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List Of Topics Related To π
This is a list of topics related to pi (), the fundamental mathematical constant. * 2 theorem * Approximations of * Arithmetic–geometric mean *Bailey–Borwein–Plouffe formula * Basel problem *Borwein's algorithm *Buffon's needle *Cadaeic Cadenza * Chronology of computation of *Circle *Euler's identity *Six nines in pi *Gauss–Legendre algorithm * Gaussian function * History of *'' A History of Pi'' (book) *Indiana Pi Bill *Leibniz formula for pi * Lindemann–Weierstrass theorem (Proof that is transcendental) *List of circle topics * List of formulae involving * Liu Hui's algorithm * Mathematical constant (sorted by continued fraction representation) *Mathematical constants and functions *Method of exhaustion *Milü * Pi *Pi (art project) *Pi (letter) * Pi Day * PiFast *PiHex *Pi in the Sky *Pilish *Pimania (computer game) * Piphilology * Proof that is irrational * Proof that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Constant
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as and occurring in such diverse contexts as geometry, number theory, statistics, and calculus. What it means for a constant to arise "naturally", and what makes a constant "interesting", is ultimately a matter of taste, with some mathematical constants being notable more for historical reasons than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places. All named mathematical constants are definable numbers, and usually are also computable numbers (Chaitin's constant being a significant exception). Basic mathematical constants These are constants which one is likely to encounter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of π
The number (; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. The number appears in many formulas across mathematics and physics. It is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as \tfrac are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an equation involving only sums, products, powers, and integers. The transcendence of implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of appear to be randomly distributed, but no proof of this conjecture has been found. For thousands of years, mathematicians have attempted to extend their understanding of , sometimes by computing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi (art Project)
''Pi'' is the name of a multimedia installation in the vicinity of the Viennese Karlsplatz. ''Pi'' is located in the Opernpassage between the entrance to the subway and the subway stop in Secession near the Naschmarkt. The individual behind the project was the Canadian artist Ken Lum from Vancouver. ''Pi'', under construction from January 2005 to November 2006 and opened in December 2006, consists of statistical information and a representation of π to 478 decimal places. A more recent project is the calculation of the decimal places of π, indicating the importance of the eponymous media for installation of their number and infinity. The exhibit is 130 meters long. In addition to the number pi, there is a total of 16 ''factoids'' of reflective display cases that convey a variety of statistical data in real time. Apart from the World population there are also topics such as the worldwide number of malnourished children and the growth of Sahara since the beginning of the yea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milü
Milü (; "close ratio"), also known as Zulü ( Zu's ratio), is the name given to an approximation to (pi) found by Chinese mathematician and astronomer Zu Chongzhi in the 5th century. Using Liu Hui's algorithm (which is based on the areas of regular polygons approximating a circle), Zu famously computed to be between 3.1415926 and 3.1415927 and gave two rational approximations of , and , naming them respectively Yuelü (; "approximate ratio") and Milü. is the best rational approximation of with a denominator of four digits or fewer, being accurate to six decimal places. It is within % of the value of , or in terms of common fractions overestimates by less than . The next rational number (ordered by size of denominator) that is a better rational approximation of is , still only correct to six decimal places and hardly closer to than . To be accurate to seven decimal places, one needs to go as far as . For eight, is needed. The accuracy of Milü to the true value of ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Exhaustion
The method of exhaustion (; ) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. If the sequence is correctly constructed, the difference in area between the ''n''th polygon and the containing shape will become arbitrarily small as ''n'' becomes large. As this difference becomes arbitrarily small, the possible values for the area of the shape are systematically "exhausted" by the lower bound areas successively established by the sequence members. The method of exhaustion typically required a form of proof by contradiction, known as ''reductio ad absurdum''. This amounts to finding an area of a region by first comparing it to the area of a second region, which can be "exhausted" so that its area becomes arbitrarily close to the true area. The proof involves assuming that the true area is greater than the second area, proving that assertion false, assuming it is less than the second area ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Constants And Functions
