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A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The n th tetrahedral number, Te n , is the sum of the first n triangular numbers , that is,
In mathematics, a centered tetrahedral number is a centered figurate number that represents a tetrahedron. That is, it counts the dots in a three-dimensional dot pattern with a single dot surrounded by tetrahedral shells. [1] The th centered tetrahedral number, starting at = for a single dot, is: [2] [3]
Figurate numbers were a concern of the Pythagorean worldview. It was well understood that some numbers could have many figurations, e.g. 36 is a both a square and a triangle and also various rectangles. The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem.
7.4 Reciprocal of tetrahedral numbers. 7.5 Exponential and logarithms. 8 See also. 9 Notes. 10 References. Toggle the table of contents. ... is a Bernoulli number, ...
A triangular-pyramid version of the cannonball problem, which is to yield a perfect square from the N th Tetrahedral number, would have N = 48. That means that the (24 × 2 = ) 48th tetrahedral number equals to (70 2 × 2 2 = 140 2 = ) 19600. This is comparable with the 24th square pyramid having a total of 70 2 cannonballs. [5]
The fourth triangular number equals the third tetrahedral number as the nth k-simplex number equals the kth n-simplex number due to the symmetry of Pascal's triangle, and its diagonals being simplex numbers; similarly, the fifth triangular number (15) equals the third pentatope number, and so forth
Reddit went public in 2024 and is a more popular, profitable site than ever in its 20-year history. BI spoke to 11 Reddit employees about the new challenges and maintaining its beloved culture.
286 is an even composite number with 3 prime factors. [1] 286 is in the smallest pair of nontotient anagrams with 268. [2] 286 is a tetrahedral number which means that represents a tetrahedron. [3] 286 is a sphenic number which means that it has exactly 3 prime factors. [4] 286 the first even pseudoprime to base 3. [5]