| quadratrix of Hippias -
01-29-2008, 12:33 PM
A friend of Socrates (450 B.C.) known only by the name of Hippias had taken to himself the task of solving the problem of measuring the area of a circle. 2 458 years later, his quadratrix arc can be argued to represent the existence of a quarter turn (p/2) around the circumference of a unit circle. This arc has a missing end point known as the indeterminate 0/0 where the numerator denotes zero ordinate and the denominator denotes zero angles. However, using arguments derived from theory of limits, the value of the limiting point is 2/p or (p/2)(2/p)=1 radian, that is a unit circle exists independent of any unit of measurement whether feet, meters, miles, or kilometers. Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c² |