# Triangular number

Equilateral triangle.

- Triangular number136 related topics

## Figurate number

The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers).

## Cube (algebra)

[[Image:CubeChart.svg|thumb|280px|

[[Image:CubeChart.svg|thumb|280px|

The sum of the first n cubes is the nth triangle number squared:

## Square number

Integer that is the square of an integer; in other words, it is the product of some integer with itself.

Integer that is the square of an integer; in other words, it is the product of some integer with itself.

. If a square number is represented by n points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers).

## Eureka (word)

Interjection used to celebrate a discovery or invention.

Interjection used to celebrate a discovery or invention.

Another mathematician, Carl Friedrich Gauss, echoed Archimedes when in 1796 he wrote in his diary, "ΕΥΡΗΚΑ! num = Δ + Δ + Δ", referring to his discovery that any positive integer could be expressed as the sum of at most three triangular numbers.

## Fermat polygonal number theorem

Sum of at most n n-gonal numbers.

Sum of at most n n-gonal numbers.

That is, every positive integer can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of five or fewer pentagonal numbers, and so on.

## 4000 (number)

Natural number following 3999 and preceding 4001.

Natural number following 3999 and preceding 4001.

4005 – triangular number

## Ramanujan–Nagell equation

Equation between a square number and a number that is seven less than a power of two.

Equation between a square number and a number that is seven less than a power of two.

The problem of finding all numbers of the form 2b − 1 (Mersenne numbers) which are triangular is equivalent:

## 190 (number)

Natural number following 189 and preceding 191.

Natural number following 189 and preceding 191.

190 is a triangular number, a hexagonal number, and a centered nonagonal number, the fourth figurate number (after 1, 28, and 91) with that combination of properties.

## 1

Number and a numerical digit used to represent that number in numerals.

Number and a numerical digit used to represent that number in numerals.

1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few.

## 91 (number)

Natural number following 90 and preceding 92.

Natural number following 90 and preceding 92.

a triangular number.