Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Eric Bainville Posts: 10 Registered: 12/6/04
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

Date Subject Author
5/22/06 Avni Pllana
5/22/06 BSK
5/22/06 Avni Pllana
5/22/06 BSK
5/22/06 Avni Pllana
5/22/06 BSK
5/22/06 Avni Pllana
5/22/06 BSK
5/22/06 Valeri Astanoff
5/23/06 João Pedro Afonso
5/22/06 Eric Bainville
5/22/06 João Pedro Afonso
5/23/06 Avni Pllana