Equilateral Spiral with Ray
- Bill Lombard
- Equilateral Triangles
Equilateral Spiral with Ray Sequence of equilateral triangles with midpoint ray Interesting pattern for side lengths: 1,1,1,2,2,3,4,5,7,9,12,16,21,28,37,49,65,86,114,151,200 . . . As the triangles grow in size, the ratio of successive side lengths approaches 1.3245, and is reminiscent of the behavior of the ratio of successive terms of the Fibonacci sequence, phi (approx. 1.618). The angle made by the Midpoint Spiral Ray and the triangle sides may tend toward some fixed value (≈25°) also as the side lengths grow. -inspired by http://easymatica.blogspot.com/2014/03/espiral-triangular.html
1- What does the angle made by the Midpoint Spiral Ray and the triangle sides tend toward as the side lengths grow? 2- Can the side lengths of the pattern be predicted?