 days overdue. Failure to pay the full balance by the 15th of the month following the month in which payment was overdue will result in immediate disenrollment from Circle of Friends. A fee of $20.00 will apply for returned checks.
Late Pickup – If a parent is late in picking up a child or drops off earlier than their scheduled program hours, a fee of $2.00 per minute will be charged to their account
Circle of Friends 14379 Us Route 9w, Ravena, NY 12143
Circle of Friends 14379 Us Route 9w, Ravena, NY 12143 – YP.com
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Details
Phone: (518) 756-3124
Address: 14379 Us Route 9w, Ravena, NY 12143
Website: https://www.circleoffriendsprek.com
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Early Childhood Learning Center, Inc.
· Circle of Friends · 14379 Route 9w, Ravena, NY 12143-3703, US
Early Childhood Learning Center, Inc.
· Circle of Friends · NPI #1336392216
Early Intervention Provider Agency 14379 Route 9w, Ravena, NY 12143-3703, US
Early Childhood Learning Center, Inc. is a health care provider registered with Centers for Medicare & Medicaid Services (CMS), National Plan and Provider Enumeration System (NPPES). The National Provider Identifier (NPI) is #1336392216. The practice address is 14379 Route 9w, Ravena, NY 12143-3703, US. Published on October 23, 2008. Last updated on May 14, 2020.
Provider Information
NPI | 1336392216 |
Entity Type | Organization |
Organization Name | EARLY CHILDHOOD LEARNING CENTER, INC. |
Provider Name | EARLY CHILDHOOD LEARNING CENTER, INC. |
Other Organization Name | CIRCLE OF FRIENDS (Doing Business As Name) |
Other Name | CIRCLE OF FRIENDS |
Mailing Address | 14379 Route 9w Ravena NY 12143-3703 US |
Mailing Telephone | 5187563124 |
Mailing Fax Number | 5187569476 |
Practice Address | 14379 Route 9w Ravena NY 12143-3703 US |
Practice Telephone | 5187563124 |
Practice Fax Number | 5187569476 |
Certification Date | 2020-05-14 |
Enumeration Date | 2008-10-23 |
Last Update Date | 2020-05-14 |
Is Organization Subpart | N |
Authorized Official Information
Official Name | MS. APARNA SHENOY |
Official Title | EXECUTIVE DIRECTOR |
Telephone | 5187563124 |
Taxonomy and Licenses
Primary | Code | Classification | Specialization | Taxonomy Group | License Number |
---|---|---|---|---|---|
Y | 252Y00000X | Early Intervention Provider Agency | SED# 010402880287 (NY) |
Other Provider Names
Other Organization Name | Type |
---|---|
Circle of Friends | Doing Business As Name |
Secondary Practice Locations
Address | Telephone | Fax |
---|---|---|
2 Bethlehem Ct, Delmar, NY 120541306, US | 5187563124 | |
2 Bethlehem Ct, Delmar, NY 120541306, US | 5187563124 ext. |
Providers with the same name
Provider Name | Address | Taxonomy | Enumeration Date |
---|---|---|---|
National Association for The Treatment of Sexual Abuse · Circle of Friends | 105 N Rose St Ste 211, Escondido, CA 92027-3109 | Emotionally Disturbed Childrens’ Residential Treatment Facility | 2020-11-12 |
Life Steps Foundation · Circle of Friends | 365 E Beach Ave, Inglewood, CA 90302-3101 | Alzheimer Center (Dementia Center) | 2007-05-15 |
National Association for The Treatment of Sexual Abuse · Circle of Friends | 1223 Sarahfaye Ct, Escondido, CA 92026-2128 | Emotionally Disturbed Childrens’ Residential Treatment Facility | 2020-11-16 |
Primary Taxonomy
Code | 252Y00000X |
Taxonomy | Early Intervention Provider Agency |
Classification | Early Intervention Provider Agency |
Grouping | Agencies |
Definition: Early intervention services are an effective way to address the needs of infants and toddlers who have developmental delays or disabilities. The services are made available through a federal law known as the Individuals with Disabilities Education Act (IDEA). IDEA provides states and territories with specific requirements for providing early intervention services to infants and toddlers with special needs. In turn, each state and territory develops its own policies for carrying out IDEA and its requirements. Broadly speaking, early intervention services are special services for eligible infants and toddlers and their families. These services are designed to identify and meet children’s needs in five developmental areas. These areas are: physical development, cognitive development, communication, social or emotional development, and adaptive development. |
Notes: Source: National Dissemination Center for Children with Disabilities [7/1/2007: new] http://www.nichcy.org/pubs/parent/pa2txt.htm |
Providers with the same taxonomy
Provider Name | Address | Taxonomy | Enumeration Date |
---|---|---|---|
A Sprout Ahead Early Intervention, LLC | 130 Brookhill Pl, Mauldin, SC 29662-3217 | Early Intervention Provider Agency | 2022-07-30 |
Abreu Learning Services LLC | 865 Quincy Ave # 2, Bronx, NY 10465-2216 | Early Intervention Provider Agency | 2022-08-04 |
Daphnee Roseau | 16430 108th Dr, Jamaica, NY 11433-2904 | Early Intervention Provider Agency | 2022-07-29 |
Monsey Medical, P. C. | 20 Robert Pitt Dr Ste 212, Monsey, NY 10952-3340 | Early Intervention Provider Agency | 2022-08-04 |
Hwk Systems Inc. | 18635 80th Dr, Jamaica, NY 11432-5804 | Early Intervention Provider Agency | 2022-08-04 |
Tammy E Torocsik | 4840 Waller Rd Ste 200, Richmond, VA 23230-2912 | Early Intervention Provider Agency | 2022-07-26 |
The Resiliency Initiative Inc | 466 E Main St Ste 200, Middletown, NY 10940-2534 | Early Intervention Provider Agency | 2022-07-26 |
Bridget Rooney | 2235 Frederick Douglass Blvd Apt 2d, New York, NY 10027-6129 | Early Intervention Provider Agency | 2022-07-26 |
Jessica Ann Karcher | 68 Allison Ave, Taunton, MA 02780-6958 | Early Intervention Provider Agency | 2022-07-27 |
Danielle Amy Kestenbaum · Danielle Amy Robinson | 321 Doughty Blvd, Inwood, NY 11096-1348 | Early Intervention Provider Agency | 2022-07-25 |
Find all providers with the same taxonomy |
Providers with similar names
Provider Name | Address | Taxonomy | Enumeration Date |
---|---|---|---|
Early Childhood Learning Center of Greene County | 2395 Route 23b, South Cairo, NY 12482 | Early Intervention Provider Agency | 2008-04-10 |
Barbara and Jack Kay Early Childhood Learning Center | 5221 Hood Rd, Palm Beach Gardens, FL 33418-8924 | Occupational Therapist | 2015-11-10 |
The Florida Center for Early Childhood, Inc. | 4610 17th St, Sarasota, FL 34235-1843 | Occupational Therapist | 2008-10-10 |
The Florida Center for Early Childhood | 6929 Outreach Way, North Port, FL 34287-3493 | Community/Behavioral Health Agency | 2014-09-02 |
The Florida Center for Early Childhood, Inc. | 4620 17th St, Sarasota, FL 34235-1843 | Mental Health Counselor | 2011-09-14 |
Little Meadows Early Childhood Center | 6725 188th St, Fresh Meadows, NY 11365-3767 | Early Intervention Provider Agency | 2008-09-25 |
The Lucy Daniels Center for Early Childhood | 9003 Weston Pkwy, Cary, NC 27513-2201 | Group Psychotherapy Psychologist | 2007-01-24 |
The Florida Center for Early Childhood, Inc. | 4620 17th St, Sarasota, FL 34235-1843 | Mental Health Counselor | 2007-01-05 |
Chicot County Early Childhood Center | 422 Annex St, Lake Village, AR 71653-1809 | Developmentally Disabled Services Day Training Agency | 2007-03-13 |
Aba Early Childhood Support Center LLC | 514 W Moore St, Hackettstown, NJ 07840-2144 | Community/Behavioral Health Agency | 2017-03-07 |
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Storm Closings
Here are the latest closings, cancellations and delays.
