Spirolateral (original) (raw)

dbo:abstract

• 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. The number of repeats needed is called its cycles. A simple spirolateral has only positive angles. A simple spiral approximates of a portion of an archimedean spiral. A general spirolateral allows positive and negative angles. A spirolateral which completes in one turn is a simple polygon, while requiring more than 1 turn is a star polygon and must be self-crossing. A simple spirolateral can be an equangular simple polygon

  with p vertices, or an equiangular star polygon <p/q> with p vertices and q turns. Spirolaterals were invented and named by Frank C. Odds as a teenager in 1962, as square spirolaterals with 90° angles, drawn on graph paper. In 1970, Odds discovered triangular and hexagonal spirolateral, with 60° and 120° angles, can be drawn on isometric (triangular) graph paper. Odds wrote to Martin Gardner who encouraged him to publish the results in Mathematics Teacher in 1973. The process can be represented in turtle graphics, alternating turn angle and move forward instructions, but limiting the turn to a fixed rational angle. The smallest golygon is a spirolateral, 790°4, made with 7 right angles, and length 4 follow concave turns. Golygons are different in that they must close with a single sequence 1,2,3,..n, while a spirolateral will repeat that sequence until it closes. (en)

rdfs:comment

• 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. The number of repeats needed is called its cycles. A simple spirolateral has only positive angles. A simple spiral approximates of a portion of an archimedean spiral. A general spirolateral allows positive and negative angles. The process can be represented in turtle graphics, alternating turn angle and move forward instructions, but limiting the turn to a fixed rational angle. (en)