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Centered Dodecahedral Number
A centered dodecahedral number is a centered figurate number that represents a dodecahedron In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagon .... The centered dodecahedral number for a specific ''n'' is given by :(2n+1)\left(5n^2+5n+1\right) The first such numbers are 1, 33, 155, 427, 909, 1661, 2743, 4215, 6137, 8569, … . Congruence Relations * CDC(n) \equiv 1 \pmod * CDC(n) \equiv 1-n \pmod * CDC(n) \equiv 2n+1 \pmod {{Num-stub Figurate numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedral Number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean * polygonal number * a number represented as a discrete -dimensional regular geometric pattern of -dimensional balls such as a polygonal number (for ) or a polyhedral number (for ). * a member of the subset of the sets above containing only triangular numbers, pyramidal numbers, and their analogs in other dimensions. Terminology Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". In historical works about Greek mathematics the preferred term used to be ''figured number''. In a use going back to Jacob Bernoulli's Ars Conjectandi, the term ''figurate number'' is used for triangular numbers made up of successive integers, tetrahedral numbers made up of successive triangular numbers, etc. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
33 (number)
33 (thirty-three) is the natural number following 32 (number), 32 and preceding thirty-four, 34. In mathematics 33 is: * the largest positive integer that cannot be expressed as a sum of different triangular numbers. * the smallest odd repdigit that is not a prime number. * the sum of the first four positive factorials. * the sum of the sum of the divisors of the first 6 positive integers. * the Sums of three cubes#Computational results, sum of three cubes: 33=8866128975287528^+(-8778405442862239)^+(-2736111468807040)^. * equal to the sum of the squares of the digits of its own square in bases 9, 16 and 31. ** For numbers greater than 1, this is a rare property to have in more than one radix, base. * the smallest integer such that it and the next two integers all have the same number of divisors. * the first member of the first cluster of three semiprimes (33, 34, 35); the next such cluster is 85, 86, 87. * the first double digit centered dodecahedral number. * divisible by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
155 (number)
155 (one hundred ndfifty-five) is the natural number following 154 and preceding 156. In mathematics 155 is: *a composite number *a semiprime. *a deficient number, since 1+ 5+ 31= 37<155. * odious, since its binary expansion has a total of 5 ones in it. There are 155 primitive permutation groups of degree 81. If one adds up all the primes from the least through the greatest prime factors of 155, that is, 5 and 31, the result is 155. Only three other "small" semiprimes (10, 39, and 371) share this attribute. In the military * was a |
427 (number)
400 (four hundred) is the natural number following 399 and preceding 401. Mathematical properties 400 is the square of 20. 400 is the sum of the powers of 7 from 0 to 3, thus making it a repdigit in base 7 (1111). A circle is divided into 400 grads, which is equal to 360 degrees and 2π radians. (Degrees and radians are the SI accepted units). 400 is a self number in base 10, since there is no integer that added to the sum of its own digits results in 400. On the other hand, 400 is divisible by the sum of its own base 10 digits, making it a Harshad number. Other fields Four hundred is also * The Four Hundred (oligarchy) of ancient Athens. * An HTTP status code for a bad client request. * The Four Hundred (sometimes The Four Hundred Club) a phrase meaning the wealthiest, most famous, or most powerful social group (see, e.g., Ward McAllister), leading to the generation of such lists as the Forbes 400. * The Atari 400 home computer. * A former limited stop bus route which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
909 (number)
900 (nine hundred) is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number. In other fields 900 is also: * A telephone area code for "premium" phone calls in the North American Numbering Plan * In Greek number symbols, the sign Sampi ("ϡ", literally "like a pi") * A skateboarding trick in which the skateboarder spins two and a half times (360 degrees times 2.5 is 900) * A 900 series refers to three consecutive perfect games in bowling * Yoda's age in Star Wars Integers from 901 to 999 900s * 901 = 17 × 53, centered triangular number, happy number * 902 = 2 × 11 × 41, sphenic number, nontotient, Harshad number * 903 = 3 × 7 × 43, sphenic number, triangular number, Schröder–Hipparchus number, Mertens function (903) returns 0, little Schroeder number * 904 = 23 × 113 or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Number
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 centered ''k''-gonal number contains ''k'' more dots than the previous layer. Examples Each centered ''k''-gonal number in the series is ''k'' times the previous triangular number, plus 1. This can be formalized by the expression \frac +1, where ''n'' is the series rank, starting with 0 for the initial 1. For example, each centered square number in the series is four times the previous triangular number, plus 1. This can be formalized by the expression \frac +1. These series consist of the *centered triangular numbers 1, 4, 10, 19, 31, 46, 64, 85, 109, 136, 166, 199, ... (), *centered square numbers 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, ... ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Figurate Number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes (polygonal numbers) and different dimensions (polyhedral numbers). The term can mean * polygonal number * a number represented as a discrete -dimensional regular geometry, geometric pattern of -dimensional Ball (mathematics), balls such as a polygonal number (for ) or a polyhedral number (for ). * a member of the subset of the sets above containing only triangular numbers, pyramidal numbers, and their analogs in other dimensions. Terminology Some kinds of figurate number were discussed in the 16th and 17th centuries under the name "figural number". In historical works about Greek mathematics the preferred term used to be ''figured number''. In a use going back to Jacob Bernoulli's Ars Conjectandi, the term ''figurate number'' is used for triangular numbers made up of successive integers, tetrahedral numbers made up of successi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dodecahedron
In geometry, a dodecahedron (Greek , from ''dōdeka'' "twelve" + ''hédra'' "base", "seat" or "face") or duodecahedron is any polyhedron with twelve flat faces. The most familiar dodecahedron is the regular dodecahedron with regular pentagons as faces, which is a Platonic solid. There are also three regular star dodecahedra, which are constructed as stellations of the convex form. All of these have icosahedral symmetry, order 120. Some dodecahedra have the same combinatorial structure as the regular dodecahedron (in terms of the graph formed by its vertices and edges), but their pentagonal faces are not regular: The pyritohedron, a common crystal form in pyrite, has pyritohedral symmetry, while the tetartoid has tetrahedral symmetry. The rhombic dodecahedron can be seen as a limiting case of the pyritohedron, and it has octahedral symmetry. The elongated dodecahedron and trapezo-rhombic dodecahedron variations, along with the rhombic dodecahedra, are space-filling. There ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
