Wednesday, July 13, 2011

Vyasardha, the Radius of the Circle


Aryabhata, one of the earliest mathematicians and astronomers, ( circa 476-550 CE ) postulated that Vysasardha, the Radius of the Circle is 3438 minutes and Arc is 5400 minutes.

Circumference = 2 Pi R
R = 360/2 Pi
R = 57.3 degrees
R = 57.3 * 60 = 3438 arcminutes
R = 3438 * 60 = 206265 arcseconds

Half Chord of 90 degrees = 90*60 = 5400 arcminutes.

In his astronomical treatise, the Aryabhatiya, he postulated that the Circumference of the Circle is 360*60 = 21600 minutes. All these formulae are useful for the computation of half chords of certain sets of arcs in a circle and became the base of Hindu Trignometry.

In his Sine Tablest, he called 3 degrees 45 minutes divisions by many Sanskrit names, given below.

मखि भखि फखि धखि णखि ञखि ङखि हस्झ स्ककि किष्ग श्घकि किघ्व |
घ्लकि किग्र हक्य धकि किच स्ग झश ङ्व क्ल प्त फ छ कला-अर्ध-ज्यास् ||

Aryabhata's Sine Table is not a set of values of the trignometric sine functions, but rather is a table of the first differences of the values of trignometric sines expressed in arcminutes. Because of this, this Table is referred to as the Table of Sine Differences.
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