Fayl:Seki Kowa Katsuyo Sampo Bernoulli numbers.png

(1.614 × 2.124 piksel, fayl həcmi: 5,41 MB, MIME növü: image/png)

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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, , 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 一 in the margin after the numerator n. So for example the fraction in the third column from the right (representing ) is written as 六分之一, which means 1/6; the fraction in the seventh column () is written 四十二分之一, which means 1/42. The sign is given by the characters under the marginal 一 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
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1712

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Original text :
Müəllif Seki Kowa
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Original text : public domain

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Public domain

This work is in the public domain in its country of origin and other countries and areas where the copyright term is the author's life plus 70 years or fewer.


You must also include a United States public domain tag to indicate why this work is in the public domain in the United States.

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  • 2009-08-21 20:05 Dominus 1614×2124 (5670611 bytes) correct orientation
  • 2009-08-21 19:19 Dominus 2124×1614 (5592933 bytes) {{Information |Description = Pages from ''Katsuyo Sampo'' tabulating binomial coefficients and Bernoulli numbers |Source = http://mathdl.maa.org/mathDL/46/pa=content&sa=viewDocument&nodeId=2591&bodyId=3549 |Date = 1712 |Author = Seki Kowa

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