Storm Closings as of 7:15am Thurs. 10/8/2020
Albany, NY
Achievements & Kids Express Mplwood | Closed |
Albany Pine Bush Discovery Center | Closed |
Berne-Knox-Westerlo CSD | Closed, No AM BOCES, No PM BOCES, Power outage Offices closed |
Bethlehem CSD | Closed, No in-person or virtual. Offices closed. Essential O&M staff 0nly |
Capital Region BOCES CTE Albany | Open, No virtual Adult LPN classes |
Christ the King Early Childhood Ctr | Closed, Closed due to power issues |
Circle Of Friends (Delmar) | Closed, Daycare closed too No power |
Cloverpatch (Albany) | Closed, Closed no power |
Colonie Youth Centers | Open, Shaker Road, Loudonville, and Southgate Only No BSP/ASP |
Executive Woods Childcare | Closed, due to power outage |
Guilderland CSD | Closed, Remote classes cancelled Offices open except LES |
Helderberg Christian School | Closed, Closed due to power outages |
Kidz Korner (Latham) | Delayed Until 10a, Final decision to closed by 9:30am |
Kidz Korner After School | Open, Kidz Korner After School will open at 7am! Please pack a lunch!, Kidz Korner After School is opening at 7am. Please pack a bagged lunch! |
Langan School | Closed, no power, school staff do not report |
Loudonville Christian School | Closed, Power Outage |
Maria College | Closed, College closed. All classes cancelled. |
Mater Christi School | Closed |
Mercy Cares for Kids | Delayed 2-1/2 Hrs |
North Colonie CSD | Open, Loudonville and Southgate closed due to power outage; All other buildings open |
Pineview Comm Church Pre-School | Closed, No Power |
Ravena-Coeymans-Selkirk CSD | Closed, Due to power and internet outages throughout the district |
RiverRun Community Montessori | Closed |
Saint Gregory’s School | Closed |
School’s Out, Inc. | Closed |
Siena College | Closed, Classes Cancelled, Classes cancelled Thursday. Offices closed. Only essential personnel report. |
South Colonie CSD | Open, SHAKER ROAD Elem CLOSED COLONIE Academy AM closed SR staff will not report, Shaker Road Elementary Closed 10/8 due to power outages. Staff will not report. Colonie Academy AM Session closed. Staff will report. All other South Colonie Schools remain open as normal. |
St Colman’s School | Closed, Closed due to power outages across the area. Please be safe. |
St Madeleine Sophie School | Closed, No Virtual learning |
St Pius X School | Closed, Due to power outage |
St Thomas the Apostle School | Closed, No power. |
Tech Valley High School | Closed, Classes Cancelled, Online classes cancelled |
Voorheesville CSD | Closed, No AM BOCES, No PM BOCES, Power outages within the district Offices will be open |
Watervliet City SD | Closed, No AM BOCES, No PM BOCES, No Power No before/after care |
YMCA (Bethlehem) | Closed, No power |
Schenectady, NY
Achievements St Kateri Tekakwitha | Closed |
An Nur Islamic School | Closed, No school today Due to power outages and lack of available busing . |
Brown School | Closed, Closed due to power and internet outages. Remote classes cancelled. |
Duanesburg CSD | Open, Elementary School Remote Learning Day, Due to a power outage, today will be a Remote Learning day for all students in the Elementary School. Students should login to Seesaw or Google Classroom at 9 AM for instructions from their homeroom teacher. |
Early Childhood (ECEC) Schenectady | Closed, All ECEC Sites |
Mekeel Christian Academy | Closed, Closed due to power and internet outages |
Mohonasen CSD | Closed, Mohonasen is closed on Thursday October 8 due to Power and internet outages, Due to the recent windstorm and the associated power and Internet outages Mohonasen will be closed on Thursday, October 8, to all students whether in person or remote. |
Niskayuna Community Day Care Center | Closed |
Niskayuna CSD | Closed |
Notre Dame-Bishop Gibbons | Closed |
Pooh’s Corner Early Childhood Ctr | Closed, Early Childhood Center CLOSED due to power outage! |
Schenectady City SD | Closed, Classes Cancelled, District closed. O&M report to work. Central Office work remote., No classes in person or virtually due to power and internet outages. Central office staff work remotely; Operations and Maintenance staff still report to work. |
Schenectady Jewish CC Day Care | Delayed, Child Care opening 8:30 am More information to follow |
Scotia-Glenville CSD | Closed, No AM BOCES, No PM BOCES |
St Kateri Tekakwitha School | Closed |
YMCA – Thelma P. Lally Center | Delayed 2 Hrs, Power Outage Will reaccess at 8:30 and update if needed |
Rensselaer, NY
Averill Park CSD | Closed, Due to power outages |
Averill Park Pre School | Closed, due to power outages |
Berlin CSD | Closed |
Brunswick (Brittonkill) CSD | Closed |
Catholic Central HS | Closed, Due to power, Internet, and Phone outages. No remote Instruction. |
Early Childhood (ECEC) Troy | Closed, Remote Program, Remote Program, Staff check email |
East Greenbush CSD | Closed, No AM BOCES, No PM Activities, Due to power and internet outages |
Emma Willard School | Closed, No Morning Classes, Decision to hold afternoon classes remotely by 9 AM. Campus closed. |
Greenbush Child Caring | Closed |
Hoosick Falls CSD | Closed |
Jubilee Child Day Care Center | Closed, Due to power outages and road closures. |
Lansingburgh CSD | Closed, Due to loss of power |
Our Lady of Victory Early Childhood | Closed, due to power outage |
Questar III George Washington Sch’l | Closed, Due to power outages and loss of internet |
Questar III Sackett Educational Ctr | Closed, Remote instruction. |
Sacred Heart School (Troy) | Closed, No power No in person or virtual classes today |
Schodack CSD | Closed, No in-person or remote. |
Sunshine Day Nursery & DC East Grbh | Closed, Staff Report at 10am |
Susan Odell Taylor School | Closed, Due to power outage |
TLC Christian Day Care | Delayed 2 Hrs, No Breakfast, We have no power. Recheck Back no power by 9 we will Have to close, We have no power, recheck back frequently. If no power by 9 we will have to close. |
Troy City SD | Closed, District closed due to power and internet outages |
Troy Prep | Closed, Today will be an Asynchronous learning day due to power outages |
YMCA (East Greenbush) | Closed, due to a power outage, Remote Day Care is canceled |
Saratoga, NY
Clover Patch Pre-School (Glenville) | Closed, Closed no power, closed (No Power) |
Galway CSD | Closed |
Maple Leaf Childcare (Glenville) | Closed, Closed due to power outages |
Greene, NY
Circle of Friends (Ravena) | Closed, No Power and Roads closed |
Schoharie, NY
Jefferson CSD | Closed |
Washington, NY
Dix Ave. LEAP Head Start Center | Closed, Center Closed 10/8 – 10/14 Reopens 10/15 Staff Report |
Fort Edward UFSD | Closed, FE main campus full remote |
River St LEAP Head Start Center | Closed, Center Closed 10/8 – 10/14 Reopens 10/15 Staff Report |
Herkimer, NY
Owen D. Young CSD | Closed, Staff Report |
Tell me who your friend is: how to shape your environment correctly
The influence of others on our lives can hardly be overestimated, because our relatives and friends can both inspire and pull to the bottom. Coach and author of programs for the transformation of women Irina Pracheva tells how to create an environment for a successful and happy person.
