A Car Crash Solved-with a Swiss Army Knife

• Autores: Marc Frantz
• Localización: Mathematics magazine, ISSN 0025-570X, Vol. 84, Nº. 5, 2011, págs. 327-338
• Idioma: inglés
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• Resumen

  • Though not well known, Eves�s theorem is a fundamental result of projective geometry�a tool as versatile as a Swiss Army knife. Named for the late Howard W. Eves (1911�2004), the theorem establishes a class of numerical projective invariants, of which the famous cross ratio is a special case. We illustrate the versatility of Eves�s theorem by applying it to accident scene reconstruction, to the circular products in the theorems of Ceva and Menelaus, and to perspective illustrations of the geometric mean. In addition, we show that the theorem is illustrated by everyday photographs of buildings and other common objects.