ThePythagoreans dealt with theregular solids, but the pyramid, prism, cone and cylinder were not studied until thePlatonists.Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height. He was probably also the discoverer of a proof that the volume enclosed by a sphere is proportional to the cube of itsradius.[3]
Whereas asphere is the surface of aball, for other solid figures it is sometimes ambiguous whether the term refers to the surface of the figure or the volume enclosed therein, notably for acylinder.
Major types of shapes that either constitute or define a volume.
Some sources also require that each of the faces is arectangle (so each pair of adjacent faces meets in aright angle). This more restrictive type of cuboid is also known as arectangular cuboid,right cuboid,rectangular box,rectangularhexahedron,right rectangular prism, orrectangularparallelepiped.[5]
Various techniques and tools are used in solid geometry. Among them,analytic geometry andvector techniques have a major impact by allowing the systematic use oflinear equations andmatrix algebra, which are important for higher dimensions.
.png)
