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147 (one hundred ndforty-seven) is the
natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following 146 and preceding 148.


In mathematics

147 is the fourth centered icosahedral number. These are a class of figurate numbers that represent points in the shape of a
regular icosahedron The regular icosahedron (or simply ''icosahedron'') is a convex polyhedron that can be constructed from pentagonal antiprism by attaching two pentagonal pyramids with Regular polygon, regular faces to each of its pentagonal faces, or by putting ...
or alternatively points in the shape of a
cuboctahedron A cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertex (geometry), vertices, with 2 triangles and 2 squares meeting at each, and 24 identical edge (geometry), edges, each separating a tr ...
, and are magic numbers for the face-centered cubic lattice. Separately, it is also a magic number for the
diamond cubic In crystallography, the diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adopt this structure, in ...
. It is also the fourth Apéry number a_3 following 19, where a_n=\sum_^n\binom^2\binom, with 147 the composite index of the nineteenth
triangle number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
, 190. There are 147 different ways of representing one as a sum of unit fractions with five terms, allowing repeated fractions, and 147 different self-avoiding
polygonal chain In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points (A_1, A_2, \dots, A_n) called its vertices. The curve itself consists of the line segments co ...
s of length six using horizontal and vertical segments of the
integer lattice In mathematics, the -dimensional integer lattice (or cubic lattice), denoted , is the lattice (group), lattice in the Euclidean space whose lattice points are tuple, -tuples of integers. The two-dimensional integer lattice is also called the s ...
.


See also

* 147 (disambiguation)


References

{{DEFAULTSORT:147 (Number) Integers