In geometry, a diagonal is a line segment joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The most notable of the rules (the Sulbasūtra-s do not contain any proofs of the rules which they describe, since they are sūtra-s, formulae, concise) in the Baudhāyana Sulba Sūtra says: dīrghasyākṣaṇayā rajjuḥ pārśvamānī, tiryaḍam mānī, cha yatpṛthagbhūte kurutastadubhayāṅ karoti. A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together. ” This appears to be referring to a rectangle, although some tro consider this to refer to a square. In either case, it states that the square of the hypotenuse equals the sum of the squares of the sides. If restricted to right-angled isosceles triangles, HOWEVER, IT WOULD CONSTITUTE A LESS GENERAL CLAIM, BUT THE TEXT SEEMS TO BE QUITE OPEN TO UNEQUAL SIDES. As mentioned earlier Diagonal can be any line joining non consecutive vertices of a polygon, so in the statement Baudhayana doesnt specify if it is Right angled triangle or Obtuse triangle or Acute triangle. Pythagoras probably improvised the statement !!! And as we all know Precision matters a lot in math! In my opinion if someone asks who pioneered the formula, Id say to the best of what I know BABYLONIANS, and other just removed flaws and improvised or elaborated it with all precisions:-)
Posted on: Sun, 04 Jan 2015 17:02:21 +0000
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