Estudiante

New Generation Christian School

Math Fair, 2013

Student´s name: Delmer Ibsen López Raudales

Teacher´s name: Ms. Gracia Sanchez

Tesellation with Spidrons


Index
1.Introduction……………………………………………………………………pg. 3

2. Background………………………………………………………………….pg. 4-5

3. Conclusion……………………………………………………………………...pg. 6

4. Bibliography……………………………………………………………………pg. 75. Annexes……………………………………………………………………….pg. 8-9

Introduction
Sometime in the early 1970's, Daniel Erdély was inspired to doodle a sequence of triangles inside a hexagon. He discovered that he couldmake a pattern of alternating equilateral and isosceles triangles, and that six of these patterns would fill the entire space inside the hexagon. Erdély put two of these patterns together;back-to-back to make a geometric object that he named a spidron.

The upper case letters show the four initial triangles in one 'arm' of the spidron. The lower case letters show the four initial triangles inthe other 'arm.' Each arm consists of a sequence of alternating isosceles (A, a, C, c, etc.) and equilateral (B, b, D, d, etc.) triangles.



Background
What is a spidron?
A spidron is a planefigure consisting of an alternating sequence of equilateral and isosceles (30°, 30°, 120°) triangles. Within the figure, one side of a regular triangle coincides with one of the sides of an isoscelestriangle, while another side coincides with the hypotenuse of another, smaller isosceles triangle. The sequence can be repeated any number of times in the direction of the smaller and smallertriangles, and the entire figure is centrally projected through the mid-point of the base of the largest unilateral triangle.
What is a semi-spidron?
The semi-spidron is half of the above figure,consisting of increasingly densely packed and smaller regular and isosceles triangles. The sequence can also be continued in the opposite direction, with ever larger triangles, ad infinitum.
What is a...