|
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'' * 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 *Piphilology * Proof that is irrational * Proof that 22/7 exceeds * Proof of Wallis product *Rabbi Nehemiah *Radian *Ramanujan–Sato series *Rhind Mathematical Pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Constant
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an Letter (alphabet), 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 pi, occurring in such diverse contexts as geometry, number theory, statistics, and calculus. Some constants arise naturally by a fundamental principle or intrinsic property, such as the ratio between the circumference and diameter of a circle (). Other constants are notable more for historical reasons than for their mathematical properties. The more popular constants have been studied throughout the ages and computed to many decimal places. All named mathematical constants are Definable real number, definable numbers, and usually are also computable numbers (Chaitin's constant being a significant exception). Basic mathematical constants These a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A History Of Pi
''A History of Pi'' (also titled ''A History of '') is a 1970 non-fiction book by Petr Beckmann that presents a layman's introduction to the concept of the mathematical constant pi (). Author Beckmann was a Czechoslovakian who fled the Communist regime to go to the United States. His dislike of authority gives ''A History of Pi'' a style that belies its dry title. For example, his chapter on the era following the classical age of ancient Greece is titled "The Roman Pest"; he calls the Catholic Inquisition the act of "insane religious fanatic"; and he says that people who question public spending on scientific research are "intellectual cripples who drivel about 'too much technology' because technology has wounded them with the ultimate insult: 'They can't understand it any more.'" Beckmann was a prolific scientific author who wrote several electrical engineering textbooks and non-technical works, founded Golem Press, which published most of his books, and published his own month ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi Day
Pi Day is an annual celebration of the mathematical constant (pi). Pi Day is observed on March 14 (the 3rd month) since 3, 1, and 4 are the first three significant figures of , and was first celebrated in the United States. It was founded in 1988 by Larry Shaw, an employee of a science museum in San Francisco, the Exploratorium. Celebrations often involve eating pie or holding pi recitation competitions. In 2009, the United States House of Representatives supported the designation of Pi Day.United States. Cong. House. Supporting the designation of Pi Day, and for other purposes. 111th CongLibrary of Congress UNESCO's 40th General Conference designated Pi Day as the International Day of Mathematics in November 2019. Other dates when people celebrate pi include Pi Approximation Day on July 22 (22/7 in the ''day/month'' format), another approximation of ; and June 28 (6.28), an approximation of 2 or (tau). History In 1988, the earliest known official or large-scale ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pi (letter)
Pi (; Ancient Greek or , uppercase Π, lowercase π, cursive ϖ; ) is the sixteenth letter of the Greek alphabet, representing the voiceless bilabial plosive . In the system of Greek numerals it has a value of 80. It was derived from the Phoenician alphabet, Phoenician letter Pe (Semitic letter), Pe (). Letters that arose from pi include Latin alphabet, Latin P, Cyrillic script, Cyrillic Pe (Cyrillic), Pe (П, п), Coptic alphabet, Coptic pi (Ⲡ, ⲡ), and Gothic alphabet, Gothic pairthra (𐍀). Uppercase Pi The uppercase letter Π is used as a symbol for: * In textual criticism, ''Codex Petropolitanus (New Testament), Codex Petropolitanus'', a 9th-century uncial codex of the Gospels, now located in St. Petersburg, Russia. * In legal shorthand, it represents a plaintiff. * In Mathematical finance, it represents a portfolio. Greek letters used in mathematics, science, and engineering, In science and engineering: * The product (mathematics), product operator in mathematics, i ... [...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 ye ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Milü
''Milü'' (), also known as Zulü (Zu's ratio), is the name given to an approximation of ( pi) found by the Chinese mathematician and astronomer Zu Chongzhi during the 5th century. Using Liu Hui's algorithm, which is based on the areas of regular polygons approximating a circle, Zu computed as being between 3.1415926 and 3.1415927 and gave two rational approximations of , and , which were named ''yuelü'' () and ''milü'' respectively. 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 , though it is still only correct to six decimal places. 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 can be explained using the co ... [...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 (one at a time) 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 ... [...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 sticky-header sort-under" , - ! rowspan="2" , Name ! rowspan="2" , Symbol ! rowspan="2" , Decimal expansion ! rowspan="2" , Formula ! rowspan="2" , Year ! colspan="3" , Set , - ! \mathbb{Q} ! \mathbb{A} ! \mathcal{P} , - , One , 1 , 1 , Multiplicative identity of \mathbb{C}. , data-sort-value="-2 ... [...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 ie . 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 diamet ... [...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 = \frac C where is the circumference of a circle, is the diameter, and is the radius. 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. More generally, : A = \pi ab where is the area enclosed by an ellipse with semi-major axis and semi-minor axis . : C=\frac\left(a_1^2-\sum_^\infty 2^(a_n^2-b_n^2)\right) where is the circumference of an ellipse with semi-major axis and semi-minor axis and a_n,b_n are the arithmetic and geometric iterations of \operatorname(a,b), the arithmetic-geometric mean of and with the initial values a_0=a and b_0=b. : A=4\pi r^2 where is the area between the witch of Agnesi and its asymptotic line; is the ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Circle Topics
A list is a set of discrete items of information collected and set forth in some format for utility, entertainment, or other purposes. A list may be memorialized in any number of ways, including existing only in the mind of the list-maker, but lists are frequently written down on paper, or maintained electronically. Lists are "most frequently a tool", and "one does not ''read'' but only ''uses'' a list: one looks up the relevant information in it, but usually does not need to deal with it as a whole". Lucie Doležalová,The Potential and Limitations of Studying Lists, in Lucie Doležalová, ed., ''The Charm of a List: From the Sumerians to Computerised Data Processing'' (2009). Purpose It has been observed that, with a few exceptions, "the scholarship on lists remains fragmented". David Wallechinsky, a co-author of '' The Book of Lists'', described the attraction of lists as being "because we live in an era of overstimulation, especially in terms of information, and lists help ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
