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Re: Triangular spiral
Posted:
May 22, 2006 10:38 AM


Using complex numbers, J = exp(2*I*Pi/3) corresponds to the ratio between directions of consecutive sides of the equilateral triangle, and K = (4/5)*J is the ratio between direction&length of consecutive segments of the spiral.
The spiral end point is then:
z = 1 + K + K^2 + ... = 1 / (1  K) = (35 + 10 * sqrt(3) * i) / 61
The distance is the norm of z: 5/sqrt(61) = 0.64018439966447986837
 Eric
At 14:11 22/05/2006, Avni Pllana wrote: >A spiral consists of infinitely many linear segments parallel to the >sides of the equilateral triangle with unit length side. The first >segment of the spiral is the side AB of the equilateral triangle, >and the ratio of any two consecutive segments is 5/4. Determine the >distance between the starting point and final point of the spiral. > >Best regards, > Avni



