Somayaji's Theorems

Vyaasaath vanasangunithaath pruthagaaptam thryaadyayugvimoola ghanai:

thrigunavygaase svamrunam kramasa:

kruthvaapi paridhiraaneyu:

  Multiply the diameter of a circle with 4 and keep it at different places and divide each with the odd numbers beginning from 3, 5, 7,… as their cubes subtracted by the same value. Repeat this and add/subtract alternatively the results to three times the diameter of the circle to get the circumference with the highest degree of accuracy. This theorem can be mathematically represented as follows: Circumference = 3D+4D/(33-3)-4D/(53-5)+4D/73 7)-..  

Vargairyujaam vaa dvigunairnirekair vargeekruthair varji thayugma vargai:

vyaasam cha chadghnam vibhajeth phalam

svam vyaase thrinighne paridhi sthadaasyaath

  Six times the diameter is divided separetely by the square of twice the square of even integers 2,4,6…. minus one, diminished by the squares of even integers themselves. The sum of the resulting quotient by thrice the diameter is the circumference. This can be mathematically written as follows:Circumference = 3D+6D([1/2×22-1]2-22) + ([1/2×42-1]2-42)+[(1/2×62-1)2-62])+….]]>