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Figurate numbers have played a significant role in modern recreational mathematics. [9] In research mathematics, figurate numbers are studied by way of the Ehrhart polynomials, polynomials that count the number of integer points in a polygon or polyhedron when it is expanded by a given factor. [10]
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The n th octahedral number can be obtained by the formula: [1] = (+). The first few octahedral numbers are:
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.
A triangular number or triangle number counts objects arranged in an equilateral triangle. 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 ...
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]
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a broader topic of figurate numbers representing the numbers of points forming regular patterns within different shapes.
This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative : many famous topics in number theory have origins in challenging problems posed purely for their own sake.