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10000000 (number)
10,000,000 (ten million) is the natural number following 9,999,999 and preceding 10,000,001. In scientific notation, it is written as 107. In South Asia except for Sri Lanka, it is known as the crore. In Cyrillic numerals, it is known as the vran (''вран'' — raven). Selected 8-digit numbers (10,000,001–99,999,999) 10,000,001 to 19,999,999 * 10,000,019 = smallest 8-digit prime number * 10,001,628 = smallest triangular number with 8 digits and the 4,472nd triangular number * 10,004,569 = 31632, the smallest 8-digit square * 10,077,696 = 2163 = 69, the smallest 8-digit cube * 10,172,638 = number of reduced trees with 32 nodes * 10,321,920 = double factorial of 16 * 10,556,001 = 32492 = 574 * 10,600,510 = number of signed trees with 14 nodes * 10,609,137 = Leyland number using 6 & 9 (69 + 96) * 10,976,184 = logarithmic number * 11,111,111 = repunit * 11,316,496 = 33642 = 584 * 11,390,625 = 33752 = 2253 = 156 * 11,405,773 = Leonardo prime * 11,436,171 = Keith number * 11, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hebdo-
Hebdo- (symbol H) is an obsolete decimal metric prefix equal to 107. It is derived from the Greek ''hebdοmos'' () meaning ''seventh''. The definition of one hebdomometre or hebdometre as was originally proposed by Rudolf Clausius for use in an absolute electrodynamic system of units named the quadrant–eleventhgram–second system (QES system) in the 1880s. It was based on the meridional definition of the metre, which established one ten-millionth of an Earth quadrant, or the distance from the geographical pole to the equator, as a metre. See also * 10,000,000 *Crore, South Asian term for 107 *Metric prefix *Metric units *Numeral prefix References {{reflist, refs= {{cite journal , author-first=M. , author-last=Rothen , title=L'état actuel de la question des unités électriques , language=French , journal=Journal Télégraphique , publisher=Le Bureau International des Administrates Télégraphiques , date=1883-04-25 , volume=VII , number=4 , series=15 , location=Berne, Swi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automorphic Number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square "ends" in the same digits as the number itself. Definition and properties Given a number base b, a natural number n with k digits is an automorphic number if n is a fixed point of the polynomial function f(x) = x^2 over \mathbb/b^k\mathbb, the ring of integers modulo b^k. As the inverse limit of \mathbb/b^k\mathbb is \mathbb_b, the ring of b-adic integers, automorphic numbers are used to find the numerical representations of the fixed points of f(x) = x^2 over \mathbb_b. For example, with b = 10, there are four 10-adic fixed points of f(x) = x^2, the last 10 digits of which are: : \ldots 0000000000 : \ldots 0000000001 : \ldots 8212890625 : \ldots 1787109376 Thus, the automorphic numbers in base 10 are 0, 1, 5, 6, 25, 76, 376, 625, 9376, 90625, 109376, 890625, 2890625, 7109376, 12890625, 87109376, 212890625, 787109376, 1787109376, 82 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Motzkin Number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have diverse applications in geometry, combinatorics and number theory. The Motzkin numbers M_n for n = 0, 1, \dots form the sequence: : 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, ... Examples The following figure shows the 9 ways to draw non-intersecting chords between 4 points on a circle (): : The following figure shows the 21 ways to draw non-intersecting chords between 5 points on a circle (): : Properties The Motzkin numbers satisfy the recurrence relations :M_=M_+\sum_^M_iM_=\fracM_+\fracM_. The Motzkin numbers can be expressed in terms of binomial coefficients and Catalan numbers: :M_n=\sum_^ \binom C_k, and inversely, :C_=\sum_^ \binom M_k This gives :\sum_^C_ = 1 + \sum_^ \binom M_. The generating function m(x) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Woodall Number
In number theory, a Woodall number (''W''''n'') is any natural number of the form :W_n = n \cdot 2^n - 1 for some natural number ''n''. The first few Woodall numbers are: :1, 7, 23, 63, 159, 383, 895, … . History Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly defined Cullen numbers. Woodall primes Woodall numbers that are also prime numbers are called Woodall primes; the first few exponents ''n'' for which the corresponding Woodall numbers ''W''''n'' are prime are 2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, ... ; the Woodall primes themselves begin with 7, 23, 383, 32212254719, ... . In 1976 Christopher Hooley showed that almost all Cullen numbers are composite. In October 1995, Wilfred Keller published a paper discussing several new Cullen primes and the efforts made to factorise other Cullen and Woodall numbers. Included in that paper is a personal communication to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
24-bit Color
