169_RH-Tower

 

Sándor Kabai - January 12, 2010

Challenge: Calculate the height of tower consisting of n RHs placed on each other, where each RH is reduced by the golden ratio relative to the previous one.

This is an example of infinite series having finite sum.

The dimensions to be used can be calculated from the dimensions of a golden rhombohedron.

f

 

=GoldenRatio;

e is the edge length of golden rhombus

e=Sqrt[1+1/f^2];

p is the edge length of the corresponding Penrose rhombus, and a characteristic size of RH.

p=1/(f Sin[2Pi/10]);

dist is the distance the second RH has to be elevated for placing it on the first RH, i.e the spacing of the centers of No. 1 and No. 2 RH.

This distance is reduced in proportion to the golden ratio in each consecutive RH in the tower.

 

Main image: 
169_RH-Tower
Other images: 
169_RH-Tower
169_RH-Tower