The number π is a mathematical constant. It is defined as the ratio of a circle's circumference to its diameter, and it also has various equivalent definitions. It appears in many formulas in all areas of mathematics and physics. The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by Welsh mathematician William Jones in 1706. It is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, and is spelled out as "pi". It is also referred to as Archimedes' constant.
Pi Day is an annual celebration of the mathematical constant π (pi). Pi Day is observed on March 14 since 3, 1, and 4 are the first three significant digits of π. It was founded in 1988 by Larry Shaw, an employee of 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. UNESCO's 40th General Conference designated Pi Day as the International Day of Mathematics in November 2019. Alternative dates for the holiday include July 22 and June 28.
The IEEE Standard for Floating-Point Arithmetic is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.
Piphilology comprises the creation and use of mnemonic techniques to remember many digits of the mathematical constant π. The word is a play on the word "pi" itself and of the linguistic field of philology.
A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation.
The Vienna U-Bahn, where U-Bahn is an abbreviation of the German term Untergrundbahn, is a rapid transit system serving Vienna, Austria. With the September 2017 opening of the 4.6 kilometers (2.9 mi), five-station extension of the U1 line, the five-line U-Bahn network consists of 83.1 kilometers (51.6 mi) of route, serving 109 stations. It is the backbone of one of the best performing public transport systems worldwide according to UITP in June 2009. More than 1.3 million passengers rode the Vienna U-Bahn every day in 2009, and 567.6 million passengers used the U-Bahn in 2011, which declined to 428.8 million passengers in 2013. The network is undergoing expansion and rolling stock renewal. Since 1969, 200 million euros have been invested annually in the extension of the Vienna U-Bahn.
In mathematics, the Leibniz formula for π, named after Gottfried Leibniz, states that
Directional statistics is the subdiscipline of statistics that deals with directions, axes or rotations in Rn. More generally, directional statistics deals with observations on compact Riemannian manifolds.
In mathematics, Viète's formula is the following infinite product of nested radicals representing the mathematical constant π:
Karlsplatz Stadtbahn Station is a former station of the Viennese Stadtbahn. The buildings above ground on Karlsplatz are a well-known example of Jugendstil architecture. These buildings were included in The Vienna Secession, as they followed many of the artistic styles of that movement. They were designed by Otto Wagner, adviser to the Transport Commission in Vienna, and Joseph Maria Olbrich and are, unlike the other Stadtbahn stations, made of a steel framework with marble slabs mounted on the exterior. These stations allowed Otto Wagner to achieve his goal of creating two modern axes of architecture in a city that was becoming one of the most modern cities of its time. These buildings went on to become the most modern monument of the modern city. Architectural critic and poet Friedrich Achleitner commented on the Stadtbahn stations as follows "...In these two station buildings Wagner reached a highpoint of his dialectic between function and poetry, construction and decoration, whereby a severe rationalism engages in competition with an almost Secessionist kind of decoration."
Karlsplatz is a town square on the border of the first and fourth districts of Vienna. It is one of the most frequented and best connected transportation hubs in Vienna. The Karlskirche is located here.
Kenneth Robert Lum, OC is a Chinese-Canadian artist and educator. Working in a number of media including painting, sculpture and photography, his art ranges from conceptual in orientation to representational in character and is generally concerned with issues of identity in relation to the categories of language, portraiture and spatial politics.
Approximations for the mathematical constant pi in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.
Milü, also known as Zulü, is the name given to an approximation to π (pi) found by Chinese mathematician and astronomer, Zǔ Chōngzhī (祖沖之), born 429 AD. Using Liu Hui's algorithm, Zu famously computed π to be between 3.1415926 and 3.1415927 and gave two rational approximations of π, 22/7 and 355/113, naming them respectively Yuelü 约率 and Milü.
A sequence of six 9's occurs in the decimal representation of the number pi, starting at the 762nd decimal place. It has become famous because of the mathematical coincidence and because of the idea that one could memorize the digits of π up to that point, recite them and end with "nine nine nine nine nine nine and so on", which seems to suggest that π is rational. The earliest known mention of this idea occurs in Douglas Hofstadter's 1985 book Metamagical Themas, where Hofstadter states
I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes "999999", so that I could recite it out loud, come to those six 9's, and then impishly say, "and so on!"
The Vienna Künstlerhaus is an art exhibition building in Vienna. It is located on Karlsplatz near the Ringstraße, next to the Musikverein.
In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length, no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.
In statistics, the Horvitz–Thompson estimator, named after Daniel G. Horvitz and Donovan J. Thompson, is a method for estimating the total and mean of a pseudo-population in a stratified sample. Inverse probability weighting is applied to account for different proportions of observations within strata in a target population. The Horvitz–Thompson estimator is frequently applied in survey analyses and can be used to account for missing data.
Kunsthalle Wien is the exhibition hall for contemporary art in Vienna. At its two locations in the MuseumsQuartier and at Karlsplatz, it shows themed group exhibitions, and solo presentations of established and upcoming artists to provide insight into the Austrian and international art scene. Kunsthalle Wien is dedicated to art and its relations to social change. It produces exhibitions, researches art practices, and supports local and international artists. It seeks to ground its knowledge of international contemporary art in and for Vienna, and advocates for the usefulness of artistic thinking in the wider public sphere.
The Opernpassage in the Inner City of Vienna is a Grade II listed pedestrian underpass under the ring road (Ringstraße). It was opened in 1955, a day before the re-opening of the nearby Vienna State Opera.
