New York: Abrams, Derbyshire, J. New York: Penguin, Dickau, R. Dodson, C. A User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer, pp. Escher, M. Forty, S. Gardner, M. New York: Vintage, pp. Geometry Center. Gray, A. Henle, M. A Combinatorial Introduction to Topology. New York: Dover, p. Hunter, J. Mathematical Diversions. After two loops, the ant would be back at the beginning—but dizzy.
We might ask ourselves after , where are we? Have we spun around after so much chaos, and found our position stagnated, back where we started? Or are we at a new beginning? Artists and authors explore this phenomenon as well. But the strip was long thought never to occur in the natural world. The symbol seeks to represent the three interdependent aspects of a sustainable loop: the collection of materials to be recycled, the manufacturing of recycled materials into new products, and the purchase and use of the products made from recycled materials.
Each arrow pleats and pivots itself, as all three arrows pursue and power one another. Scientists can confine light to certain planes depending on its orientation in space. Try it with three or more twists. The loop of paper with a twist was first described by a German mathematician called Johann Benedict Listing. You must be logged in to post a comment. Menu Home About All Articles. The concept of orientability has important implications. Take enantiomers. These chemical compounds have the same chemical structures except for one key difference: They are mirror images of one another.
For example, the chemical L-methamphetamine is an ingredient in Vicks Vapor Inhalers. Its mirror image, D-methamphetamine, is a Class A illegal drug. If we lived in a nonorientable world, these chemicals would be indistinguishable. The study of topology continues to produce stunning results.
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