Projection of your future
Since childhood, many people remember the saying “Tell me who your friend is, and I will tell you who you are”, so first you should evaluate who is your main social circle now. Our environment today is a projection of our future tomorrow – after all, whatever one may say, over time we become like those with whom we communicate.
If you want to be slim and start running, and your social media feed is full of recipes for delicious desserts, and you like to meet your friends in a cute cozy pastry shop for a cup of delicious hot chocolate, then you can easily assume that in a year you will not become slimmer and unlikely to run. Therefore, if we want to build weight, then we need slender friends in the environment who are already leading a healthy lifestyle, preferring green salads to delicious cakes and long walks in the fresh air for many hours of gatherings in a cafe. And if we want to run, then we need to join a running club, where running is part of the life of this community, and the marathon is a full-fledged rule, not an exception. Within a month, you will notice that running in the morning has become the norm for you – after all, you are doing it surrounded by your like-minded people.
Assess the focus of your interests
Analysis of the social circle also helps to understand what you are currently focused on, whether you have any distortions and in which direction you need to move. For example, if you are a mother on maternity leave, then, most likely, most of your contacts, one way or another, will be connected with children. However, if your phone book is filled exclusively with numbers like “pediatrician” and “developmental”, and on social networks you only discuss children’s successes or illnesses, it’s worth considering. Don’t focus on just one aspect of your life. We all understand that one of the recipes for a happy family life is to develop independently, to discover new and new facets in ourselves, including finding new hobbies and hobbies. In the end, no one is interested in hearing a story about “diapers” every day – if you think about it, it is precisely such stories that underlie many Hollywood comedies that we love to laugh at so much (the main thing is not to be in the role of such a heroine).
To be a harmonious and successful person with whom it is interesting to communicate, it is advisable to get rid of all distortions and fill your life with bright acquaintances and new interests (or remember those hobbies that inspired you so much in childhood).
Remove obstacles on the way
However, it is very difficult to change, dive into a new hobby, start a new business or project, investing your strength and energy when close people and the environment do not support you, but constantly only criticize and find a lot of reasons, why you shouldn’t do it or why you definitely won’t succeed. In this case, I have one hack.
Take your notebook and put a “+” sign next to the contact of a friend who supports you at any moment, inspires you to new achievements, believes in you and your abilities, and the “─” sign next to the one who cuts down any of your ideas at the root , constantly shows you your flaws and shortcomings, constantly dissatisfied with the world around him, likes to condemn and criticize.
If you want a bright and beautiful life, try to limit communication with people you gave a “minus” or at least not tell them about your plans and goals, but increase the time you spend together with those who support you and believes in you, who brings you closer to your dream.
Toxicity test
Surely, everyone has had a case of communication with the so-called energy vampire in their life. It seems that the person did not do anything wrong, and in itself he is good, and after communicating with him, his mood deteriorates sharply or his head starts to hurt. If you feel overwhelmed after the meeting or find yourself feeling like you’ve been taken advantage of, you’re most likely under the influence of a toxic person ( read : “How to Recognize and Neutralize Toxic People”). Constant contact with toxic people leads to emotional burnout and even depression, self-esteem and self-confidence drops. For your own good, it is worth ending or minimizing any relationship with people who take away your energy or manipulate you.
Check your earnings
The theory that your monthly income is actually equal to the arithmetic average of the income of 10 of your closest people (with whom you communicate the most) in a month is very fashionable. Therefore, do not be surprised if you have not made new acquaintances for many years and earn the same as your girlfriends, and you have not had a salary increase for 7 years. If you want to increase your well-being, then you need to include in your social circle people whose incomes today are much higher than yours.
Reach out for successful people
50 to 70 percent of success depends on the environment, and the rest – on ourselves. The environment shapes our values, our beliefs, our way of thinking and our way of life, so the formation of a social circle should be given special attention. Networking is now becoming a very fashionable direction, as businessmen have begun to realize how much the success of their business is connected with their acquaintances and connections.
Communication with successful and happy people motivates for new achievements. Try to be in the company of successful, in your opinion, people as often as possible, communicate, recharge with energy and optimism. Mark the qualities that you would like to develop in yourself, set yourself new goals.
About the author:
Coach, author of the transformational program “Awakening the Goddess”. Irina built a successful career on her own: she managed non-core assets at VTB, held the position of First Deputy General Director of Donstroy. She graduated with honors from MGIMO, the Executive MBA program at the Moscow School of Management Skolkovo and the Leader as a Coach program at the European Business Coaching Center together with the Ernst & Young Academy of Business. Since March 2018, by her own decision, she left the development company, deciding to devote her time to the author’s program for the development and improvement of women.
Marie Claire Editorial
Circumference and Circle – Umskul Textbook
On this page you will learn
- Where is the chord hidden in the dream catcher?
- What is the difference between a circle and a pizza?
- Why, if we want to change something dramatically, is it better to turn life around 180 degrees instead of 360?
Take a look around: geometric figures surround us everywhere, and in mathematics they are found in almost every task. The circle and the circle were no exception, which fall into puzzles more often than it might seem. Therefore, this article will be useful: you will master all the wisdom necessary for life and exams.
Hoop and circumference
Let’s remember one of the items of rhythmic gymnastics equipment – a hoop. This is a narrow ring of large diameter, inside of which there is nothing. The hoop consists only of a “contour”, that is, of the same ring. It is with the help of the hoop that we approach the term “circumference”.
Circle is a closed curve, all points of which are equidistant from the center.
Let’s analyze a little more, what does the phrase “equidistant from the center” mean . Suppose we know exactly where the center of our hoop is, and through this center we will stretch many, many ribbons. Then it turns out that the length of each ribbon from the center to the hoop will be the same.
That is, a circle consists of an infinite number of points that are located at an equal distance from the center.
Elements of a circle
Radius is a segment drawn from the center of the circle to any point on the circle.
If you remember the hoop with ribbons, then one ribbon is the radius. The radius is denoted by the letter R. In a circle, you can build many radii, and they will all be equal to each other.
Diameter is a line segment that connects two points on a circle and passes through the center of the circle.
You can immediately notice that diameter will consist of two radii , which are drawn on opposite sides of the center of the circle.
The diameter is denoted by the letter D and is equal to two radii.
D = 2R
Chord is a line segment joining any two points on the circle. In this case, the chord does not necessarily pass through the center of the circle.
Where is the notochord hidden in the dream catcher?
Imagine a dream catcher. When it is made, the thread is pulled from a point on the rim to a point on the other end of the rim. To get a beautiful pattern, the threads must be of different lengths and pass through different points – not necessarily through the center. |
Thus, a chord can have any size and any direction, the main thing is that its beginning and end lie on a circle.
Consider properties of chords.
1 property. When two chords intersect, the products of their segments are equal.
Let chords AB and CD be drawn in a circle and intersect at point O. Then the equality AO * OB = CO * OD is fulfilled.
2 property. Equal chords subtend equal arcs.
3 property. The diameter perpendicular to the chord divides this chord and the arcs subtracted by it in half.
If diameter CD is perpendicular to chord AB, then AE = EB.
Consider why this property is true. Let us complete the triangle AOB, in which AO and OB are radii. The radii in the circle are equal, therefore, the triangle is isosceles.
Consider OE – the height in an isosceles triangle drawn to the base.
The height in an isosceles triangle, drawn to the base, coincides with the median and the bisector, therefore, OE is the median, and therefore AE = EB.
Arc is a part of a circle whose beginning and end are two arbitrary points.
