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Lazy Caterer's Sequence
The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a disk (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point inside the circle, but up to seven if they do not. This problem can be formalized mathematically as one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, ''see'' arrangement of hyperplanes. The analogue of this sequence in three dimensions is the cake number. Formula and sequence The maximum number ''p'' of pieces that can be created with a given number of cuts , where , is given by the formula : p = \frac. Using binomial coefficients, the formula can be expressed as :p = 1 + \dbinom = \dbinom+\dbinom+\dbinom. Simply put, each number equals a triangular number plus 1. As the third ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
16 (number)
16 (sixteen) is the natural number following 15 and preceding 17. 16 is a composite number, and a square number, being 42 = 4 × 4. It is the smallest number with exactly five divisors, its proper divisors being , , and . In English speech, the numbers 16 and 60 are sometimes confused, as they sound very similar. Sixteen is the fourth power of two. For this reason, 16 was used in weighing light objects in several cultures. The British have 16 ounces in one pound; the Chinese used to have 16 ''liangs'' in one ''jin''. In old days, weighing was done with a beam balance to make equal splits. It would be easier to split a heap of grains into sixteen equal parts through successive divisions than to split into ten parts. Chinese Taoists did finger computation on the trigrams and hexagrams by counting the finger tips and joints of the fingers with the tip of the thumb. Each hand can count up to 16 in such manner. The Chinese abacus uses two upper beads to represent the 5s and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
172 (number)
172 (one hundred ndseventy-two) is the natural number following 171 and preceding 173. In mathematics 172 is a part of a near-miss for being a counterexample to Fermat's last theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been ..., as 1353 + 1383 = 1723 − 1. This is only the third near-miss of this form, two cubes adding to one less than a third cube. It is also a "thickened cube number", half an odd cube (73 = 343) rounded up to the next integer. See also * 172 (other) References {{DEFAULTSORT:172 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
154 (number)
154 (one hundred ndfifty-four) is the natural number following 153 and preceding 155. In mathematics 154 is a nonagonal number. Its factorization makes 154 a sphenic number There is no integer with exactly 154 coprimes below it, making 154 a noncototient, nor is there, in base 10, any integer that added up to its own digits yields 154, making 154 a self number 154 is the sum of the first six factorials, if one starts with 0! and assumes that 0!=1. With just 17 cuts, a pancake can be cut up into 154 pieces (Lazy caterer's sequence). The distinct prime factors of 154 add up to 20, and so do the ones of 153, hence the two form a Ruth-Aaron pair. 154! + 1 is a factorial prime. In music * 154 is an album by Wire, named for the number of live gigs Wire had performed at that time In the military * was a United States Navy ''Trefoil''-class concrete barge during World War II * was a United States Navy ''Admirable''-class minesweeper during World War II * was a United States ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
137 (number)
137 (one hundred ndthirty-seven) is the natural number following 136 and preceding 138. In mathematics 137 is: * the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime. * an Eisenstein prime with no imaginary part and a real part of the form 3n - 1. * the fourth Stern prime. * a Pythagorean prime: a prime number of the form 4''n'' + 1, where ''n'' = 34 (137 = 4x34 + 1) or the sum of two squares 112 + 42 (121 + 16). * a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes. * a strictly non-palindromic number and a primeval number. * a factor of 10001 (the other being 73) and the repdigit 11111111 (= 10001 × 1111). * using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle) and 222°. * 1/137 = 0.007299270072992700..., so its period value is palindromic and has a period length of only 8. In physics * Since th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
121 (number)
121 (one hundred [and] twenty-one) is the natural number following 120 (number), 120 and preceding 122 (number), 122. In mathematics ''One hundred [and] twenty-one'' is * a Square (algebra), square (11 times 11) * the sum of the powers of 3 from 0 to 4, so a repunit in ternary numeral system, 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). * 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 add up to the same value as its factorizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
106 (number)
106 (one hundred ndsix) is the natural number following 105 and preceding 107. In mathematics 106 is a centered pentagonal number, a centered heptagonal number, and a regular 19-gonal number. There are 106 mathematical trees with ten vertices. See also * 106 (other) 106 may refer to: *106 (number), the number *AD 106, a year in the 2nd century AD *106 BC, a year in the 2nd century BC *106 (emergency telephone number), an Australian emergency number *106 (MBTA bus), a route of the Massachusetts Bay Transportatio ... References {{DEFAULTSORT:106 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
