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Centered Tetrahedral Number
In mathematics, a centered tetrahedral number is a centered figurate number that represents a tetrahedron In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet .... That is, it counts the dots in a three-dimensional dot pattern with a single dot surrounded by tetrahedral shells. The nth centered tetrahedral number, starting at n=0 for a single dot, is:Deza numbers the centered tetrahedral numbers at n=1 for a single dot, leading to a different formula. The first such numbers are: References Figurate numbers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is something which is boundless, endless, or larger than any natural number. It is denoted by \infty, called the infinity symbol. From the time of the Ancient Greek mathematics, ancient Greeks, the Infinity (philosophy), philosophical nature of infinity has been 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 Guillaume de l'Hôpital, l'Hôpital and Johann Bernoulli, 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 (mathematics), 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 ... [...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 ancient Greek mathematicians already considered triangular numbers, polygonal numbers, tetrahedral numbers, and pyramidal numbers, ReprintedG. E. Stechert & Co., 1934 and AMS Chelsea Publishing, 1944. and subsequent mathematicians have included other classes of these numbers including numbers defined from other types of polyhedra and from 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
15 (number)
15 (fifteen) is the natural number following 14 (number), 14 and preceding 16 (number), 16. Mathematics 15 is: * The eighth composite number and the sixth semiprime and the first odd and fourth discrete semiprime; its proper divisors are , , and , so the first of the form (3.q), where q is a higher prime. * a deficient number, a lucky number, a bell number (i.e., the number of partitions for a set of size 4), a pentatope number, and a repdigit in Binary numeral system, binary (1111) and quaternary numeral system, quaternary (33). In hexadecimal, and higher bases, it is represented as F. * with an aliquot sum of 9 (number), 9; within an aliquot sequence of three composite numbers (15,9 (number), 9,4 (number), 4,3 (number), 3,1 (number), 1,0) to the Prime in the 3 (number), 3-aliquot tree. * the second member of the first cluster of two discrete semiprimes (14 (number), 14, 15); the next such cluster is (21 (number), 21, 22 (number), 22). * the first number to be Polygonal numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
35 (number)
35 (thirty-five) is the natural number following 34 (number), 34 and preceding 36 (number), 36. In mathematics 35 is the sum of the first five triangular numbers, making it a tetrahedral number. 35 is the 10th discrete semiprime (5 \times 7) and the first with 5 (number), 5 as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a higher prime. 35 has two prime factors, (5 (number), 5 and 7 (number), 7) which also form its main factor pair (5 x 7) and comprise the second Twin prime, twin-prime distinct semiprime pair. The aliquot sum of 35 is 13 (number), 13, within an aliquot sequence of only one composite number (35,13 (number), 13,1 (number), 1,0) to the Prime in the 13 (number), 13-aliquot tree. 35 is the second composite number with the aliquot sum 13 (number), 13; the first being the cube 27 (number), 27. 35 is the last member of the first triple cluster of semiprimes 33 (number), 33, 34 (number), 34, 35. The second such triple distinct se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
69 (number)
69 (sixty-nine; ) is the natural number following 68 (number), 68 and preceding 70 (number), 70. An odd number and a composite number, 69 is divisible by 1, 3, 23 (number), 23 and 69. The number and its pictograph give its name to the sexual position of 69ing, the same name. The association of the number with this sex position has resulted in it being associated in meme culture with sex. People knowledgeable of the meme may respond "nice" in response to the appearance of the number, whether intentionally an innuendo or not. In mathematics 69 is a semiprime because it is a natural number that is the product (mathematics), product of exactly two prime numbers (3 and 23), and it is an interprime between the numbers of 67 (number), 67 and 71 (number), 71. 69 is not divisible by any square number other than 1, making it a square-free integer. 69 is a Blum integer since the two factors of 69 are both Gaussian primes, and an Ulam number—an integer that is the sum of two distinct prev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
121 (number)
121 (one hundred ndtwenty-one) is the natural number following 120 and preceding 122. In mathematics ''One hundred ndtwenty-one'' is * a square (11 times 11) * the sum of the powers of 3 from 0 to 4, so a repunit in ternary. Furthermore, 121 is the only square of the form 1 + p + p^2 + p^3 + p^4, where ''p'' is prime (3, in this case). * the sum of three consecutive prime numbers (37 + 41 + 43). * As 5! + 1 = 121, it provides a solution to Brocard's problem. There are only two other squares known to be of the form n! + 1. Another example of 121 being one of the few numbers supporting a conjecture is that Fermat conjectured that 4 and 121 are the only perfect squares of the form x^-4 (with being 2 and 5, respectively).Wells, D., '' The Penguin Dictionary of Curious and Interesting Numbers'', London: Penguin Group. (1987): 136 * It is also a star number, a centered tetrahedral number, and a centered octagonal number. * In decimal, it is a Smith number since its digits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
195 (number)
195 (one hundred ndninety-five) is the natural number following 194 and preceding 196. In mathematics 195 is: * the sum of eleven consecutive primes: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 * the smallest number expressed as a sum of distinct square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...s in 16 different ways * a centered tetrahedral number * in the middle of a prime quadruplet (191, 193, 197, 199). See also * 195 (other) References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...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 ancient Greek mathematicians already considered triangular numbers, polygonal numbers, tetrahedral numbers, and pyramidal numbers, ReprintedG. E. Stechert & Co., 1934 and AMS Chelsea Publishing, 1944. and subsequent mathematicians have included other classes of these numbers including numbers defined from other types of polyhedra and from 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tetrahedron is the simplest of all the ordinary convex polytope, convex polyhedra. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean geometry, Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid (geometry), pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron, the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such net (polyhedron), nets. For any tetrahedron there exists a sphere (called th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
295 (number)
295 is the natural number following 294 and preceding 296. In mathematics *295 is an odd composite number with two prime factors. *295 is a centered tetrahedral number meaning that it can be represented as a tetrahedron In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet .... *295 Is a structured deltoidal hexecontahedral number which can be represented as a deltoidal hexecontahedron. *295 can be written as the sum of 4 nonzero perfect squares. *295 is the second suspected Lychrel number. References {{Improve categories, date=November 2023 Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