Let’s say some part is cut out of our hoop. Then both the cut part and the remaining part will be arcs.
Pizza and a circle
We have considered a circle. Here the question may already arise: what is the difference between a circle and a circle?
What is the difference between a circle and a pizza?
Imagine pizza. Is it round? Yes. Does she look like a hoop? No. Both the pizza and the hoop are shaped like a circle. The difference is that the hoop is hollow inside, while the pizza consists entirely of dough and toppings. In other words, the pizza contains not only the outline in the form of a crust, but also everything that lies inside it. |
Circle is a geometric figure that is bounded by a circle.
Circle elements
Consider elements of the circle.
Radius, chord diameter in a circle have the same definitions as in a circle. Since we are now considering not only the contour, but the entire figure, new elements appear.
Let’s say our friends are visiting us and now we need to share a pizza among everyone. Of course, we will cut it into several pieces.
The shape of the pizza slices is very reminiscent of a sector of a circle.
Sector is the part of the circle that is bounded by radii and an arc.
In this case, two radii divide the circle into two sectors: one larger and the other smaller. In the figure, one of them is painted purple and the other white.
If we want to cut only one slice of pizza, then both the cut slice and the remaining pizza will be sectors of the circle.
Now let’s cut the pizza differently. Let’s cut a slice in a straight line without passing through its middle:
Thus, we will cut off not a sector, but a segment from pizza.
Segment is the part of the circle that is bounded by a chord and an arc.
Moreover, one chord is the boundary for two segments: both the cut off piece of pizza and the rest will be segments. In the image below, one segment is colored purple and the other white.
Let’s summarize: Both in a circle and in a circle you can find radius, diameter, chord and arc. A sector and a segment additionally appear in the circle. |
Formulas for a circle and a circle
We have considered circles and a circle, as well as their elements, but no problem can be solved without formulas. Let’s look at them.
Before doing this, however, a few more terms must be entered.
Circumference is the length of the curve that forms the circles.
If we use a measuring tape to measure the length of our hoop, we will just get the circumference.
Arc length is the length of the part of the curve that forms the circle.
The only difference from the circumference of a circle is that not the entire curve is measured here, but only part of it.
The table below lists the basic formulas that may be encountered when solving problems.
Circular arc
An arc can be measured not only in units of length, but also in degrees. The entire arc of a circle has a degree measure of 360 \(\circ\) . Then half of the arc of the circle will be equal to 180.
In this case, the arc equal to 180 \(\circ\) is called a semicircle. The semicircle is limited by the two ends of the diameter.
We think that at least once in your life you have heard the phrase “turn 180 \(\circ\) degrees” or “change your mind to 180 \(\circ\) degrees”. This means that a person changes his mind literally to the opposite. Consider the example of a circle: let a person stand at point A. He needs to go along the circle exactly 180 \(\circ\) .
Since a person needs to go through a semicircle, it is limited by the diameter. Let’s complete the diameter AB, then our person will be at point B, that is, on the opposite side of the circle.
And if he passes the semicircle twice, he will again be at point A, that is, he will pass an arc of 2 * 180 = 360 degrees.
Therefore, if a person is at point O and wants to turn 180 degrees, then instead of point A, he will look at point B. When turning 360 degrees, the person will again look at point A.
Why, if we want to change something dramatically, is it better to turn life around 180 degrees, and not 360?
When we turn 180 degrees, we look at something from a completely opposite direction. But if we turn 360 degrees, then we will look at the same point that we looked at initially. |
Angles in a circle
Central angle is an angle whose vertex lies at the center of the circle. In this case, the angle rests on the arc of the circle.
In the figure, the AOB angle will be central.
Feature central angle:
- The central angle is equal to the degree measure of the arc on which it rests.
For example, the arc AB is equal to 36 \(\circ\) , then the angle AOB is also equal to 36 \(\circ\) .
An inscribed angle is an angle whose vertex lies on the circle. The inscribed angle must also be based on the arc of the circle.
Angle ACB is an inscribed angle in the figure.
inscribed angle properties:
- An inscribed angle is equal to half the degree measure of the arc on which it rests.
For example, the arc AB is 50 \(\circ\) , then the angle ACB is 25 \(\circ\) .
- Inscribed angles based on the same arc are equal.
Let the angles DIA, AEB and AKB rest on the soul AB. Then these angles will be equal to each other.
- The inscribed angle based on the diameter is 90 \(\circ\) .
Recall that the diameter divides a circle into two semicircles whose measures are 180 \(\circ\) . Then the inscribed angle will be 180 \(\circ\) : 2 = 90 \(\circ\) .
It is also important to note that inscribed angle is equal to half of the central angle. In this case, these angles must necessarily rely on one arc.
This is easy to prove if we recall that:
- the central angle is equal to the degree measure of the arc on which it rests,
- the inscribed angle is equal to half the degree measure of the arc on which it rests.
Hence \(∠ACB = \frac{1}{2}∠AOB\).
Fact check
- Circle is a closed curve, all points of which are equidistant from the center. The elements of a circle are radius, diameter, chord, arc.
- Circle is a geometric figure that is bounded by a circle. In addition to the radius, diameter and chord, a segment and a sector can occur in a circle.
- The entire arc of a circle has a value of 360 degrees. Then half of the arc will be 180 degrees.
- A circle has central and inscribed angles. In this case, the inscribed angle is equal to half the arc on which it rests, and the central angle is equal to the degree measure of the arc on which it rests. As a consequence, if the central and inscribed angles are based on the same arc, then the central angle is equal to two inscribed angles.
Test yourself
Task 1.
What is a circle?
- Closed curve, all points of which are equidistant from the center;
- Geometric figure bounded by a closed curve, all points of which are equidistant from the center;
- A geometric figure that has a round shape;
- Part of a plane bounded by a closed curve, all points of which are equidistant from the center.
Task 2.
What is the diameter of a circle?
- This is a line segment connecting the center of the circle and any point on the circle;
- This is a segment connecting two arbitrary points on the circle;
- This is a line segment that connects two points on a circle and passes through the center of the circle;
- This is half the arc of a circle.
Task 3.
What is the formula for finding the circumference of a circle?
- \(l = \frac{R}{180} * n\)
- \(C=2 \pi R\)
- C=2R
- \(l = \pi R\)
Task 4.
An arc of 60 degrees was selected on the circle. What fraction of the entire circle does this arc occupy?
- \(\frac{1}{2}\)
- \(\frac{1}{3}\)
- \(\frac{1}{6}\)
- \(\frac{ 1}{4}\)
Task 5.
The inscribed angle is 50 degrees. What is the central angle subtended by the same arc?
- 200
- 50
- 100
- 150
Answers: 1. – 1 2. – 3 3. – 2 3 5. – 3
BROOOKS RAVENNA 6
The
Ravenna 6 is a running shoe with a good balance of cushioning and support.
Store shelves are filled with plenty of running shoes with stability or overpronation control properties, but none of them have the same feel on the feet. In the design of such shoes, one common element is used – a rigid insert under the arch of the foot in the middle part. But how running shoes behave when running also depends on the density of the foam, the location and size of this rigid insert. Therefore, shoes with support for overpronators can have both a soft and inelastic ride, as well as either pronounced lateral support or little overpronation control. The main thing is to understand which sneakers are for whom. Easier said than done.
Fig.1 Functionally, the Ravenna 6 model acts as a bridge between neutral sneakers and shoes with serious stabilization.
Some runners want a cushioned shoe with good support thanks to the stiff midsole. The Brooks Ravenna 6 is designed specifically for this category along with other models such as the New Balance 860 V5 and the adidas Sequence 7 Boost. Although these sneakers belong to this category of shoes only partially.
Fig. 2 The insert in the middle of these shoes is present, but differs from other models with support.
