Spirolateral
In Euclidean geometry, a spirolateral is a polygon created by a sequence of fixed vertex internal angles and sequential edge lengths 1,2,3,...,n which repeat until the figure closes.
[4] Odds wrote to Martin Gardner who encouraged him to publish the results in Mathematics Teacher[5] in 1973.
[2] The smallest golygon is a spirolateral, 790°4, made with 7 right angles, and length 4 follow concave turns.
[2] It is denoted by nθ, where n is the number of sequential integer edge lengths and θ is the internal angle, as any rational divisor of 360°.
This defines an equiangular polygon of the form
An irregular unexpected closed spirolateral is one that returns to the first point but from the wrong direction.
[2] A modern spirolateral, also called a loop-de-loops[7] by Educator Anna Weltman, is denoted by (i1,...,in)θ, allowing any sequence of integers as the edge lengths, i1 to in.
Opposite direction turns can be given a negative integer edge length.
The number of cycles it takes to close a spirolateral, nθ, with k opposite turns can be computed like so.
if the fraction (p-2q)(n-2k)/2p is reduced fully to a/b, then the figure repeats after b cycles, and complete a total turns.
