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62. SOLID GEOMETRY Webster defines geometry as the mathematics of the properties, measurements and relationships of points, lines, angles, surfaces, and solids none of http://myweb.cableone.net/amkalenak/solid_geometry.html

SOLID GEOMETRY SOLIDS THE TETRAHEDRON The OCTAHEDRON THE ICOSAHEDRON An icosahedron is a polyhedron of 20 faces. A spherical icosahedron is an icosahedron 'exploded' onto the surface of a sphere ; it bears the same relation to an icosahedron as a spherical triangle to a plane triangle - the edges of the faces of the spherical icosahedron are all geodesic lines. The icosahedron is the least strong prime structural system but encloses the greatest volume per unit of invested energy. See the appendix for models of the 3 basic solids. POLYHEDRAL MULTIPLICATION Next Table of Contents

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Read Books Online Free Alphabetical Index Solid geometry In mathematics solid geometry was the traditional name for the geometry of three-dimensional Euclidean space space we live in. It was studied as a sequel to plane geometry Stereometry deals with the measurements of volumes of various solid figuress cylinder , circular cone , truncated cone, sphere prismss blades , wine casks. Table of contents showTocToggle("show","hide") 1 History 2 Basic topics of solid geometry 3 Other topics History The Pythagoreans had dealt with the sphere and regular solids, but the pyramid , prism, cone and cylinder were but little known until the Platonistss took them in hand. Eudoxus established their mensuration, proving the pyramid and cone to have one-third the content of a prism and cylinder on the same base and of the same height, and was probably the discoverer of a proof that the volumes of spheres are as the cubes of their radii See also: Archimedes Demiurge Johannes Kepler , planimetry, Plato , Plato's Timaeus ...partly from the 1911 Encyclopaedia Britannica Basic topics of solid geometry Basic topics are: incidence of planess and lines dihedral angle and solid angle the cube cuboid parallelopiped the tetrahedron and other pyramids prismss octahedron dodecahedron ... icosahedron cones and cylinders the sphere other quadrics spheroid ellipsoid paraboloid and hyperboloids.

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