The resemblance to soft overpronation-control shoes like the New Balance 860 V5 starts and ends with the amount of midsole cushioning. The difference becomes clear when running as the Ravenna is similar to a neutral pronator shoe, unlike the New Balance 860.
Let’s now look at the Saucony Guide 8 and the Asics GT 2000 3. Both models lean outward during planting. to the surface. Can they be compared to Brooks Ravenna? No, because all three models deviate to the outside in different ways.
The point of it all is that even in the common category of overpronation control shoes, it is difficult to find shoes with the expected properties. The only way to understand what sneakers you have in front of you is to try them on.
As you can guess, I’ll be comparing the Brooks Ravenna with other shoes from this manufacturer next. But first, let’s see where the Ravenna model is located on the Brooks playing field. There are several models in the Brooks line of pronation control shoes. The Brooks Beast 14 has the most pronounced lateral support. Next is the Adrenaline GTS 15 model. And finally, the Ravenna is the most inexpensive sneaker.
Just try on the Brooks Beast 14 once and you’ll immediately see how this shoe differs from Adrenaline and Ravenna. Let me explain the difference between the above two models.
Adrenaline GTS 15 have more support. In other words, the midsole, due to its lesser elasticity, begins to control the hyperpronator’s foot a little earlier at the time of its landing on the surface. An important point is related to how both models deviate to the outside. Outer midsole deflection is controlled, unlike competing Nike Structure 17 running shoes.
Fig. 3 Ravenna 6 have a soft ride, despite the DRB insert under the arch, the density of which varies.
Fig.4 The landing segment occupies a fairly large area. It is made from a stiffer foam than the white midsole. Together with the insert under the arch, it provides a stable ride.
The midsole of the Ravenna 6 is made from three different densities of foam. The arch insert is made of the densest and most rigid foam, the main part consists of the softest Biomogo DNA foam. The landing segment on the outside is painted green and made of inelastic foam.
Near the heel, the DRB unit is almost as soft as the white DNA foam. Moving towards the middle part, the density of the foam in the DRB increases, at the point above the plastic segment, the foam practically does not compress.
Fig.5 The landing segment is located on the outside from the heel to the middle part. Two segments on the heel are made of hard rubber, the rest of the sole is covered with soft foam rubber.
Fig.6 The flex grooves and slots in the outsole are plentiful, providing flexibility and smooth transitions from planting to pushing off.
The sole is almost completely covered with soft foam rubber, except for the heel area. Tough carbon rubber covers it in a horseshoe shape. The outsole at the heel is split in two by a flex groove that allows the landing segment to work independently while the foot is on the ground. Slots and grooves are located throughout the outsole, which contribute to improved flexibility and smooth transitions from placing the foot on the support to repulsion.
Fig. 7 The rubber on the outsole has good grip, I recommend Brooks engineers slightly increase its wear resistance.
Fig. 8 Removable anatomical insole. An indispensable attribute of many models Brooks .
Removable anatomic footbed made of Biomogo EVA foam with soft-touch fabric on top. The EVA foam pad under the insole is a standard component used throughout the Brooks shoe line. The midsole acts as a leveling layer of cushioning over the multi-component midsole.
Fig.9 Under the heel area has good cushioning.
The Ravenna 6 lateral support shoe has a good level of midsole softness comparable to the Ghost 7 and Glycerin 12 models. The heel area is made with a lot of padding. Thickly padded sidewalls on both sides hold the foot in place, preventing excessive outward flopping. The transitions from planting the foot to pushing off are smooth as the midsole is primarily composed of soft, uniform foam. These shoes may not be very responsive, but they are very soft and comfortable.
I summarized the overpronation control features of Ravenna 6 at the beginning of the review, and now I will add one small detail. The arch insert is located closer to the midfoot than the heel, and its density varies throughout its length. Therefore, a sense of control of overpronation occurs as the foot passes the midpoint as it moves across the surface. The work of the segment under the arch of the top is felt during the run, but is not felt noticeably.
The ride of the Brooks Ravenna 6 is close to neutral and will suit a lot of runners. Among them will be those who love a neutral ride. Therefore, Ravenna is well suited to both moderate overpronators and neutral pronators. The shoes are stabilizing, centered and have a wide forefoot.
Brooks BioMogo DNA Foam doesn’t really work the way marketers claim. They say the BioMogo foam material is non-Newtonian. Non-Newtonian materials change their density depending on the impact that is applied to them. Which means the foam will be soft when you walk and inelastic when you run. The original Brooks DNA Gel had this property. But the BioMogo DNA foam in every single new shoe (Ghost, Glycerin and Transcend) does not behave like a non-Newtonian material. Take Brooks Ravenna sneakers as an example. Foam stays soft no matter how fast you run. Claims that the shoe will “adapt to your running style” are purely marketing and have nothing to do with running practice. The midsole just cushions well, is made from eco-friendly materials, and is reasonably responsive. This is how Brooks had to describe their sneakers.
Fig.10 The fit in the midfoot is very tight as the Ravenna 6 uses split straps connected to the laces.
Fig.11 The strap covers the entire middle part of the top and is connected to the laces
Fig.12 The straps form elastic loops for the laces. The laces can be used to adjust the shoes to the foot.
The upper of the Ravenna 6 wraps around the foot tightly. Separate straps run between the outside of the upper and the interior trim. The straps pass into elastic loops and wrap around the foot well when laced up. These loops work better than other lace holes because they work independently and fit the shoe neatly around the foot.
Fig.13 The heel wrap is made from premium materials to keep your heel securely in place when you run.
Fig.14 Achilles recess made of soft elastic material.
Fig.15 The size of the sneakers corresponds to the declared one. The area of the fingers is covered with thin overlays.
The forefoot is tight around the foot. The shoes are true to size. Subtle overlays cover the toe.
________________________________________________________________________________
There are no seams inside the sneakers, but the areas under the overlays become like stiffeners that can rub your fingers.
Fig.15a This overlay forms a stiffener that rubs the thumb.
They bothered me and will be felt by other runners. Especially noticeable when running downhill, when your feet slide forward a little towards the toe.
________________________________________________________________________________
Overall, the Ravenna 6 is a great shoe with some great features and a smooth ride. Let’s start with quality upper materials with good functional elements. Pleasant to the touch mesh upper is made with a minimum of overlaps, which reduces the number of internal seams (reduces the risk of possible chafing of the foot when running without socks). An additional loop keeps the tongue in place and prevents it from slipping on your foot while you run. A thin layer of foam material was placed in the tongue to dissipate pressure from the laces on the foot.
Fig.16 The upper of the shoe feels nice to the touch. You can run in these shoes with or without socks.
Fig.17 Softly padded tongue with soft-touch fabric inside.
Fig.18 This loop holds the tongue in place and prevents it from slipping on the foot while running. Has reflective properties.
Fig.19 There is a thin layer of foam inside the tongue of the shoe.
You won’t get the feeling that Brooks engineers have skimped on material quality anywhere. The Ravenna 6 sneakers are an excellent choice in their price segment in terms of materials. The Ravenna 6 is a shoe with a good balance of cushioning and support.
Author: Alexander Crazy
Lesson 37. geometric probability – Algebra and the beginning of mathematical analysis – Grade 110003
Lesson #37. geometric probability.
The list of issues considered in the topic:
- Geometric probability
- Tasks for geometric probability
Glossary on the topic
testing
event is any fact that can occur as a result of a test.
Any test result is called outcome .
Reliable is an event that will definitely occur as a result of testing .
Impossible is an event that obviously will not occur as a result of the test.
