Mathematics in Jewish Sources

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 πr2. 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 r2

The proof can be justified mathematically (David Garber and Boaz Tsaban, A mechanical derivation of the area of the sphere, The American Mathematical Monthly 108 (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.
  1. Every [Circle] whose Circumference, Higayon 3 (1995), Department of Mathematics, Bar-Ilan University, Ramat-Gan, pp. 103--131. [in Hebrew]

  2. A Circular Booth, Magal 10 (1994), The Institute for Advanced Torah Studies, Bar-Ilan University, Ramat-Gan, pp. 117--134.

  3. A Circular Booth II, Magal 11 (1995), pp. 127--134. [in Hebrew]

  4. Caveret (A Beehive), HaMa'ayan 35 (1995), pp. 57--69. [in Hebrew]

  5. On the Ratio of the Circumference of a Circle to its Diameter, Sinai 117 (1996), pp. 186--191. [in Hebrew]

  6. The Sathon Method for Exstracting Square Roots, MacroMathematics 2, pp. 29--34. [in Hebrew]

  7. Geometric discussions in Rabbinical writings, Higayon 4 (1998), Department of Mathematics, Bar-Ilan University, Ramat-Gan, pp. 4--17. [in Hebrew]

  8. On the Rabbinical Approximation of Pi, Historia Mathematica 25 (1998), pp. 75-84. [in English]
    Video presentation: slides, lecture

    You may also enjoy reading the Texas Mathematics Teacher issue on Pi.

  9. A mechanical derivation of the area of the sphere, to appear in The American Mathematical Monthly. [in English]

  10. 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...

  11. A laid down pillar, preprint. [in Hebrew]

  12. An early source for a mathematical method appearing in the TASHBETS responsa book, unpublished. [in Hebrew]

  13. Mathematical appendix to the TASHBETS responsa, preprint. [in Hebrew]

Short papers in Hebrew

1. Exact values of Pi in Jewish sources, preprint. [in Hebrew]

2. The slope of the altar's ramp (?), preprint. [in Hebrew]

3. Pi and a laid down pillar, preprint. [in Hebrew]

Related papers by other authors

Yuval Roichman, Rambam on Dimua and Isuraita DeRabi, preprint.

Ron Adin and Yuval Roichman, Mathematical aspects of combininig testimonies, Bechol Deracheicha Daehu (BDD) 30, 2015, 7-20.

Harir Shlomo (Z"L), Using mathematical Talmudic discussions in teaching, PhD thesis, Israrl Institute of Technology, 1999.

On the ratio of the circumference of a circle to its diameter, Avigdor Amitai.

Rabbi Daniel Hershkovitz, Mathematical problems in the Halacha and in Jewish sources

Alex Lubotzky, The Biblical Messorah as an error correction code, Tarbits, to appear. Chidushei Tora@NDS: Volumes 5 and 6 of this journal, online.

Imber David, A mathematical discussion in Section Succah, available in pdf format.

Michael A. B. Deakin and Hans Lausch, The Bible and Pi, The Mathematical Gazette 82 (1998), 162-166. Available online [pdf].

Binomial coefficients in Ben-Ezra's writings, by Yuval Roichman.

The mathematics of Levi Ben Gershon, The Ralbag, by Shai Simonson.

Book of Numbers: Exploring Jewish Mathematics and Culture at a Jewish High School, by Lawrence Mark Lesser.

Do Scripture and Mathematics Agree on the Number pi?, by Isaac Elishakoff and Elliot Pines, published in B’Or Ha’Torah 17 (2007).

Truth of land: Contains several interesting papers on mathematics and Jewish sources.

More papers

From the sages: Papers on mathematics in Jewish sources, which were published in Aleph Ephes.

Hidushei Tora @ NDS

A nice journal published by NDS, dealing with various topics related to Tora and Science. Issues 5+6+7 are available here.

Astronomy and Judaism

Wise Observatory's cite in Tel-Aviv University.

Mathematics in Islamic era: A comprehensive bibliography of papers on the subject including papers related to Jewish mathematicians.

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