MindYourDecisions | Why is πr² the formula for a circle's area? @MindYourDecisions | Uploaded 4 months ago | Updated 2 minutes ago
This formula has been known since ancient times. How did they figure it out?
0:00 intro
3:10 Archimedes
6:25 Leonardo and Sato Moshun
8:20 RABH
en.wikipedia.org/wiki/File:%E4%B9%9D%E7%AB%A0%E7%AE%97%E8%A1%93%E7%B4%B0%E8%8D%89%E5%9C%96%E8%AA%AA.jpg
en.wikipedia.org/wiki/William_Jones_(mathematician)#/media/File:Synopsis_Palmariorum_Matheseos_pi.jpg
en.wikipedia.org/wiki/Aryabhata#Approximation_of_%CF%80
Archimedes
en.wikipedia.org/wiki/Area_of_a_circle#Archimedes's_proof
Leonardo and Sato Moshun
en.wikipedia.org/wiki/Area_of_a_circle#Rearrangement_proof
Cut The Knot area of a circle
cut-the-knot.org/Curriculum/Geometry/AreaOfCircle.shtml
Area of a circle, formula explained (mathematicsonline)
youtube.com/watch?v=YokKp3pwVFc
Understanding the Formula for Area of a Circle #shorts (mathematicsonline)
youtu.be/0RGz_rvXVpk
Rabbi Abraham bar Hiyya Hanasi
cut-the-knot.org/Curriculum/Geometry/RABH.shtml
Area of a Circle by Rabbi Abraham bar Hiyya Hanasi
https://u.cs.biu.ac.il/~tsaban/Circles.html
David Garber and Boaz Tsaban, A mechanical derivation of the area of the sphere, The American Mathematical Monthly 108 (2001), 10--15.
https://u.cs.biu.ac.il/~tsaban/Pdf/PublishedBackUp/RabhsphereBU.pdf
Wikipedia
en.wikipedia.org/wiki/Abraham_bar_Hiyya#mathematicsvideo
en.wikipedia.org/wiki/Archimedes#/media/File:Archimedes_Palimpsest.jpg
References
en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
en.wikipedia.org/wiki/Aryabhata#Approximation_of_%CF%80
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This formula has been known since ancient times. How did they figure it out?
0:00 intro
3:10 Archimedes
6:25 Leonardo and Sato Moshun
8:20 RABH
en.wikipedia.org/wiki/File:%E4%B9%9D%E7%AB%A0%E7%AE%97%E8%A1%93%E7%B4%B0%E8%8D%89%E5%9C%96%E8%AA%AA.jpg
en.wikipedia.org/wiki/William_Jones_(mathematician)#/media/File:Synopsis_Palmariorum_Matheseos_pi.jpg
en.wikipedia.org/wiki/Aryabhata#Approximation_of_%CF%80
Archimedes
en.wikipedia.org/wiki/Area_of_a_circle#Archimedes's_proof
Leonardo and Sato Moshun
en.wikipedia.org/wiki/Area_of_a_circle#Rearrangement_proof
Cut The Knot area of a circle
cut-the-knot.org/Curriculum/Geometry/AreaOfCircle.shtml
Area of a circle, formula explained (mathematicsonline)
youtube.com/watch?v=YokKp3pwVFc
Understanding the Formula for Area of a Circle #shorts (mathematicsonline)
youtu.be/0RGz_rvXVpk
Rabbi Abraham bar Hiyya Hanasi
cut-the-knot.org/Curriculum/Geometry/RABH.shtml
Area of a Circle by Rabbi Abraham bar Hiyya Hanasi
https://u.cs.biu.ac.il/~tsaban/Circles.html
David Garber and Boaz Tsaban, A mechanical derivation of the area of the sphere, The American Mathematical Monthly 108 (2001), 10--15.
https://u.cs.biu.ac.il/~tsaban/Pdf/PublishedBackUp/RabhsphereBU.pdf
Wikipedia
en.wikipedia.org/wiki/Abraham_bar_Hiyya#mathematicsvideo
en.wikipedia.org/wiki/Archimedes#/media/File:Archimedes_Palimpsest.jpg
References
en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
en.wikipedia.org/wiki/Aryabhata#Approximation_of_%CF%80
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 purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
Book ratings are from January 2023.
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 4.3/5 stars on 290 reviews
http://amzn.to/1uQvA20
"The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias" rated 4.1/5 stars on 33 reviews
http://amzn.to/1o3FaAg
"40 Paradoxes in Logic, Probability, and Game Theory" rated 4.2/5 stars on 54 reviews
http://amzn.to/1LOCI4U
"The Best Mental Math Tricks" rated 4.3/5 stars on 116 reviews
http://amzn.to/18maAdo
"Multiply Numbers By Drawing Lines" rated 4.4/5 stars on 37 reviews
http://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 112 reviews
http://amzn.to/1GhUUSH
"Math Puzzles Volume 2" rated 4.2/5 stars on 33 reviews
http://amzn.to/1NKbyCs
"Math Puzzles Volume 3" rated 4.2/5 stars on 29 reviews
http://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.com/preshtalwalkar
instagram.com/preshtalwalkar
Merch
teespring.com/stores/mind-your-decisions
Patreon
patreon.com/mindyourdecisions
Press
mindyourdecisions.com/blog/press
