Abstract
This is a great science fair project for someone who is interested in both mathematics and art. Spidrons are geometric forms made from alternating sequences of equilateral and isosceles (30°, 30°, 120°) triangles. Spidrons were discovered and named by Daniel Erdély in the early 1970's, and have since been studied by mathematicians and artists alike. This project is a great way to learn about the mathematics and art of tiling patterns.Objective
The goal of this science fair project is to find three or more different ways to tile the plane (i.e. an infinite two-dimensional surface) with spidron-based shapes as the tiling elements.
Introduction
Sometime in the early 1970's, Daniel Erdély was inspired to doodle a sequence of triangles inside a hexagon. He discovered that he could make a pattern of alternating equilateral and isosceles triangles, and that six of these patterns would fill the entire space inside the hexagon (Figure 1). Erdély put two of these patterns together, back-to-back to make a geometric object that he named a spidron (Figure 2).
![]() |
| Figure 1. A single 'arm' of a spidron (blue) inscribed in a hexagon. |
![]() |
| Figure 2. An example of the geometric figure that Erdély 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 in the other 'arm.' Each arm consists of a sequence of alternating isosceles (A, a, C, c, etc.) and equilateral (B, b, D, d, etc.) triangles. |
Erdély continued to experiment with spidrons. He realized, for example, that the sum of the areas of the sequence of triangles following an equilateral triangle in a spidron is equal to the area of the equilateral triangle itself. He also discovered many patterns for tiling two-dimensional space with spidrons, which is what you will try to do in this project. Mathematicians have a special name for tiling: tessellation. Tesselation has important applications in the study of crystals and quasi-crystals in chemistry and materials science. If you are interested in taking your study of spidrons to three dimensions, you will discover, as Erdély did, that spidrons have amazing properties when folded into three dimensional structures. This is a great project for someone with interests in either math or art.
Terms, Concepts and Questions to Start Background Research
To do this project, you should do research that enables you to understand the following terms and concepts:
Questions
Bibliography
Materials and Equipment
Experimental Procedure
![]() |
![]() |
![]() |
Variations
Credits
Andrew Olson, PhD, Science Buddies
Sources
This science fair project was inspired by Jason's entry to the 2007 Sciencepalooza, sponsored by Synopsis.
![]() |
Last edit date: 2010-01-04 16:30:00
If you like this project, you might enjoy exploring careers in Pure Mathematics.
![]() |
Statistician Statisticians use the power of math and probability theory to answer questions that affect the lives of millions of people. They tell educators which teaching method works best, tell policy-makers what levels of pesticides are acceptable in fresh fruit, tell doctors which treatment works best, tell builders which type of paint is the most durable. They are employed in virtually every type of industry imaginable, from engineering, manufacturing, and medicine to animal science, food production, transportation, and education. Everybody needs a statistician! |
|
Join Science Buddies
Become a Science Buddies member! It's free! As a member you will be the first to receive our new and innovative project ideas, news about upcoming science competitions, science fair tips, and information on other science related initiatives. |