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Topic: Triangular spiral
Replies: 12   Last Post: May 23, 2006 4:13 AM

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Eric Bainville

Posts: 10
Registered: 12/6/04
Re: Triangular spiral
Posted: May 22, 2006 10:38 AM
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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

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