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| Keywords: Seki Kowa Katsuyo Sampo Bernoulli numbers.png This is a facsimile of the pages from the Katsuyo Sampo of en Seki Kowa that tabulate the binomial coefficients and the Bernoulli numbers Seki died in 1708 and the work was published in 1712 so it is in the public domain I obtained the file itself from the the web site of the Mathematical Association of America http //mathdl maa org/mathDL/46/ pa content sa viewDocument nodeId 2591 bodyId 3549 here then converted it from TIFF to PNG format The main portion of the table displays the binomial coefficients arranged in Pascal's triangle The coefficients are written using rod numerals The bottommost row tabulates the Bernoulli numbers The rightmost value is a special case 全 everything Each of the other entries is either 空 zero literally empty or a fraction n/d in the form d分之n See en Chinese_numerals Fractional_values for an elaboration of this notation There is a small double mark 二 in the margin before the denominatord and a small single mark in the margin after the numerator n So for example the fraction in the third column from the right representing <math>B_2</math> is written as 六分之 which means 1/6; the fraction in the seventh column <math>B_6</math> is written 四十二分之 which means 1/42 The sign is given by the characters under the marginal mark with 爲加 add indicating positive values and 爲減 reduce indicating negative values The complete reading of the bottom row right to left is everything 1/2 1/6 0 -1/30 0 1/42 0 -1/30 0 5/66 0 Dominus en wikipedia <br/> Original text http //mathdl maa org/mathDL/46/ pa content sa viewDocument nodeId 2591 bodyId 3549 1712<br/> Original file history Seki Kowa Original text public domain PD-old original upload log page en wikipedia Seki_Kowa_Katsuyo_Sampo_Bernoulli_numbers png 2009-08-21 20 05 Dominus 1614×2124 5670611 bytes <nowiki>correct orientation</nowiki> 2009-08-21 19 19 Dominus 2124×1614 5592933 bytes <nowiki> Pages from Katsuyo Sampo tabulating binomial coefficients and Bernoulli numbers http //mathdl maa org/mathDL/46/pa content sa viewDocument nodeId 2591 bodyId 3549 1712 Seki Kowa </nowiki> Mathematics books book covers single pages etc Recreational mathematics Arithmetic functions Combinatorics Integers Bernoulli numbers Seki Takakazu 1712 books 1712 in science | ||||
