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Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, starting with the 0th triangular number ...
The number 153 is the 17th triangular number. The colours show that 153 is also the sum of the first five positive factorials. The number 153 is associated with the geometric shape known as the Vesica Piscis or Mandorla. Archimedes, in his Measurement of a Circle, referred to this ratio (153/265), as constituting the "measure of the fish", this ...
Doubly triangular number. There are 21 colorings of the four corners of a square using three colors (up to symmetry), a doubly triangular number, formed by combining two of the six colorings of two opposite corners. In mathematics, the doubly triangular numbers are the numbers that appear within the sequence of triangular numbers, in positions ...
Ten is the sum of all products p × q where (p, q) are ordered pairs and p + q = n + 1. Ten is the number of (n + 2)-bit numbers that contain two runs of 1's in their binary expansion. The largest tetrahedral number of the form. 2 a + 3 b + 1 {\displaystyle 2^ {a}+3^ {b}+1} for some integers. a {\displaystyle a}
Square triangular number 36 depicted as a triangular number and as a square number. In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a square number. There are infinitely many square triangular numbers; the first few are: 0, 1, 36, 1225, 41 616, 1 413 721, 48 024 900, 1 ...
Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...
The infinite sequence of triangular numbers diverges to +∞, so by definition, ... Why –1/12 is a gold nugget follow-up Numberphile video with Edward Frenkel;
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). The term can mean. polygonal number. a number represented as a discrete r -dimensional regular geometric pattern of r ...