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A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids , prisms (and other polyhedrons ), cubes , cylinders , cones (and truncated cones ).
Italian mathematician Bonaventura Cavalieri (1598–1647), from a 1682 publication of his Trattato della sfera. Cavalieri's principle was originally called the method of indivisibles, the name it was known by in Renaissance Europe. [2]
Clifford's circle theorems (Euclidean plane geometry) Commandino's theorem ; Constant chord theorem ; Conway circle theorem (Euclidean plane geometry) Crossbar theorem (Euclidean plane geometry) Dandelin's theorem (solid geometry) De Bruijn–Erdős theorem (incidence geometry) De Gua's theorem ; Desargues's theorem (projective geometry)
Pages in category "Arithmetic problems of solid geometry" The following 2 pages are in this category, out of 2 total. This list may not reflect recent changes. E.
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges congruent), and the same number of faces meet at each vertex.
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. [1] Some authors exclude uniform polyhedra (in which all vertices are symmetric to each other) from the definition; uniform polyhedra include Platonic and Archimedean solids as well as prisms and antiprisms. [2]
Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes . Solid modeling is distinguished within the broader related areas of geometric modeling and computer graphics , such as 3D modeling , by its emphasis on physical fidelity. [ 1 ]
Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
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