Ｋｉｄｓはこんなこと（エジプト・ギリシャ以前の古代数学）ばかりに興味を持って困る。一方で学校の教師は数学に歴史など不要と豪語する。
ARYAN TRIGONOMETRY
By Dinanath Atmaran Dalvi, M.A., LL.B.
theosociety.org/pasadena/theosoph/theos1c.htm#aryantrig
Western mathematicians call Hipparchus, the Nicaean, the father of trigonometry, although they confessedly know nothing whatever about him beyond what they find in the works of his disciple Ptolemy.
These pretended authorities suggest that Hipparchus
"probably employed mechanical contrivances 考案 for the construction of solid angles"
(Art. Mathematics, New Am. Cyc. XI., 283); on the presumption that the infant science of trigonometry was then just being evolved in its rudest beginnings.
en.wikipedia.org
But I shall give the THEOSOPHIST's readers an ancient Indian trigonometrical rule, for finding the sine of an angle, that long antedates より日時が古いHipparchus, and that is superior even to some of the European rules of our days.
I have used in certain places the Greek letters Pi and Theta for angles, agreeably to modern custom. The professional reader will, of course, understand that it is not meant that the Hindu mathematicians employed the Greek letters themselves at a period when, as yet, there was no such thing as the Greek alphabet; but only that they were aware of the numerical values represented by these symbols at the present time. The Hindu rule is as follows: —
This is an ancient Hindu expression approximating to the sine of an angle in terms of the degrees in numbers of that angle.
The expression is to be met with in Hindu works on astronomy; ex gratia: The Graha-la-ghava, not in its original pure form.
Its help is taken in the Hindu expressions for finding the equation of the centre.
The above is a regular proof for the satisfaction of professed Mathematicians, and shows that my Hindu ancestors, before the beginning of the Christian Era, were in possession of the supposed recent trigonometrical discoveries of Euler.
It is noteworthy that notwithstanding the great utility of this expression in Hindu trigonometry and astronomy, its author is unknown, or, at least, its authorship cannot be traced to a particular ancient Hindu at present.
This would almost imply a pre-historic antiquity for this branch of the "Divine Science" of Mathematics.
The approximative fractions used in the above proof are true to two decimal places, and consequently the expression is exactly true to two decimal places. It is therefore superior in accuracy to the common expressions
Sin or Sin to be met with in European works on Trigonometry, which are barely true to one place of decimals. It will please even a beginner in trigonometry to find the greater accuracy that distinguishes the Hindu expression from its European compeers. To take the simplest examples, viz., the sines of 90 degrees, 30 degrees and 45 degrees =
The first example shows that the mistake lies one in three hundred and twenty-three; that is, the expression is true to two decimal places, and the second example is open to a similar remark; the third clearly points out that the error lies in the third decimal of the denominator of the resulting fraction.
The expression is moreover neat and easily remembered. The expression for the cosecant will become shorter and neater still, thus:
en.wikipedia.org