# Topologies *

 Difficulty Time Required Average (6-10 days)
*Note: This is an abbreviated Project Idea, without notes to start your background research, a specific list of materials, or a procedure for how to do the experiment. You can identify abbreviated Project Ideas by the asterisk at the end of the title. If you want a Project Idea with full instructions, please pick one without an asterisk.

## Abstract

What do knots, maps, mazes, driving directions, and doughnuts have in common? The answer is topology, a branch of mathematics that studies the spatial properties and connections of an object. Topology has sometimes been called rubber-sheet geometry because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing) (Wikipedia contributors, 2006). A common joke is that topologists are people who don't know the difference between a coffee cup and a doughnut. A project in topology can have many forms. Can "Euler's Solution" help you efficiently run your errands? Can you figure out the number of possible routes to get to school? What is the minimum number of colors needed to color in a U.S. map so that no two states that are touching have the same color? Use topology to untangle knots or to discover knots that cannot be untangled. Use topology to solve mazes, draw circuit diagrams, make phylogenetic trees, or fold origami! The possibilities are endless... (Britton, 2006)

### MLA Style

Science Buddies Staff. "Topologies" Science Buddies. Science Buddies, 30 June 2014. Web. 28 May 2017 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p030.shtml>

### APA Style

Science Buddies Staff. (2014, June 30). Topologies. Retrieved May 28, 2017 from http://www.sciencebuddies.org/science-fair-projects/project_ideas/Math_p030.shtml

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Last edit date: 2014-06-30

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