pLeonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. iEuler's Gemi tells the illuminating story of this indispensable mathematical idea.pbrp From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of iVi vertices, iEi edges, and iFi faces satisfies the equation iVi-iEiiFi2. David Richeson tells how the Greeks missed the formula entirely how Descartes almost discovered it but fell short how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes and how twentieth-century mathema