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Mathematics has beauties of its own -- a symmetry and proportion in its results, a lack of superfluity, an exact adaptation of means to ends, which is exceedingly remarkable and to be found only in the works of the greatest beauty. When this subject is properly ... presented, the mental emotion should be that of enjoyment of beauty, not that of repulsion from the ugly and the unpleasant.
In H. Eves, Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
Loci: Convergence
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Mathematical Treasures
Seki Kowa's Essentials of Mathematics
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 π to 10 decimal places and the computation of the volume of a sphere using a “method of circles”, enri; “Newton’s” interpolation formula; properties of spirals and ellipses; derivation of “Bernoulli” numbers and the “Pappus-Guldin “ theorem.
These are two pages in vol 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.