Jump to navigation Jump to search This article is about the number. For the year, see AD 9. Look up nine in Wiktionary, the free dictionary. In the beginning, various Indians wrote a digit 9 similar in shape 9jafoodie the modern closing question mark without the bottom dot.

The Kshatrapa, Andhra and Gupta started curving the bottom vertical line coming up with a 3-look-alike. The modern digit resembles an inverted 6. To disambiguate the two on objects and documents that can be inverted, they are often underlined. Another distinction from the 6 is that it is sometimes handwritten with two strokes and a straight stem, resembling a raised lower-case letter q. In a seven-segment display, the number 9 can be constructed in two ways, either with a hook at the end of its stem or without one. Most LCD calculators use the former, but some VFD models use the latter.

Nine is the fourth composite number, and the first composite number that is odd. 9 is the highest single-digit number in the decimal system. By Mihăilescu’s theorem, 9 is the only positive perfect power that is one more than another positive perfect power, since the square of 3 is one more than the cube of 2. 9 is the number of derangements of 4, or the number of permutations of four elements with no fixed points. A number that is 4 or 5 modulo 9 cannot be represented as the sum of three cubes. 9 is the number of non-intersecting segments between four points on a circle. 9 is a Motzkin number, for the number of ways of drawing non-intersecting chords between four points on a circle.

A polygon with nine sides is called a nonagon. There are a maximum of nine semiregular or Archimedean tilings by convex regular polygons, when including both chiral forms of the snub hexagonal tiling. Catalan solids: the rhombic dodecahedron and the rhombic triacontahedron, which are duals to the only two quasiregular polyhedra. Nine distinct stellation’s by Miller’s rules are produced by the truncated tetrahedron. Euclidean honeycombs in the fourth dimension. The 621 honeycomb is made of 9-simplexes and 9-orthoplexes, with 1023 total polytope elements making up each 9-simplex. That is, if any natural number is multiplied by 9, and the digits of the answer are repeatedly added until it is just one digit, the sum will be nine.

3 the only other number aside from 9 in decimal that shares this property. The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. If dividing a number by the amount of 9s corresponding to its number of digits, the number is turned into a repeating decimal. Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers known as long ago as the 12th century.