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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.
This category includes not only articles about certain types of figurate numbers, but also articles about theorems and conjectures pertaining to, and properties of, figurate numbers. Subcategories This category has only the following subcategory.
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 ...
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
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.
All centered square numbers and their divisors have a remainder of 1 when divided by 4. Hence all centered square numbers and their divisors end with digit 1 or 5 in base 6, 8, and 12. Every centered square number except 1 is the hypotenuse of a Pythagorean triple (3-4-5, 5-12-13, 7-24-25, ...). This is exactly the sequence of Pythagorean ...
In mathematics, the centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers of dots with a constant number of sides. Each side of a polygonal layer contains one more dot than each side in the previous layer; so starting from the second polygonal layer, each layer of a ...
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.