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set. Explanations of the symbols in the right hand column can be found by clicking on them. List {, class="wikitable sortable" , - ! Name ! Symbol ! Decimal expansion ! Formula ! Year ! Set , - , One , 1 , 1 , , data-sort-value="-2000", Prehistory , data-sort-value="1", \mathbb{N} , - , Two , 2 , 2 , , data-sort-value="-2000", Prehistory , data-sort-value="1", \mathbb{N} , - , One half , 1/2 , data-sort-value="0.50000", ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Constant (sorted By Continued Fraction Representation)
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set. Explanations of the symbols in the right hand column can be found by clicking on them. List {, class="wikitable sortable" , - ! Name ! Symbol ! Decimal expansion ! Formula ! Year ! Set , - , One , 1 , 1 , , data-sort-value="-2000", Prehistory , data-sort-value="1", \mathbb{N} , - , Two , 2 , 2 , , data-sort-value="-2000", Prehistory , data-sort-value="1", \mathbb{N} , - , One half , 1/2 , data-sort-value="0.50000", 0.5 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liu Hui's π Algorithm
Liu Hui's algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei. Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter of the earth, ) or as \pi \approx \sqrt \approx 3.162. Liu Hui was not satisfied with this value. He commented that it was too large and overshot the mark. Another mathematician Wang Fan (219–257) provided . All these empirical values were accurate to two digits (i.e. one decimal place). Liu Hui was the first Chinese mathematician to provide a rigorous algorithm for calculation of to any accuracy. Liu Hui's own calculation with a 96-gon provided an accuracy of five digits: . Liu Hui remarked in his commentary to ''The Nine Chapters on the Mathematical Art'', that the ratio of the circumference of an inscribed hexagon to the diamete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Formulae Involving π
The following is a list of significant formulae involving the mathematical constant . Many of these formulae can be found in the article Pi, or the article Approximations of . Euclidean geometry :\pi = \frac Cd where is the circumference of a circle, is the diameter. More generally, :\pi=\frac where and are, respectively, the perimeter and the width of any curve of constant width. :A = \pi r^2 where is the area of a circle and is the radius. More generally, :A = \pi ab where is the area enclosed by an ellipse with semi-major axis and semi-minor axis . :A=4\pi r^2 where is the area between the witch of Agnesi and its asymptotic line; is the radius of the defining circle. :A=\frac r^2=\frac where is the area of a squircle with minor radius , \Gamma is the gamma function and \operatorname is the arithmetic–geometric mean. :A=(k+1)(k+2)\pi r^2 where is the area of an epicycloid with the smaller circle of radius and the larger circle of radius (k\in\mathbb), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Circle Topics
This list of circle topics includes things related to the geometric shape, either abstractly, as in idealizations studied by geometers, or concretely in physical space. It does not include metaphors like "inner circle" or "circular reasoning" in which the word does not refer literally to the geometric shape. Geometry and other areas of mathematics * Circle ; Circle anatomy * Annulus (mathematics) * Area of a disk * Bipolar coordinates * Central angle * Circular sector * Circular segment * Circumference * Concentric * Concyclic * Degree (angle) * Diameter * Disk (mathematics) * Horn angle * ''Measurement of a Circle'' * ** List of topics related to * Pole and polar * Power of a point * Radical axis * Radius ** Radius of convergence ** Radius of curvature * Sphere * Tangent lines to circles * Versor ; Specific circles * Apollonian circles * Circles of Apollonius * Archimedean circle * Archimedes' circles – the twin circles doubtfully attributed to Archimedes * Archimed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lindemann–Weierstrass Theorem
In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: In other words, the extension field \mathbb(e^, \dots, e^) has transcendence degree over \mathbb. An equivalent formulation , is the following: This equivalence transforms a linear relation over the algebraic numbers into an algebraic relation over \mathbb by using the fact that a symmetric polynomial whose arguments are all conjugates of one another gives a rational number. The theorem is named for Ferdinand von Lindemann and Karl Weierstrass. Lindemann proved in 1882 that is transcendental for every non-zero algebraic number thereby establishing that is transcendental (see below). Weierstrass proved the above more general statement in 1885. The theorem, along with the Gelfond–Schneider theorem, is extended by Baker's theorem, and all of these would be further generalized by Schanuel's conjecture. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leibniz Formula For Pi
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history and philology. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science: while serving as overseer of the Wolfenbüttel library in Germany, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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