The geometric probability of some event is the ratio P(A) = g/G, where G is a geometric measure expressing the total number of all equally probable outcomes of a given trial, and g is a measure expressing the number of outcomes favorable to event A
References:
Kolyagin Yu.M., Tkacheva M.V., Fedorova N.E., Shabunin M.I. Ed. A.B. Zhizhchenko. Algebra and beginning of mathematical analysis. Grade 11: textbook. for general education institutions: basic and profile. Levels. – 2nd ed. – M.: Education, 2010. – 336 p.: ill. – ISBN 978-5-09-022250
Vilenkin N. Ya., Ivashev-Musatov O. S., Shvartsburd S. I. Algebra and mathematical analysis for grade 11: Proc. allowance for school students. and classes with deepening. study mathematics. – 4th ed. – M.: Enlightenment, 1995. – 288 p.: ill. – ISBN 5-09-0066565-9. pp.253-259.
Open electronic resources:
I will solve the USE educational portal for preparing for exams https://ege.sdamgia.ru/.
Open bank of assignments for the Unified State Examination FIPI, Elements of combinatorics, statistics and probability theory, basic level. Elements of combinatorics, statistics and probability theory. A basic level of. http://ege.fipi.ru/.
Self study material
The probability of occurrence of some event A in a trial is equal to P(A) = g/G, where G is a geometric measure expressing the total number of all equally possible outcomes of this trial, and g is a measure expressing the number of outcomes favorable to event A.
Let some area D be given on the plane, the area of which is S(D) , and it contains the area d , the area of which is s ( d ). In the area D , a point is randomly placed. Then the probability of the event A is “the point falls into the region d “is equal to the number P(A) = s(d)/S(D).
Figure 1 – illustration of geometric probabilities
Let the segment l be part of the segment L. A point is randomly placed on the segment L. The probability that a point falls on the segment l is P(A) = |l|/|L|.
Let the spatial figure d form part of the figure D. A dot is placed at random in the figure D. The probability of a point hitting a shape d is P(A) = V(d)/V(D).
An example of using the geometric definition of probability in solving a problem.
Two friends agreed to meet at a certain place between 12 and 13 o’clock. The first person to arrive waits for the other for 20 minutes, after which he leaves. What is the probability of meeting friends if the arrival of each of them can happen
at random during the specified hour and the moments of arrival are independent?
Solution:
х – arrival time of the first friend
y – arrival time of the second friend
0≤х≤60, 0≤y≤60
⎮х-у⎮≤20.
Let’s make a drawing
Figure 2 – Illustration for the problem
S=60 2 –2 1/2 40 2 =2000
P(A) = 2000/60 2 = 5/9.
Answer: the probability of meeting is 5/9.
Examples and analysis of the solution of tasks of the training module
Example 1 . The meter cord is randomly cut with scissors. Find the probability that the length of the cut is at least 80 cm.
Solution:
The total number of outcomes corresponds to a cord length of 1 m. To make the cut length at least 0.8 m, you can cut no more than 0.2 m. Such cuts can be made on any side of the cord, their total length is 0.2 + 0.2 = 0.4 m. By geometric definition:
P(A)=l/L=0.4/1=0.4
Answer : 0.4
Example 2. A random point is thrown into the ball.
2a) What is the probability that it will hit the center of the ball?
Solution:
The volume of one point (the center of the ball) is equal to zero, which means that the desired probability is 0
Answer: 0
2b) What is the probability that it will fall on some diameter of the ball?
Solution:
Any point of the ball always falls on some diameter. Therefore, the probability is equal to one.
Answer: 1.
2c) How likely is it to fall into one particular hemisphere?
Solution:
When solving this problem, we use the ratio of the volumes of the figures. Let the entire volume of the ball be equal to V. All points of the ball are a three-dimensional figure Ω . The desired probability is equal to the ratio of the volume of the hemisphere V(A) to the volume of the ball V:
Answer: 0.5
Example 3. An isosceles right triangle is inscribed in a circle of radius cm. A dot is randomly placed in the circle. Find the probability that it will not fall into the given triangle. If necessary, use the value of π to the nearest integer in calculations.
Solution:
The area of a circle is
The hypotenuse of a right triangle inscribed in a circle is equal to the diameter of the circle (the right angle is based on the diameter), i.e. .
Since the triangle is isosceles, its legs are equal to each other, and by the Pythagorean theorem each leg is equal to . The area of such a triangle is0003
The probability of a point falling into a triangle is equal to the ratio of the areas of the triangle and the circle:
Answer: 1/3
Research work “Circle in our life”
Introduction.
Circle and circumference – one of the most ancient geometric figures, philosophers
ancient times attached great importance to them. Circle – the embodiment of endless Time
and Space, a symbol of all things, the Universe. “Of all the figures, the most beautiful –
circle,” said Pythagoras.
There are many round objects around us. Imagine
for a second, that a disaster suddenly happened: everything round on Earth disappeared!
It would seem – let everything be square. Is it impossible to live without round pipes,
And you can’t get used to square wheels? Is it even possible to imagine life
person without using a circle? Why so many bodies have
round shape? To find answers to all these questions, first of all,
it is necessary to consider the history of the emergence of these concepts and their further
development.
The history of the emergence and development of geometric concepts “circle” and
“circumference” .
For primitive people, the shape of the objects around them played an important role. By
shape and color, they distinguished edible mushrooms from inedible ones, suitable for
buildings of tree species from those that are suitable only for firewood, delicious nuts from
bitter, etc. Coconut palm nuts, similar to
ball. Of course, there were no special names for geometric shapes. They said:
“same as coconut” or “same as salt”, etc. Yes, mastering
the world around them, people got acquainted with the simplest geometric shapes.
Since ancient times, people have been interested in round bodies. In ancient Egypt for
the construction of the famous Egyptian pyramids, no technical structures have yet been
It was. Even huge blocks of stone had to be polished by hand, and moved
them with round logs. We noticed that rolling is easier if you take
a piece of wood with almost the same thickness at the beginning and at the end. So people
got acquainted with one of the most important bodies – cylinder . Rolling pins
women also used the cylindrical shape, rolling out linen after washing.
It was quite difficult to transport goods on skating rinks, because the wood
the trunks weighed a lot. To facilitate the work, they began to cut thin
round plates that rolled more easily and with their help dragged
cargo. This is how the first wheel appeared. Unfortunately, no direct
wheel inventor.
Not only in the process of work, people got acquainted with various figures. long time ago
they loved to adorn themselves, their clothes, their homes. And many created
a long time ago, decorations had one form or another. The beads were spherical
bracelets and rings had the shape of a circle. The ancient masters learned to give
beautiful form of bronze, gold, silver, precious stones. Painters,
those who painted palaces also used the circumference. Since the invention
potter’s wheel, people learned to make round dishes – pots, vases, amphorae.
The columns supporting the buildings were also round.
The mathematical knowledge of the Egyptians and Babylonians was scattered and represented
a set of rules tested by practice. In ancient Greece, all scattered
knowledge was brought into the system, geometry began to develop rapidly as a science. Only in
In ancient Greece, “circumference” and “circle” got their names, almost all names
geometric figures of Greek origin, like the word geometry itself (“geo”
– earth, and “metrio” – to measure). However, these words entered the Russian language not
directly from Greek, but through Latin.
In ancient Greece, many properties of figures, including circles and circles, were
formulated in the form of theorems and proved. The most successfully presented
geometry, as the science of the properties of geometric figures, by the Greek scientist Euclid
(III century BC) in his books “Beginnings”. For many centuries the “Beginnings” were
the only educational book by which young people studied geometry. And even
now, in our time, textbooks are written under the great influence of Euclid’s Elements.
