A shape with five sides is called apentagon. The pentagon is the firstregular polygon that does nottile theplane with copies of itself. It is the largestface any of the five regular three-dimensional regularPlatonic solid can have.
Thechromatic number of theplane is the minimum number ofcolors required to color the plane such that no pair of points at a distance of 1 has the same color.[10] Five is a lower depending for the chromatic number of the plane, but this may depend on the choice ofset-theoretical axioms:[11]
The plane contains a total of fiveBravais lattices, or arrays ofpoints defined by discretetranslation operations.Uniform tilings of the plane, are generated from combinations of only five regular polygons.[12]
Ahypertetrahedron, or 5-cell, is the 4 dimensional analogue of thetetrahedron. It has five vertices. Its orthographic projection ishomomorphic to the groupK5.[13]: p.120
This diagram shows thesubquotient relations of the twenty-sixsporadic groups; the fiveMathieu groups form the simplest class (colored red).
Every odd number greater than five is conjectured to be expressible as the sum of three prime numbers;Helfgott has provided a proof of this[19] (also known as theodd Goldbach conjecture) that is already widely acknowledged by mathematicians as it still undergoespeer-review. On the other hand, every odd number greater than one is the sum of at most five prime numbers (as a lower limit).[20]
The evolution of the modern Western digit for the numeral for five is traced back to theIndian system of numerals, where on some earlier versions, the numeral bore resemblance to variations of the number four, rather than "5" (as it is represented today). TheKushana andGupta empires in what is nowIndia had among themselves several forms that bear no resemblance to the modern digit. Later on, Arabic traditions transformed the digit in several ways, producing forms that were still similar to the numeral for four, with similarities to the numeral for three; yet, still unlike the modern five.[25] It was from those digits that Europeans finally came up with the modern 5 (represented in writings by Dürer, for example).
While the shape of the character for the digit 5 has anascender in most moderntypefaces, in typefaces withtext figures the glyph usually has adescender, as, for example, in.
On theseven-segment display of a calculator and digital clock, it is often represented by five segments at four successive turns from top to bottom, rotating counterclockwise first, then clockwise, and vice versa. It is one of three numbers, along with 4 and 6, where the number of segments matches the number. This makes it often indistinguishable from the letter S. Higher segment displays may sometimes may make use of a diagonal for one of the two.
The number five was an important symbolic number inManichaeism, with heavenly beings, concepts, and others often grouped in sets of five.[citation needed]
Only twelve integers up to33 cannot be expressed as the sum of five non-zero squares: {1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 18, 33} where 2, 3 and 7 are the only such primes without an expression.
^Georges Ifrah,The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: TheHarvill Press (1998): 394, Fig. 24.65