92 (number)
92 (ninety-two) is the natural number following 91 and preceding 93. In mathematics 92 is the eighth pentagonal number, and an Erdős–Woods number, since it is possible to find sequences of 92 consecutive integers such that each inner member shares a factor with either the first or the last member. For n = 8, there are 92 solutions in the n-Queens Problem. There are 92 "atomic elements" in John Conway's look-and-say sequence, corresponding to the 92 non-transuranic elements in the chemist's periodic table. 92 is palindromic in bases 6 (2326), 7 (1617), 22 (4422), and 45 (2245). The most faces or vertices an Archimedean or Catalan solid can have is 92: the snub dodecahedron has 92 faces while its dual polyhedron, the pentagonal hexecontahedron, has 92 vertices. As a simple polyhedron, the final stellation of the icosahedron has 92 vertices. There are 92 Johnson solids. In science *The atomic number of uranium, an actinide. * Messier object M92, a magnitude 7.5 gl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
79 (number)
79 (seventy-nine) is the natural number following 78 and preceding 80. In mathematics 79 is: * An odd number. * The smallest number that can not be represented as a sum of fewer than 19 fourth powers. * The 22nd prime number (between and ) * An isolated prime without a twin prime, as 77 and 81 are composite. * The smallest prime number ''p'' for which the real quadratic field Q[] has Ideal class group, class number greater than 1 (namely 3). * A cousin prime with 83. * An emirp, because the reverse of 79, 97 (number), 97, is also a prime. * A Fortunate prime. * A circular prime. * A prime number that is also a Gaussian prime (since it is of the form ). * A happy prime. * A Higgs prime. * A lucky prime. * A permutable prime, with ninety-seven. * A Pillai prime, because 23 ! + 1 is divisible by 79, but 79 is not one more than a multiple of 23. * A regular prime. * A right-truncatable prime, because when the last digit (9) is removed, the remaining number (7) is still ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
67 (number)
67 (sixty-seven) is the natural number following 66 and preceding 68. It is an odd number. In mathematics 67 is: *the 19th prime number (the next is 71). * a Chen prime. *an irregular prime. *a lucky prime. *the sum of five consecutive primes (7 + 11 + 13 + 17 + 19). *a Heegner number. *a Pillai prime since 18! + 1 is divisible by 67, but 67 is not one more than a multiple of 18. *palindromic in quinary (2325) and senary (1516). *a super-prime. (19 is prime) *an isolated prime. (65 and 69 aren't prime) In science *The atomic number of holmium, a lanthanide. Astronomy *Messier object M67, a magnitude 7.5 open cluster in the constellation Cancer. *The New General Catalogue object NGC 67, an elliptical galaxy in the constellation Andromeda. In music * "Car 67", a song by the band Driver 67 * Chicago's song "Questions 67 and 68" * Elton John's song "Old '67" on '' The Captain & The Kid'' CD, (2006) * British rap group called 67 * Rapper Drake released the song na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
56 (number)
56 (fifty-six) is the natural number following 55 and preceding 57. Mathematics 56 is: * The sum of the first six triangular numbers (making it a tetrahedral number). * The number of ways to choose 3 out of 8 objects or 5 out of 8 objects, if order does not matter. * The sum of six consecutive primes (3 + 5 + 7 + 11 + 13 + 17) * a tetranacci number and a pronic number. * a refactorable number, since 8 is one of its 8 divisors. * The sum of the sums of the divisors of the first 8 positive integers. * A semiperfect number, since 56 is twice a perfect number. * A partition number - the number of distinct ways 11 can be represented as the sum of natural numbers. * An Erdős–Woods number, since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member. * The only known number n such that , where φ(''m'') is Euler's totient function and σ(''n'') is the sum of the divisor function, see . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
46 (number)
46 (forty-six) is the natural number following 45 and preceding 47. In mathematics Forty-six is * a Wedderburn-Etherington number, * an enneagonal number * a centered triangular number. * the number of parallelogram polyominoes with 6 cells. It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that cannot be expressed as a sum of two abundant numbers. It is also the sixteenth semiprime. Since it is possible to find sequences of 46+1 consecutive integers such that each inner member shares a factor with either the first or the last member, 46 is an Erdős–Woods number. In science * The atomic number of palladium. * The number of human chromosomes. * The approximate molar mass of ethanol (46.07 g mol) Astronomy * Messier object M46, a magnitude 6.5 open cluster in the constellation Puppis. * The New General Cataloguebr>objectNGC 46, a star in the constellation Pisces. In music * Japanese idol group franchis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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