Areas of Science Pure Mathematics
Difficulty
Time Required Average (6-10 days)
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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...

Bibliography

  • Wikipedia contributors, 2006. Topology, Wikipedia, The Free Encyclopedia. Retrieved 5/20/06.

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MLA Style

Science Buddies Staff. "Topologies." Science Buddies, 20 Nov. 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p030/pure-mathematics/topologies. Accessed 20 Jan. 2021.

APA Style

Science Buddies Staff. (2020, November 20). Topologies. Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/Math_p030/pure-mathematics/topologies


Last edit date: 2020-11-20

Experimental Procedure

For this science project you will need to develop your own experimental procedure. Use the information in the summary tab as a starting place. If you would like to discuss your ideas or need help troubleshooting, use the Ask An Expert forum. Our Experts won't do the work for you, but they will make suggestions and offer guidance if you come to them with specific questions.

If you want a Project Idea with full instructions, please pick one without an asterisk (*) at the end of the title.

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