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Centered Tetrahedral Number
A centered tetrahedral number is a centered figurate number that represents a tetrahedron In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the .... The centered tetrahedral number for a specific ''n'' is given by (2n+1)\times The first such numbers are 1, 5, 15, 35, 69, 121, 195, 295, 425, 589, 791, ... . Parity and divisibility *Every centered tetrahedral number is odd. *Every centered tetrahedral number with an index of 2, 3 or 4 modulo 5 is divisible by 5. References * Figurate numbers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |