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The Kerala school of astronomy and mathematics was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar. The school flourished between the 14th and 16th centuries and the original discoveries of the school seems to have ended with Narayana Bhattathiri (1559-1632). In attempting to solve astronomical problems, the Kerala school independently created a number of important mathematics concepts. Their most important results—series expansion for trigonometric functions—were described in Sanskrit verse in a book by Neelakanta called Tantrasangraha, and again in a commentary on this work, called Tantrasangraha-vakhya, of unknown authorship. The theorems were stated without proof, but proofs for the series for sine, cosine, and inverse tangent were provided a century later in the work Yuktibhasa (c.1500-c.1610), written in Malayalam, by Jyesthadeva, and also in a commentary on Tantrasangraha.Their discovery of these three important series expansions of calculus—several centuries before calculus was developed in Europe by Leibniz and Newton—was a landmark achievement in mathematics. However, the Kerala School cannot be said to have invented calculus, because, while they were able to develop Taylor series expansions for the important trigonometric functions, they developed neither a comprehensive theory of differentiation or integration, nor the fundamental theorem of calculus.In the fields of geometry, arithmetic, and algebra, the Kerala school discovered a formula for the ecliptic, Lhuilier's formula for the circumradius of a cyclic quadrilateral by Parameshvara, decimal floating point numbers, the secant method and iterative methods for solution of non-linear equations by Parameshvara, and the Newton-Gauss interpolation formula by Govindaswami
I think we should go back to Roman Numerals.
You are ofcourse correct that duodecimal has 3 different factors in its base, on the other hand, it just about balances out when you look at the base number, and those adjacent either side of it (it is fairly easy to determine if something is divisible by 3 or 9 in a decimal system because 3 is a factor of 9, and 9 is one below 10 - the comparable numbers for the duodecimal system are 11 and 13, both of which are prime).
Quote from: another_someone on 20/03/2008 16:45:53You are ofcourse correct that duodecimal has 3 different factors in its base, on the other hand, it just about balances out when you look at the base number, and those adjacent either side of it (it is fairly easy to determine if something is divisible by 3 or 9 in a decimal system because 3 is a factor of 9, and 9 is one below 10 - the comparable numbers for the duodecimal system are 11 and 13, both of which are prime).I'm not sure what point you are trying to make. 11 is also adjacent to 10. But what difference does it make if the numbers either side of the base are prime?
I wouldn't have thought that's something an ordinary person would do every day, so it isn't really of any practical benefit.
Although your reply is accurate, it is somewhat tangential to my point.I can't recall ever needing to know if a number is divisible by 9 and I can't think of any instances where the average person in the street would need to know either - unless they've got 9 kids to share a packet of sweets among.
In any case, in all but the simplest instances, dividing a number by 3 is no slower than summing the digits and then dividing.
Quote from: DoctorBeaver on 22/03/2008 20:21:26In any case, in all but the simplest instances, dividing a number by 3 is no slower than summing the digits and then dividing.On the contrary, without using electronic aids, would you find it easier to divide 178232 by 3, than simply to sum 1+7+8+2x2+3 = 2x8+4+3 = 23, which at first glance is not divisible by 3.
It is called the Dewey Decimal system. It was invented by a guy named Dewey pronounced DOO WEE. Decimals themselves were invented by a woman. She was getting even for the fur coat her husband missed on the last hunting trip.