126 (one hundred
ndtwenty-six) 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
125 125 may refer to:
*125 (number), a natural number
*AD 125, a year in the 2nd century AD
*125 BC, a year in the 2nd century BC
*125 (dinghy), a two person intermediate sailing dinghy
*125 (New Jersey bus), a New Jersey Transit bus route
*125 Liberatr ...
and preceding
127.
In mathematics
As the
binomial coefficient
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...
, 126 is a
central binomial coefficient
In mathematics the ''n''th central binomial coefficient is the particular binomial coefficient
: = \frac \textn \geq 0.
They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first ...
, and in
Pascal's Triangle
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Bla ...
, it is a
pentatope number. 126 is a
sum of two cubes, and since 125 + 1 is σ
3(5), 126 is the fifth value of the
sum of cubed divisors function.
126 is the fifth
-perfect
Granville number, and the third such not to be a perfect number. Also, it is known to be the smallest Granville number with three distinct prime factors, and perhaps the only such Granville number.
126 is a
pentagonal pyramidal number and a
decagonal number. 126 is also the different number of ways to partition a
decagon into even polygons by
diagonal
In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word ''diagonal'' derives from the ancient Greek � ...
s, and the number of crossing points among the diagonals of a regular
nonagon
In geometry, a nonagon () or enneagon () is a nine-sided polygon or 9-gon.
The name ''nonagon'' is a prefix Hybrid word, hybrid formation, from Latin (''nonus'', "ninth" + ''gonon''), used equivalently, attested already in the 16th century in Fre ...
.
There are exactly 126
binary strings of length seven that are not repetitions of a shorter string, and 126 different
semigroup
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it.
The binary operation of a semigroup is most often denoted multiplicatively (just notation, not necessarily th ...
s on four elements (up to
isomorphism
In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between the ...
and reversal).
There are exactly 126 positive integers that are not solutions of the equation
:
where ''a'', ''b'', ''c'', and ''d'' must themselves all be positive integers.
126 is the number of
root vectors of
simple
Simple or SIMPLE may refer to:
*Simplicity, the state or quality of being simple
Arts and entertainment
* ''Simple'' (album), by Andy Yorke, 2008, and its title track
* "Simple" (Florida Georgia Line song), 2018
* "Simple", a song by John ...
Lie group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
E7.
In physics
126 is the seventh
magic number in
nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter.
Nuclear physics should not be confused with atomic physics, which studies th ...
. For each of these numbers, 2, 8, 20, 28, 50, 82, and 126, an atomic nucleus with this many protons is or is predicted to be more stable than for other numbers. Thus, although there has been no experimental discovery of element 126, tentatively called
unbihexium, it is predicted to belong to an island of stability that might allow it to exist with a long enough
half life that its existence could be detected.
References
{{DEFAULTSORT:126 (Number)
Integers