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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.
Combinatorics. 97 rules and 45 examples. [1] Generating permutations (including of a multiset), combinations, integer partitions, binomial coefficients, generalized Fibonacci numbers. [2] Narayana Pandita noted the equivalence of the figurate numbers and the formulae for the number of combinations of different things taken so many at a time. [4]
Proof without words that a hexagonal number (middle column) can be rearranged as rectangular and odd-sided triangular numbers. A hexagonal number is a figurate number.The nth hexagonal number h n is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon [1]: 2-3 . These are one type of 2-dimensional figurate numbers . Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, who investigated and discussed properties of oblong , triangular , and square numbers ...
The nth pentagonal number p n is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of ...
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, is
Pages in category "Figurate numbers" The following 51 pages are in this category, out of 51 total. This list may not reflect recent changes. ...
Number of gifts of each type and number received each day and their relationship to figurate numbers. Te 12 = 364 is the total number of gifts "my true love sent to me" during the course of all 12 verses of the carol, "The Twelve Days of Christmas". [3] The cumulative total number of gifts after each verse is also Te n for verse n.