You are here

Mathematical Treasures - Seki Kowa's Essentials of Mathematics

Frank J. Swetz and Victor J. Katz


This is the title page of Seki Kowa’s (1642-1708) Katsuyo sampo [Essentials of Mathematics, 4 vols.], published posthumously in 1712. It is a collection of Seki’s discoveries including:

  • an accurate value of \(\pi\) to 10 decimal places and the computation of the volume of a sphere using enri, which was a “method of circles”;
  • “Newton’s” interpolation formula;
  • properties of spirals and ellipses;
  • derivation of “Bernoulli” numbers; and
  • the “Pappus-Guldin” theorem.


These are two pages in Volume I showing the table employed to obtain “Bernoulli” numbers. They are given in the right column and were obtained by a technique called Ruisai Shosa-ho.

Index to Mathematical Treasures

Frank J. Swetz and Victor J. Katz, "Mathematical Treasures - Seki Kowa's Essentials of Mathematics," Convergence (January 2011)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University