Color depth, also known as bit depth, is either the number of bits used to indicate the color of a single pixel, or the number of bits used for each color component of a single pixel. When referring to a pixel, the concept can be defined as bits per pixel (bpp). When referring to a color component, the concept can be defined as bits per component, bits per channel, bits per color (all three abbreviated bpc), and also bits per pixel component, bits per color channel or bits per sample. Modern standards tend to use bits per component, but historical lower-depth systems used bits per pixel more often. Color depth is only one aspect of color representation, expressing the precision with which the amount of each primary can be expressed; the other aspect is how broad a range of colors can be expressed (the gamut). The definition of both color precision and gamut is accomplished with a color encoding specification which assigns a digital code value to a location in a color space. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexadecimal
Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen. Software developers and system designers widely use hexadecimal numbers because they provide a convenient representation of binary code, binary-coded values. Each hexadecimal digit represents four bits (binary digits), also known as a nibble (or nybble). For example, an 8-bit byte is two hexadecimal digits and its value can be written as to in hexadecimal. In mathematics, a subscript is typically used to specify the base. For example, the decimal value would be expressed in hexadecimal as . In programming, several notations denote hexadecimal numbers, usually involving a prefi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell Number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , and , so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numerators of the same sequence of approximations are half the companion Pell numbers or Pell–Lucas numbers; these numbers form a second infinite sequence that begins with 2, 6, 14, 34, and 82. Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + . As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curium
Curium is a synthetic chemical element; it has symbol Cm and atomic number 96. This transuranic actinide element was named after eminent scientists Marie and Pierre Curie, both known for their research on radioactivity. Curium was first intentionally made by the team of Glenn T. Seaborg, Ralph A. James, and Albert Ghiorso in 1944, using the cyclotron at Berkeley. They bombarded the newly discovered element plutonium (the isotope 239Pu) with alpha particles. This was then sent to the Metallurgical Laboratory at University of Chicago where a tiny sample of curium was eventually separated and identified. The discovery was kept secret until after the end of World War II. The news was released to the public in November 1947. Most curium is produced by bombarding uranium or plutonium with neutrons in nuclear reactors – one tonne of spent nuclear fuel contains ~20 grams of curium. Curium is a hard, dense, silvery metal with a high melting and boiling point for an actinide. It ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotopes Of Curium
Curium (Cm) is an artificial element with an atomic number of 96. Because it is an artificial element, a standard atomic weight cannot be given, and it has no stable isotopes. The first isotope synthesized was Cm in 1944, which has 146 neutrons. There are 19 known radioisotopes ranging from Cm to Cm. There are also ten known nuclear isomers. The longest-lived isotope is Cm, with half-life 15.6 million years – orders of magnitude longer than that of any known isotope beyond curium, and long enough to study as a possible extinct radionuclide that would be produced by the r-process. The longest-lived known isomer is Cm with a half-life of 1.12 seconds. List of isotopes , -id=Curium-233 , rowspan=2, Cm , rowspan=2 style="text-align:right" , 96 , rowspan=2 style="text-align:right" , 137 , rowspan=2, 233.050771(87) , rowspan=2, 27(10) s , β (80%) , Am , rowspan=2, 3/2+# , - , α (20%) , Pu , -id=Curium-234 , rowspan=3, Cm , rowspan=3 style="text-align:rig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The Fibonacci numbers were first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Domino Tiling
In geometry, a domino tiling of a region in the Euclidean plane is a tessellation of the region by domino (mathematics), dominoes, shapes formed by the union of two unit squares meeting edge-to-edge. Equivalently, it is a matching (graph theory), perfect matching in the grid graph formed by placing a vertex at the center of each square of the region and connecting two vertices when they correspond to adjacent squares. Height functions For some classes of tilings on a regular grid in two dimensions, it is possible to define a height function associating an integer to the vertex (graph theory), vertices of the grid. For instance, draw a chessboard, fix a node A_0 with height 0, then for any node there is a path from A_0 to it. On this path define the height of each node A_ (i.e. corners of the squares) to be the height of the previous node A_n plus one if the square on the right of the path from A_n to A_ is black, and minus one otherwise. More details can be found in . Thurston's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
