144 (one hundred ndforty-four) 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 143 and preceding 145. It is coincidentally both the

square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

of twelve (a dozen

dozen A dozen (commonly abbreviated doz or dz) is a grouping of twelve. The dozen may be one of the earliest primitive integer groupings, perhaps because there are approximately a dozen cycles of the Moon, or months, in a cycle of the Sun, or year ...

s, or one gross) and the twelfth

Fibonacci number In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many w ...

, and the only

nontrivial In mathematics, the adjective trivial is often used to refer to a claim or a case which can be readily obtained from context, or a particularly simple object possessing a given structure (e.g., group (mathematics), group, topological space). The n ...

number in the sequence that is square.

Mathematics

144 is a highly totient number. 144 is the smallest number whose fifth power is a sum of four (smaller) fifth powers. This solution was found in 1966 by L. J. Lander and T. R. Parkin, and disproved

Euler's sum of powers conjecture In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that for all integers and greater than 1, if the sum of many th powers of positive integers ...

. It was famously published in a paper by both authors, whose body consisted of only two sentences: It is also a square (12·12=144).

In other fields

* 1:144 scale is a scale used for some

scale model A scale model is a physical model that is geometrically similar to an object (known as the ''prototype''). Scale models are generally smaller than large prototypes such as vehicles, buildings, or people; but may be larger than small protot ...

s. * Several computers use 144Hz.

References

* Wells, D. '' The Penguin Dictionary of Curious and Interesting Numbers''. London: Penguin Group. (1987): 139–140.

External links

The Natural Number 144
{{Number theory Integers