Length of an elastic band around 3 circles



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Can you solve this interesting geometry problem? References Solution by "WAY TO GOVT JOB" on YouTube 🤍🤍youtube.com/watch?v=oGNWdhh5qzg Stretched length of band 🤍🤍thestudentroom.co.uk/showthread.php?t=1936482 Subscribe: 🤍🤍youtube.com/user/MindYourDecisions?sub_confirmation=1 Send me suggestions by email (address at end of many videos). I may not reply but I do consider all ideas! If you buy from the links below I may receive a commission for sales. (As an Amazon Associate I earn from qualifying purchases.) This has no effect on the price for you. My Books (worldwide links) 🤍mindyourdecisions.com/blog/my-books/#worldwide My Books (US links) Mind Your Decisions: Five Book Compilation 🤍amzn.to/2pbJ4wR A collection of 5 books: "The Joy of Game Theory" rated 4.2/5 stars on 189 reviews 🤍amzn.to/1uQvA20 "The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 3.9/5 stars on 16 reviews 🤍amzn.to/1o3FaAg "40 Paradoxes in Logic, Probability, and Game Theory" rated 4/5 stars on 28 reviews 🤍amzn.to/1LOCI4U "The Best Mental Math Tricks" rated 4.1/5 stars on 53 reviews 🤍amzn.to/18maAdo "Multiply Numbers By Drawing Lines" rated 4.1/5 stars on 22 reviews 🤍amzn.to/XRm7M4 Mind Your Puzzles: Collection Of Volumes 1 To 3 🤍amzn.to/2mMdrJr A collection of 3 books: "Math Puzzles Volume 1" rated 4.4/5 stars on 67 reviews 🤍amzn.to/1GhUUSH "Math Puzzles Volume 2" rated 4.2/5 stars on 19 reviews 🤍amzn.to/1NKbyCs "Math Puzzles Volume 3" rated 4.2/5 stars on 15 reviews 🤍amzn.to/1NKbGlp 2017 Shorty Awards Nominee. Mind Your Decisions was nominated in the STEM category (Science, Technology, Engineering, and Math) along with eventual winner Bill Nye; finalists Adam Savage, Dr. Sandra Lee, Simone Giertz, Tim Peake, Unbox Therapy; and other nominees Elon Musk, Gizmoslip, Hope Jahren, Life Noggin, and Nerdwriter. My Blog 🤍mindyourdecisions.com/blog/ Twitter 🤍twitter.com/preshtalwalkar Merch 🤍teespring.com/stores/mind-your-decisions Patreon 🤍🤍patreon.com/mindyourdecisions Press 🤍mindyourdecisions.com/blog/press

Кадры из видео
Length of an elastic band around 3 circles
Length of an elastic band around 3 circles
Length of an elastic band around 3 circles
Length of an elastic band around 3 circles
Тэги из видео
Комментарии пользователей:
2023-10-30 17:08:00

That was a fun problem to solve, I got 3+pi or around 6.14. Let's see if I'm right..
edit: i got it :D although i probably went through more steps and calculations than I needed

2023-10-12 19:31:51

My intuition was correct.

2023-10-03 22:29:52

Taking a shot 3+pi

Each of the 3 straight sections has length 1. Each of the 3 wrapped sections is 1/3rd of the circumference of a circle with diameter 1, or pi/3. So 3(1)+3(pi/3)=3+pi

2023-09-26 05:57:05


2023-09-24 13:18:25

I solved it in 10th grade in a exam

2023-09-16 18:46:04

PziKimOJ7Yg&t=2m12s 2:12 2.pi.r = pi ? Should it be 2.pi ?
Edit : R is 1/2 unit

2023-09-13 22:02:14

I would just find the circumference of the circle and then close YouTube

2023-09-06 18:36:14

Well, I just missed the last circle 😂

2023-08-24 13:48:54

Я минут за 20 решил, спросони. Только угол 120 * иначе нашёл - через достраивание внешнего треугольника и сумму углов ромба. Но так даже элегантнее.

2023-08-19 15:59:05

I literally did this in my head in like two seconds after looking at the thumbnail lmfao

2023-08-17 06:03:20

Took about 5 seconds to add it all together in my head.

2023-08-17 05:18:40


2023-08-13 06:40:27


2023-08-12 17:21:41

I find these problems easy to solve. Just draw enough lines and put variables in between and you will have it.The hard part is to find the most simple and smartest way to do it without.

2023-07-31 18:16:10

i did it yeah

2023-07-31 15:35:58

3 + pi

2023-07-31 05:52:01

А доказывать, что получаются три прямоугольника, кто будет?

2023-07-29 17:52:28

But I solved this problem in a different way and my solution didn't match witj yours. I calculated the length of the circular arcs. As every arc have same length, I multiplied the length of one arc by 3.
Length of one circular arc=(2/3)×π
Total length of the arcs=3×(2/3)×π = 2π
The straight portions of the band have a total length of 3. So the total length of tje band becomes 3+2π.

2023-07-29 04:43:35

The thing that confuses me is that the line that goes around the circles has to be a finite length, where as pi is infinite

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