Welcome! This is a webpage I prepared very long ago, and haven't modified it much since.
If you wish me to upload any paper that is not uploaded yet, email me.
This is an illustration, by Shahar Yifrah, of a mechanical proof that the area of the disk is
πr^{2}. In available sources, the proof first appears in
The Book of Mensuration of the Earth and its Division, a 12th century book by
Rabbi Abraham Bar Hiya .
The proof illustrates that the area of the disk and the resulting triangle are identical.
Thus, the area of the disk with radius r is
2p r x r/2 = p
r^{2}
The proof can be justified mathematically (David Garber and Boaz Tsaban,
A mechanical derivation of the area of the sphere,
The American Mathematical Monthly108 (2001), 10--15. Available here.)
Some papers on mathematics in Jewish sources
All papers below were jointly written with David Garber of Holon Institute of Technology.
Every [Circle] whose Circumference,
Higayon 3 (1995),
Department of Mathematics, Bar-Ilan University, Ramat-Gan, pp. 103--131. [in Hebrew]
A Circular Booth,
Magal 10 (1994),
The Institute for Advanced Torah Studies, Bar-Ilan University,
Ramat-Gan, pp. 117--134.
The Proof of Rabbi Abraham Bar Hiya Hanasi,
in preparation. [in English].
Hmmm... about twenty years have passed and we haven't finished that paper.
I guess the "in preparation" should thus be judged misleading...