Read e-book online Geometry in Ancient and Medieval India PDF

Geometry Topology

By T. A. Saraswati Amma

This e-book is a geometric survey of the Sanskrit and Prakrt medical and quasi-scientific literature and finishing with the early a part of the seventeenth century. The paintings seeks to blow up the speculation that the Indian mathematical genius was once predominantly genius used to be predominantly algebraic and computational and that's eschewed proofs and rationales.

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Basic Algebra One often uses multiplicative terminology and notation when dealing with a pre-monoid, monoid, or group. This means that one uses the term "multiplication" for the combination, one writes ab := cmb( a, b) and calls it the "product" of a and b, one calls the neutral "unity" and denotes it by 1, and one writes a-I := rev(a) and calls it the "reciprocal" of a. OO) are all multiplicative monoids and QX, RX, px, and eX are multiplicative groups. If M is a multiplicative pre-monoid and if Sand T are subsets of M, we write ST := cmb> (S X T) = {st I s E S, t E T}.

Notes 14 (1) The notations £('V, 'V') and L('V, 'V') for our Lin('V, 'V') are very common. 15. Linear Combinations. Linear Independence. Bases 51 (2) The notation Lis(V, V') was apparently first introduced by S. Lange (Introduction to Differentiable Manifolds, Interscience 1966). In some previous work, I used Invlin(V, V'). (3) The product-space VI X V2 is sometimes called the "direct sum" of the linear spaces VI and V2 and it is then denoted by VI e V2 • I believe such a notation is superfluous because the set-product VI X V2 carries the natural structure of a linear space and a special notation to emphasize this fact is redundant.

The abbreviation a - b := a + (-b) is customary. The number sets Nand P are additive monoids while l, Q, R, and C are additive groups. 13) S + T:= cmb>(S x T) = {s + tis E s, t E T}. and call it the member-wise sum of Sand T. If t EM, we abbreviate S + t:= S + {t} = {t} + S =: t + S. 14) If G is an additive group and if S is a subset of G, we write - S:= rev>(S) = {-s I s E S}. 15) and call it the member-wise opposite of S. 16) T - S := {t - sit E T, s E S}. 26 Chapter 0 Basic Mathematics and call it the member-wise difference of T and S.

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