| ||||
|---|---|---|---|---|
| Cardinal | forty-eight | |||
| Ordinal | 48th (forty-eighth) | |||
| Factorization | 24 × 3 | |||
| Divisors | 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 | |||
| Greek numeral | ΜΗ´ | |||
| Roman numeral | XLVIII | |||
| Binary | 1100002 | |||
| Ternary | 12103 | |||
| Senary | 1206 | |||
| Octal | 608 | |||
| Duodecimal | 4012 | |||
| Hexadecimal | 3016 | |||
48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozens.
48 is a highly composite number, and a Størmer number. [1]
By a classical result of Honsberger, the number of incongruent integer-sided triangles of perimeter is given by the equations for even , and for odd . [2]
48 is the order of full octahedral symmetry, which describes three-dimensional mirror symmetries associated with the regular octahedron and cube.
Forty-eight may also refer to:
In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero. However, some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0.
In geometry, an octahedron is a polyhedron with eight faces. One special case is the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex. Regular octahedra occur in nature as crystal structures. Many types of irregular octahedra also exist, including both convex and non-convex shapes.
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes.
42 (forty-two) is the natural number that follows 41 and precedes 43.
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system. The word is a portmanteau of "repeated" and "digit". Examples are 11, 666, 4444, and 999999. All repdigits are palindromic numbers and are multiples of repunits. Other well-known repdigits include the repunit primes and in particular the Mersenne primes.
33 (thirty-three) is the natural number following 32 and preceding 34.
45 (forty-five) is the natural number following 44 and preceding 46.
26 (twenty-six) is the natural number following 25 and preceding 27.
In hyperbolic geometry, the Klein quartic, named after Felix Klein, is a compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation-preserving automorphisms, and 168 × 2 = 336 automorphisms if orientation may be reversed. As such, the Klein quartic is the Hurwitz surface of lowest possible genus; see Hurwitz's automorphisms theorem. Its (orientation-preserving) automorphism group is isomorphic to PSL(2, 7), the second-smallest non-abelian simple group after the alternating group A5. The quartic was first described in (Klein 1878b).
32 (thirty-two) is the natural number following 31 and preceding 33.
49 (forty-nine) is the natural number following 48 and preceding 50.
63 (+234sixty-three) is the natural number following 62 and preceding 64.
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, hypertetrahedron, 'pentachoron, pentatope, pentahedroid, tetrahedral pyramid, or 4-simplex (Coxeter's polytope), the simplest possible convex 4-polytope, and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions. The 5-cell is a 4-dimensional pyramid with a tetrahedral base and four tetrahedral sides.
In geometry, a tetrakis hexahedron is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid.
In geometry, a disdyakis dodecahedron,, is a Catalan solid with 48 faces and the dual to the Archimedean truncated cuboctahedron. As such it is face-transitive but with irregular face polygons. It resembles an augmented rhombic dodecahedron. Replacing each face of the rhombic dodecahedron with a flat pyramid creates a polyhedron that looks almost like the disdyakis dodecahedron, and is topologically equivalent to it.
193 is the natural number following 192 and preceding 194.
168 is the natural number following 167 and preceding 169.
240 is the natural number following 239 and preceding 241.
888 is the natural number following 887 and preceding 889.
An integer triangle or integral triangle is a triangle all of whose side lengths are integers. A rational triangle is one whose side lengths are rational numbers; any rational triangle can be rescaled by the lowest common denominator of the sides to obtain a similar integer triangle, so there is a close relationship between integer triangles and rational triangles.