Circle and circle are plane figures. We live
in a world of three dimensions. And what geometric body will the circle and
circle if they fall into space? This is a sphere and a ball. “Sphere” – came from
the Greek word “sfire”, in translation – “ball”. In addition, the geometry
space also considers other round bodies – this is a “cylinder” (from the Greek
the words “kyulindros”, which means “roller”, “skating rink”) and “cone” (from the Greek word
“konos”, meaning “pine cone”). by the most
important among the round bodies was the ball.
So, in ancient Greece, the circle and circumference were considered the crown of perfection. “AT
each of its points, the circle is arranged in the same way, which allows it
move on its own.” This property of the circle was the impetus for the emergence
wheels (Appendix 5) .
(Appendix 2) .
Circle – “circulus” – a Latin word, from it also “compass”, without which
we didn’t make a circle. The compass and straightedge are the oldest drawing tools in the world.
Earth. (Appendix 3.)
Circle and circle elements (Appendix 2) :
The radius of a circle is a segment connecting the center of the circle with any of its
dot (in Latin – wheel spoke) .
The diameter of a circle is the chord passing through the center of the circle (with
Greek – “diameter”).
Chord of a circle – a segment connecting any two points on a circle ( s
Greek for “string”).
Arc of a circle – is the part of a circle bounded by two points.
Often in practical problems it is necessary to find out the circumference of a circle. And how to measure
the circumference of a circle, if the circle itself is a curved line, and the unit of length is
– line segment? There are several ways to measure the circumference
(Appendix 1) .
However, these methods of direct measurement of the circumference are not very convenient and
give approximate results. Therefore, since ancient times, they began to look for more
perfect ways to measure the circumference of a circle. During the measurements, we noticed
that between the circumference of a circle and the length of its diameter there is a definite
dependence: С:d ≈ 3.1.
Many scientists – mathematicians tried to prove that this ratio is a number
constant, independent of the size of the circle, it began to be denoted by the Greek
letter π – the first letter of the Greek word
“periphery” – a circle.
C:d = π, where C is the circumference, d is the length of the diameter, hence the formula
circumference C = πd or
C = 2pr.
After studying the research of scientists mathematicians, we made the following measurements and
calculations:
1. Calculation of the number pi : a) using a thin thread, measure the length
circle With some household items; b) to more accurately find the length of the diameter d,
attached this object to a sheet of paper and circled it with a pencil, cut it out, folded it
in half, the fold line is the diameter, measured it with a ruler; c) found
C:d ratio, data entered in the table:
Table 1.
Circumference C | Diameter d | C:d ratio | |
Cup | 22 cm | 7 cm | 3.1428 |
Bucket | 82 cm | 26 cm | 3.1538 |
Plate | 62 cm | 19.5 cm | 3.1794 |
Saucepan | 69 cm | 22 cm | 3.1363 |
Can | 52 cm | 16.5 cm | 3.1515 |
2. Limits of the value of pi :
square: if the diameter is 1, then the circumference is
π. The perimeter of a square with side 1 is 4.
Hence π is less than 4. ( Appendix
6 . Fig.1). b) a regular hexagon was inscribed in the same circle: diameter
circle is again 1, the circumference is π.
The side of a regular hexagon is equal to the radius, i.e. 0.5, and the perimeter is
6 0.5=3, so π is greater than 3 ( Application
6 . Fig.2).
As a result, we have seen that the ratio of the circumference of a circle to its diameter
(number π) is a constant number and 3 ‹ π ‹ 4 , i.e. we confirmed the studies
scientist mathematicians.
One of the mysteries of the number π is that it cannot be expressed as –
or an exact fraction. The history of the number π is admirable, many mathematicians
spent more than a dozen years on its calculations. The lower and upper
estimates of the number and unsuccessful attempts were made to represent π as a fraction and,
so finally find its value
(Appendix 4) . While the record belongs to a Japanese mathematician, in 2004
year – Yasuma Canada from Tokyo calculated the number π on a computer to 1. 24 trillion
signs.
π -3.141 592653589793238462643 383279502
884197 169 399 375 105 ….
Why do we need π, and even with such accuracy? The number pi is extremely important for scientists
and engineers. Everything that is round and everything that moves in a circle (like wheels or
planets), contains π. Without π, people could not create cars, understand movement
planets or count how many peas fit in a tin can. But a riddle
mysterious number has not been resolved until today, and, as before,
worries scientists. At present, an incomprehensible set is associated with the number π
formulas, mathematical and physical facts. Their number continues
grow rapidly. All this indicates a growing interest in the most important
mathematical constant, the study of which has more than twenty-two
centuries.
After reviewing the literature and doing your own measurement studies with
circle and circle, we came to the following conclusions:
the circle and the circle are surprisingly harmonious figures. Circumference –
the only curve that can “slide on its own”, revolving around
center. This property of the circle gives an answer to the questions why for its
drawings use compasses, and why wheels are made round and not
square or triangular.
Circle in the surrounding life.
Investigating the question of the role of the circle in the surrounding life, we spent
survey of students in grades 5-9 and teachers MO SHISP (total 90 people):
- What round bodies do you meet in your life?
- What is the significance of the circle in other sciences?
- What practical tasks of everyday life are solved using knowledge
about circle and circumference? - Why do you think there are so many round bodies in nature?
Answers to the first question are provided in presentation .
From the answers of subject teachers to the second question of the questionnaire, we understood that
the circle is of great importance not only in mathematics, but also in other sciences:
Subject | Use |
Physics and astronomy | The movement of celestial bodies occurs in circular orbits. Zodiac circle, astronomical circle. Circle with a dot in the center |
Geography | Meridians and parallels that determine the position of the body on globe, equator. Circular processes-cycles: the cycle of water and substances in nature. Change of seasons, change of day and night. |
Chemistry | The structure of the atom: the nucleus is round, the electrons rotate around the nucleus in circular orbits. |
Biology | All cells have a round nucleus.
Round shape Plant stems and tree trunks, human bones – round. Blood circulation goes in a circle. Vegetables and fruits are spherical or cone-shaped. Cyclical development of living beings. |
Russian | In Russian, the word “round” means high degree of something: “round honors”, “round orphans” and even “round fool”. Many different words are formed from the word circle: round, Rounded shapes, round face, round cheeks, all year round, head |
History and social studies | “Round table” – conferences, circulation of capital, family circle, wheel of history, “large and small circle of history” – historical cycles. |
After analyzing the answers to the third question of the questionnaire, we realized that knowledge about the circle
and circles allow a person to solve many practical problems in everyday life.
life: break a flower bed or fountain, make a round roof, window or cover, sew
headdress, tie a napkin, make a Christmas toy, make a pattern
dresses or skirts, draw a pattern, etc.
Thus, the circle in a person’s life has a very important role, and in life
it is impossible to do without round objects.
Not everyone we interviewed was able to answer the fourth question.
Here we put the most interesting and common answers:
- Only round objects can roll and are therefore easier to move.
- Because wherever we go, we return, i.e. we go in a circle.
- The circle has no corners and is therefore easy to use, e.g. round
coins cannot tear a pocket, you won’t prick on them, you won’t cut yourself. - The ball cannot be square, it will not bounce.
- The dishes were made of clay, and it was easier to give a rounded shape than
square. Round dishes are easier to wash, no need to scrape out of the corners, in it
easier to stir. - It is easier to make round than angular. Many technical processes
easier for bodies of revolution. - There is less material for a round mold than for a square mold.
- A round manhole cover will never fail, unlike a square one.
- All jars and lids are round, as every point on the circle is
stress concentration point and easy to open, rectangular shape
only corners are such points. - Because the sun is round, and without the sun we could not exist.
- The round shape is universal in nature.
Why are there really so many round bodies? We turned to
scientific sources. This question can be answered by considering a soap bubble,
because it is perfectly round. Surface tension keeps it from bursting
soap bubble and strive to give the soap bubble the most compact
shape. The most compact shape in nature is a sphere. When spherical, air
inside the bubble evenly presses on all parts of its inner wall.
