|
907 (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 o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bowling
Bowling is a target sport and recreational activity in which a player rolls a ball toward pins (in pin bowling) or another target (in target bowling). The term ''bowling'' usually refers to pin bowling (most commonly ten-pin bowling), though in the United Kingdom and Commonwealth countries, bowling could also refer to target bowling, such as lawn bowls. In pin bowling, the goal is to knock over pins on a long playing surface known as a ''lane''. Lanes have a wood or synthetic surface onto which protective lubricating oil is applied in different specified oil patterns that affect ball motion. A strike is achieved when all the pins are knocked down on the first roll, and a spare is achieved if all the pins are knocked over on a second roll. Common types of pin bowling include ten-pin, candlepin, duckpin, nine-pin, and five-pin. The historical game skittles is the forerunner of modern pin bowling. In target bowling, the aim is usually to get the ball as close to a mark as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overlay Plan
Overlay may refer to: Computers *Overlay network, a computer network which is built on top of another network *Hardware overlay, one type of video overlay that uses memory dedicated to the application *Another term for exec, replacing one process by another *Overlay (programming), a technique to reduce the amount of memory used by a program *Overlay keyboard, a specialized keyboard with no pre-set keys * Keyboard overlay, a sheet of printed text sitting between the keys, depicting an alternate keyboard layout *Vector overlay, an analysis procedure in a geographic information system for integrating multiple data sets Other uses *Overlay architecture, temporary elements that supplement existing buildings and infrastructure for major sporting events or festivals *Overlay control, in semiconductor manufacturing, for monitoring layer-to-layer alignment on multi-layer device structures *Overlay plan, a method of introducing new area codes in telephony *Historic overlay district, a zonin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greater Toronto Area
The Greater Toronto Area, commonly referred to as the GTA, includes the City of Toronto and the regional municipalities of Durham, Halton, Peel, and York. In total, the region contains 25 urban, suburban, and rural municipalities. The Greater Toronto Area begins in Burlington in Halton Region, and extends along Lake Ontario past downtown Toronto eastward to Clarington in Durham Region. According to the 2021 census, the Census Metropolitan Area (CMA) of Toronto has a total population of 6,202,225. However, the Greater Toronto Area, which is an economic area defined by the Government of Ontario, includes communities which are not included in the CMA as defined by Statistics Canada. Extrapolating the data for all 25 communities in the Greater Toronto Area from the 2021 Census, the total population for the economic region included 6,712,341 people. The Greater Toronto Area is a part of several larger areas in Southern Ontario. The area is also combined with the city of Hamilton to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Area Codes 905, 289 And 365
Area codes 905, 289, 365, and 742 are telephone area codes in the North American Numbering Plan (NANP) for the Golden Horseshoe region that surrounds Lake Ontario in Southern Ontario, Canada. The numbering plan area (NPA) comprises (clockwise) the Niagara Peninsula, the city of Hamilton, the regional municipalities of Halton, Peel, York, Durham, and parts of Northumberland County, but excludes the City of Toronto. The area codes form an overlay plan for the same geographic region, where area code 905 was established in October 1993 in an area code split from area code 416. When 289 was overlaid on June 9, 2001, all local calls required ten-digit dialing. On April 13, 2010, the Canadian Radio-television and Telecommunications Commission (CRTC) introduced another overlay code, area code 365, which became operational on March 25, 2013. The numbering plan area surrounds the city of Toronto (area codes 416/647/437), leading locals to refer to the primarily suburban cities surroundi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A001003
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguish it fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mertens Function
In number theory, the Mertens function is defined for all positive integers ''n'' as : M(n) = \sum_^n \mu(k), where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: : M(x) = M(\lfloor x \rfloor). Less formally, M(x) is the count of square-free integers up to ''x'' that have an even number of prime factors, minus the count of those that have an odd number. The first 143 ''M''(''n'') values are The Mertens function slowly grows in positive and negative directions both on average and in peak value, oscillating in an apparently chaotic manner passing through zero when ''n'' has the values :2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427, 428, ... . Because the Möbius function only ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schröder–Hipparchus Number
In combinatorics, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals. These numbers begin :1, 1, 3, 11, 45, 197, 903, 4279, 20793, 103049, ... . They are also called the super-Catalan numbers, the little Schröder numbers, or the Hipparchus numbers, after Eugène Charles Catalan and his Catalan numbers, Ernst Schröder and the closely related Schröder numbers, and the ancient Greek mathematician Hipparchus who appears from evidence in Plutarch to have known of these numbers. Combinatorial enumeration applications The Schröder–Hipparchus numbers may be used to count several closely related combinatorial objects:.. *The ''n''th number in the sequence counts the number of different ways of subdividing of a polygon with ''n'' +&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotient if there is no integer ''x'' that has exactly ''n'' coprimes below it. All odd numbers are nontotients, except 1, since it has the solutions ''x'' = 1 and ''x'' = 2. The first few even nontotients are : 14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, 158, 170, 174, 182, 186, 188, 194, 202, 206, 214, 218, 230, 234, 236, 242, 244, 246, 248, 254, 258, 266, 274, 278, 284, 286, 290, 298, ... Least ''k'' such that the totient of ''k'' is ''n'' are (0 if no such ''k'' exists) :1, 3, 0, 5, 0, 7, 0, 15, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 25, 0, 23, 0, 35, 0, 0, 0, 29, 0, 31, 0, 51, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 69, 0, 47, 0, 65, 0, 0, 0, 53, 0, 81, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphenic Number
In number theory, a sphenic number (from grc, σφήνα, 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers. Definition A sphenic number is a product ''pqr'' where ''p'', ''q'', and ''r'' are three distinct prime numbers. In other words, the sphenic numbers are the square-free 3-almost primes. Examples The smallest sphenic number is 30 = 2 × 3 × 5, the product of the smallest three primes. The first few sphenic numbers are : 30, 42, 66, 70, 78, 102, 105, 110, 114, 130, 138, 154, 165, ... the largest known sphenic number is :(282,589,933 − 1) × (277,232,917 − 1) × (274,207,281 − 1). It is the product of the three largest known primes. Divisors All sphenic numbers have exactly eight divisors. If we express the sphenic number as n = p \cdot q \cdot r, where ''p'', ''q'', and ''r'' are distinct primes, then the set of divisors of ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Happy Number
In number theory, a happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. For instance, 13 is a happy number because 1^2+3^2=10, and 1^2+0^2=1. On the other hand, 4 is not a happy number because the sequence starting with 4^2=16 and 1^2+6^2=37 eventually reaches 2^2+0^2=4, the number that started the sequence, and so the process continues in an infinite cycle without ever reaching 1. A number which is not happy is called sad or unhappy. More generally, a b-happy number is a natural number in a given number base b that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2. The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia" . Happy numbers and perfect digital invaria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.gif "Click for more on -> Lazy Caterer's Sequence")
