## commutative rings

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)

Bibliography

- Britton, J., 2006. "R-U-B-B-E-R Geometry (Topology)," Camosun College, Victoria, BC, Canada. [accessed: 5/1/06] http://britton.disted.camosun.bc.ca/jbrubbergeom.htm
- Wikipedia contributors, 2006. "Topology," Wikipedia, The Free Encyclopedia. [accessed 5/20/06] http://en.wikipedia.org/w/index.php?title=Topology&oldid=59314342

Variations

- For more science project ideas in this area of science, see Pure Mathematics Project Ideas.

## Career Focus

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)

Bibliography

- Britton, J., 2006. "R-U-B-B-E-R Geometry (Topology)," Camosun College, Victoria, BC, Canada. [accessed: 5/1/06] http://britton.disted.camosun.bc.ca/jbrubbergeom.htm
- Wikipedia contributors, 2006. "Topology," Wikipedia, The Free Encyclopedia. [accessed 5/20/06] http://en.wikipedia.org/w/index.php?title=Topology&oldid=59314342

Variations

- For more science project ideas in this area of science, see Pure Mathematics Project Ideas.

## Career Focus

If you like this project, you might enjoy exploring related careers.

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