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aryabhata-part2

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A paper on Indian Maths.
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  NPTEL C OURSE ON M ATHEMATICS IN  I NDIA :F ROM  V EDIC PERIOD TO  M ODERN TIMES L ECTURE  8¯Aryabhat.¯ıya of ¯Aryabhat.a - Part 2K. Ramasubramanian IIT Bombay  Outline ¯ Aryabhat .¯ıya   of  ¯Aryabhat.a  – Part 2   Area of a triangle  Bh¯askara’s commentary introducing  ¯ ab¯ adhas   Numerical example   Area of a circle   Area of a trapezium   Generalized approach to finding area + verification   Chord of one-sixth of a circle   Approximate value of  π   Bh¯askara’s discussion on the word  ¯ asanna    Construction of sine-table  General principle  Geometrical approach  Analytic approach (discrete version of harmonic equation)  Area of a triangle   The formula for the area is presented in half  ¯ ary¯ a  :          The product of the perpendicular [dropped from the vertexon the base] and half the base gives the measure of the areaof a triangle.   Bh¯askara in his commentary observes: 1. the term  samadalakot .i   means ‘the perpendicular droppedfrom the vertex on the base of a triangle’, i.e., ‘the altitudeof a triangle’.2. it should not be interpreted as ‘the upright which bisects the triangle into two equal parts’3. if we do so, the applicability of the above rule will berestricted to equilateral ( sama-trya´sra  ) and isoscelestriangles ( dvisama-trya´sra  ).  Classification of a triangles Bh¯askara’s commentary Bh¯askara while commenting on the verse presenting the formula for area of a triangle,provides some edifying notes starting with the classification of triangles.                  -         -     (a)     (b)           (c)      Figure: Types of triangles
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