Course Guide - USAID Teacher Education Project

e) Still other tessellations can be created by distorting triangles, quadrilaterals, andcertain hexagons to create carefully designed shapes such as the polygons in the fishpattern and the non-polygonal shapes in M. C. Escher's men on horseback:f) Tessellations depend on the previously discussed 360° angle around a point in aplane. Unless a point in a plane can be completely surrounded by shapes (withoutgaps or overlaps) a tessellation cannot exist. This is not to say that all arrangementsof polygons around a point where the angles total 360° are tessellations.This is an important mathematical point for pre-service teachers to grasp: thedifference between necessary and sufficient requirements. While it is necessary thatall tessellations require 360° surrounding a point, not all combinations totaling 360°around a point are sufficient to create a tessellation.g) Tessellations are not simply an abstract mathematical construct. They are found ineveryday life, such as in these floor tiles from ancient Pompeii (tessellatingparallelograms) and this design from a modern tile catalog (the octagon and squarepattern mentioned above).