江戸時代の円周率の値 : 江戸時代の学問と通俗書の間

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In the books of the native mathematics of Japan published in the first part of the Edo Period, as the value of pi, (√<10>=) 3,16... had been widely adopted. But in 1663 S. Muramatsu demonstrated, in his Sanso, that the correct value of pi is 3. 14"-, and by 1680 almost all books of mathematics in Japan appeared to have adopted the correct value. In the history heretofore of Japanese mathematics, the value of pi had not been studied further. But we perceived that several books of mathematics published in the later Edo Period also had adopted 3.16... as the value of pi. We, therefore, attempted to check up the value of pi given in all the books of mathematics published in the Bunsei Era (1818-1830), when the publication of mathematical books was at the last zenith of prosperity in the Edo Period. According to "A Chronological Table of the Published Books of Mathematics and Astronomy" (ed. by T. Hirayama) the books of the native mathematics of Japan published during the Bunsei Era were assumed to number 51, of which 43 could be subjected to our examination. After these books of mathematics were divided into four, investigations were made of the value of pi in them. The results were as follows: 1. There were fifteen advanced books regarded as special works. In one of them the value of pi was mentioned as 3. 14, and in another one it was recorded as both 3. 14 and 3. 16, and the rest had nothing on the subject. 2. There were seven bulky books containing general remarks all together totalling over 200 pages, all of which gave 3. 14... as the value of pi. 3. There were ten guide-books of the Japanese paper size all together totalling 200 pages and less. In one of them the value of pi was mentioned as both 3. 14 and 3. 16, in two the subject was not mentioned, and in the remaining seven it was recorded as 3.16... 4. There were eleven guide-books smaller than the Japanese paper size numbering 200 pages and less. In two of them the value of pi was mentioned as 3. 14, in three the subject was not mentioned, and in the remaining six it was recorded as 3.16... The results of the inquiry above mentioned showed that the majority of the books of the native mathematics of Japan had adopted 3. 16 as the value of pi and that the books, which had adopted 3. 16 had been the guide.books assumed to have been read by children and the public at large. As a result it was shown that in the knowledge of the value of pi people who had read bulky books containing general remarks (300-500 pages) had been different from those of the general public in the Edo Period.
日本科学史学会の論文
1982-10-29

江戸時代の円周率の値 : 江戸時代の学問と通俗書の間

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