Fermat polygonal number theoremIn additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers. That is, every positive integer can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of five or fewer pentagonal numbers, and so on. That is, the n-gonal numbers form an additive basis of order n. Three such representations of the number 17, for example, are shown below: 17 = 10 + 6 + 1 (triangular numbers) 17 = 16 + 1 (square numbers) 17 = 12 + 5 (pentagonal numbers).
Transcendental numberIn mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are π and e. Though only a few classes of transcendental numbers are known – partly because it can be extremely difficult to show that a given number is transcendental – transcendental numbers are not rare: indeed, almost all real and complex numbers are transcendental, since the algebraic numbers form a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set.
Reciprocal lengthReciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre (symbol: m−1), the reciprocal centimetre or inverse centimetre (symbol: cm−1). Quantities measured in reciprocal length include: absorption coefficient or attenuation coefficient, in materials science curvature of a line, in mathematics gain, in laser physics magnitude of vectors in reciprocal space, in crystallography more generally any spatial frequency e.
Snub disphenoidIn geometry, the snub disphenoid, Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron is a convex polyhedron with twelve equilateral triangles as its faces. It is not a regular polyhedron because some vertices have four faces and others have five. It is a dodecahedron, one of the eight deltahedra (convex polyhedra with equilateral triangle faces), and is the 84th Johnson solid (non-uniform convex polyhedra with regular faces).
Quotient groupA quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo n can be obtained from the group of integers under addition by identifying elements that differ by a multiple of and defining a group structure that operates on each such class (known as a congruence class) as a single entity.
Conversion of unitsConversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors which change the measured quantity value without changing its effects. Unit conversion is often easier within the metric or the SI than in others, due to the regular 10-base in all units and the prefixes that increase or decrease by 3 powers of 10 at a time. The process of conversion depends on the specific situation and the intended purpose.
