Mathematics Principles in Native American Petroglyphs

Recursion

Recursion is a repeated process with an increase or decrease in size.

Similitude

Similitude is similar to recursion. Here a figure is repeated in congruent dimensions with an increase or decrease in size. Each repetition is the same proportion of the previous figure. If the similitude involves a decrease in dimensions, the figure being repeated becomes infinitely small and in practice difficult to reproduce. In the example, the decorator chose to paint out the troublesome part.

Line Symmetry

A figure has line symmetry if it can be divided into two mirror images around an axis of symmetry.

Rotational Symmetry

A figure has rotational symmetry if it can be rotated until it looks exactly the same.

Tiling

Tiling refers to the filling in of a plane with repetitions of the same shape so that no gaps appear. The result is called a mosaic or tessellation. The petroglyph below can be tiled to give the tesselation at the right.