There are many round objects in the sky: Sun, Moon, planets, stars. Why not be
at least one non-circular planet? Well, let one be cubic or
pyramidal. But this is impossible? There is a force that in the whole universe
turns worlds into smooth balls. This force is the force of gravity. Each item has
its gravity, attracts other bodies to itself, as well as its parts. How
the larger the body, the more gravity increases. Our earth is huge, so it
has its own great gravity, which causes everything to be attracted to it
center, and the body is transformed into a ball. If for some reason it was possible
change our planet and give it a different shape, not a ball, then after some
time it would again become spherical. This does not happen with bodies on the ground,
because their force is very small and the gravity of the Earth prevents this. But
if you take, for example, a drop of water and launch it into space, it immediately
turns into a ball. It is the liquid that is able to transform into a spherical
shape. The earth is composed mainly of magma (liquid) and therefore has the shape of a ball.
Thus, we came to the conclusion that nature itself chooses this convenient and
compact spherical shape.
In addition, the circle and circle in the form of a sphere and a ball are the most common
form in the universe.
A circle and a circle are also the trajectory of the Earth around the Sun, this
the movement of stars in the sky is the cyclicity of all processes occurring in the world.
If it were necessary to choose a form that most accurately transmits the device
world, then it would be a circle and a circle.
After studying the scientific literature, we concluded that from time immemorial people
use a circle in their life.
1. Around 3300 BC, the potter’s wheel was used to make
round dishes – plates, vases, pots, pots, pans. The dishes have
circle (top edge) and circle (bottom).
2. We cannot imagine our life without cars: bus, tractor, bicycle,
sewing, washing and typewriter, aircraft, all-terrain vehicle, lunar rover, various
machine tools, a crane … They are not similar to each other, but take a closer look at them
take a closer look. They all have similar parts – details, and one of them –
wheel. At first the wheels were round and smooth, so that they rolled easily on the ground, and
then man came up with many different wheels. The gears are hidden inside
many machines, one wheel makes the other rotate, grooved wheels are blocks,
helping to lift heavy loads. Machines have improved over the centuries and
improved, but the use of a wheel in them remains unchanged, as
main detail.
3. Circle and circumference are widely used in architecture and art: round
arches, vaults, domes. The circle is a form of nomadic tents and settlements, many
peoples symbolizing dynamism and endless movement as opposed to squares
houses, plots of land and cities of settled and grain-growing peoples. More ancient Greeks
discovered that with the help of a compass and straightedge, many figures can be constructed,
including hexagons, squares and other regular polygons, and create
magical patterns.
4. The scope of the circle in mathematics is boundless: the trigonometric circle,
Euler circles, building problems, pie charts, etc. Many appliances
have a round scale, in mathematics such a device is a protractor
(Appendix 7) .
There are problems in mathematics that have not yet been solved, for example,
the famous problem of “squaring the circle” – about constructing a square of equal area
this circle, etc.
5. Pictures with magic circles are used by people for medical purposes when
you look at them, it seems that they are moving. If you look at them a few
minutes, then the headache goes away (Appendix 8) .
6. Also, a person uses a circle as a universal symbol, meaning
integrity, continuity, original perfection, infinity,
lack of beginning and end, top and bottom, cyclicity, repetition,
completeness. The three concentric circles symbolize the past, present and
future; three spheres of the earth: earth, air and water; heavenly worlds, earth and
hell; Moon phases; rising, noon and setting sun. many nations
use the circle in religion as a symbol of the earthly connection with the cosmos.
Recently, circles have begun to appear in different places on the globe.
fields that are created by messengers from other worlds, wishing to warn earthlings about something.
(Appendix 9) .
7. In the encyclopedia we found many more concepts related to the circle:
circular knitting machine, circular stocking machine, round pliers, round gauge,
“circular system” in sports, horizons, circle of friends, social circle, rescue
circle, holy circle, spiritualistic circle, all-round defense, mutual responsibility,
24-hour pharmacy, circles around the eyes.
Conclusion.
- The circle in a person’s life has a very important role, and without the use
round objects can not be dispensed with. - Circumference and circle – amazingly harmonious, perfect, simple
figures. The circle is the only closed curve that can “slide”
by itself”, rotating around the center, so the wheels are made round, and not
square or triangular. - A circle is a wheel. The wheel is progress – moving forward. If a
If the wheel stops, then the wheel of History will stop. Stop all kinds
transport, all clocks and mechanisms, factories and plants will stop. - Circle – a symbol of cyclicity, repetition. Everything moves in a circle.
- The circle gives a sense of interconnection with the Cosmos.
- Nature herself chooses this convenient and compact form as a sphere and a circle.
Phystech in jokes — Moscow Institute of Physics and Technology
15.09.2016 11:02:02
Phystech in jokes
You can understand whether you are a physicist at heart or not by whether you understand the jokes of the physicists. Most often they require knowledge of physics, mathematics, programming, the history of science, although sometimes just general erudition is enough.
Test yourself – at what level are you ready to give up?
Level 1 – Humanities
-
In the 2D world, dogs are nicknamed Circle
-
A woman is easy to understand: she is like an open book… a book on quantum physics in Chinese
-
Be as hard as ice, move like water and pffff like steam
-
Every age has its charm: 51 years old, for example, is divisible by 17
-
Once in my life there were graph paper, efficiency and a complex lunch. Now – flipchart, KPI and coffee break
-
The Romans thought math was pretty easy because they always had X equal to 10
-
When physicists joke – people are evacuated
-
Scientists from the Institute of Intrigue found that
-
Two first-graders did not share a guy, because the division takes place only in the third grade
-
From the point of view of computer science in the European Union, 1GB of space has been freed up
Level 2 Advanced Humanities
-
If you break the wall between the cafe and the anti-cafe, they will annihilate
-
Coincidence? I don’t think so, said Rene Descartes and disappeared
-
Dictionary for Mathematicians: Recursion (noun) – see recursion.
-
Only integrals are definite in this life, but not only angles are obtuse
-
Everything that is done – everything to non-decreasing entropy
-
If a triangular blanket is given to a sleepy person, he will go into an endless loop
-
Mathematicians are simple people, divided only by themselves and by one
-
To some extent, two is also eight
94″ – mathematician laughs
-
How do you know if borscht is salted? It is enough to immerse two electrodes into it and turn on the current, if the smell of chlorine appears – the borscht is salted!
-
Hello, I am the correct 65537-gon, and for friends just a circle
-
If you divide your rightness by zero, you will be infinitely right
-
If the experimental data on the graph do not correspond to theoretical calculations, make the points bolder
-
Three things can be looked at endlessly: isochoric compression, isothermal heating, and adiabatic heat transfer
-
Do it normally, it will be okay (c) Carl Gauss
-
Documentaries about the ionization of argon fall into the 18+ category
-
At school, Georg Ohm could teach one subject or several at once. It was parallel to him, he still strained the same way
-
Differentiate is a craft, integrate is an art
Level 4 Phystech
-
Bartender: “We don’t serve tachyons.” Somehow tachyon comes into bar
-
Mathematicians could not calculate surface integrals for a long time. And then Jordan had to take action
-
The picture “Bessel Equation” was almost ready – only a couple of strokes were missing
-
The whole world is ether, and you are in it Michelson
-
For a real physicist, BDSM is Boltzmann, Dirac, Sivukhin and Maxwell
-
From the point of view of quantum mechanics, it was not labor that made a man out of a monkey, but an operator of evolution
-
There are almost no straight curves in mathematics and there are no straight curves at all
-
What does “B” mean in the name of the creator of fractal geometry, Benoit B.