Why is πr² the formula for a circle's area?

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%A…
en.wikipedia.org/wiki/William_Jones_(mathematician…
en.wikipedia.org/wiki/Aryabhata#Approximation_of_%…
Archimedes
en.wikipedia.org/wiki/Area_of_a_circle#Archimedes'…
Leonardo and Sato Moshun
en.wikipedia.org/wiki/Area_of_a_circle#Rearrangeme…
Cut The Knot area of a circle
www.cut-the-knot.org/Curriculum/Geometry/AreaOfCir…
Area of a circle, formula explained (mathematicsonline)
   • Area of a circle, formula explained  
Understanding the Formula for Area of a Circle #shorts (mathematicsonline)
   • Understanding the Formula for  Area o...  
Rabbi Abraham bar Hiyya Hanasi
www.cut-the-knot.org/Curriculum/Geometry/RABH.shtm…
Area of a Circle by Rabbi Abraham bar Hiyya Hanasi
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.
u.cs.biu.ac.il/~tsaban/Pdf/PublishedBackUp/Rabhsph…
Wikipedia
en.wikipedia.org/wiki/Abraham_bar_Hiyya#mathematic…
en.wikipedia.org/wiki/Archimedes#/media/File:Archi…


References
en.wikipedia.org/wiki/Proof_that_%CF%80_is_irratio…
en.wikipedia.org/wiki/Aryabhata#Approximation_of_%…


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