How to Build an Impossible Polyhedron    

written by Evelyn Lamb. added about 1 year ago by @icyflame ARCHIVES

mathematics imperfection    

Mathematical near misses show the power and playfulness of the human touch in mathematics. Johnson, Kaplan, and others made their discoveries by trial and error—by exploring, like biologists trudging through the rainforest to look for new species. But with mathematics it can be easier to search systematically. For instance, Jim McNeill, a mathematical hobbyist who collects near misses on his website, and Robert Webb, a computer programmer, have developed software for creating and studying polyhedra. Near misses live in the murky boundary between idealistic, unyielding mathematics and our indulgent, practical senses. They invert the logic of approximation. Normally the real world is an imperfect shadow of the Platonic realm. The perfection of the underlying mathematics is lost under realizable conditions. But with near misses, the real world is the perfect shadow of an imperfect realm. An approximation is “a not-right estimate of a right answer,” Kaplan says, whereas “a near-miss is an exact representation of an almost-right answer.”

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