pi

Dictionary

the ratio of the circumference to the diameter of a circle

approximately equal to 3.14159265358979323846... someone who can be employed as a detective to collect information the scientist in charge of an experiment or research project the 16th letter of the Greek alphabet an antiviral drug used against HIV

interrupts HIV replication by binding and blocking HIV protease

often used in combination with other drugs

Wikipedia

otherusespie The mathematical constant π is the ratio of a circle's circumference (Greek languageGreek περιφέρεια, periphery) to its diameter and is commonly used in mathematics, physics, and engineering. The name of the Greek alphabetGreek letter Pi (letter)π is pi (pronounced ''pie''), and this spelling can be used in typographical contexts where the Greek letter is not available. π is also known as '''Archimedes' constant''' (not to be confused with Archimedes numberArchimedes' number) and '''Ludolph van CeulenLudolph's number'''.In plane geometryEuclidean plane geometry, π may be defined either as the ratio of a circle's circumference to its diameter, or as the ratio of a circle's area to the area of a square whose side is the radius. Advanced textbooks define π mathematical analysisanalytically using trigonometric functions, for example as the smallest positive ''x'' for which trigonometric functionsin(''x'') = 0, or as twice the smallest positive ''x'' for which trigonometric functioncos(''x'') = 0.All these definitions are equivalent.The numerical value of π rounded to 50 decimaldecimal places A000796 !is::3.14159 26535 89 793 23846 26433 ;83279 50288 41971&n bsp;69399 37510Although? this precision is more than sufficient for use in engineering and science, much effort over the last few centuries has been put into computing more digits and investigating the number's properties. Despite much analytical work, in addition to supercomputer calculations that have determined over 1 trillion digits of π, no pattern in the digits has ever been found. Digits of π are available from multiple resources on the Internet, and a regular personal computer can be used to compute billions of digits.

Properties - π is an irrational number; that is, it cannot be written as the ratio of two integers, as was proven in 1761 by Johann Heinrich Lambert. π is also transcendental numbertranscendental, as was proven by Ferdinand von Lindemann in 1882. This means that there is no polynomial with rational numberrational coefficients of which π is a root. An important consequence of the transcendence of π is the fact that it is not constructible numberconstructible. Because the coordinates of all points that can be constructed with ruler and compass are constructible numbers, it is impossible to squaring the circlesquare the circle, that is, it is impossible to construct, using ruler-and-compass constructionruler and compass alone, a square whose area is equal to the area of a given circle.

Formulae involving π -

Geometry -

\pi

appears in many formulae in geometry involving circles and spheres. \pi r^3 = \frac \pi d^3 \,\!-Surface area of sphere of radius ''r''

A = 4 \pi r^2 \,\!

-Volume of cylinder of height ''h'' and radius ''r''

V = \pi r^2 h \,\!

-Surface area of cylinder of height ''h'' and radius ''r''

A = 2 ( \pi r^2 ) + ( 2 \pi r ) h = 2 \pi r (r + h) \,\!

-Volume of cone of height ''h'' and radius ''r''

V = \frac   \pi r^2 h \,\!

-Surface area of cone of height ''h'' and radius ''r''

A = \pi r \sqrt  + \pi r^2 =  \pi r (r + \sqrt ) \,\!

}(All of these are a consequence of the first one, as the area of a circle can be written as''A'' = ∫(2''πr'')d''r'' ("sum of annulusannuli of infinitesimal width"), and others concern a surface or solid of revolution.)Also, the angle measure of 180° (Degree (angle)degrees) is equal to π radians.

Analysis - Many formulae in Mathematical analysisanalysis contain π, including infinite series (and infinite product) representations, integrals, and so-called List of mathematical functionsspecial functions.

François Viète, 1593 (Viète formula!proof)::

\frac2\pi= \frac? 2\frac }2\frac }}2\ldots

Gottfried LeibnizLeibniz' formula (Leibniz formula for piproof)::

\frac   - \frac   + \frac   - \frac   + \frac   - \cdots = \frac

:This commonly cited infinite series is usually written as above, but is more technically expressed as::

\sum_ ^  \frac }  = \frac

Wallis productWallis's product (see that article for a proof)::

\frac   \cdot \frac   \cdot \frac   \cdot \frac   \cdot \frac   \cdot \frac   \cdot \frac   \cdot \frac   \cdots = \frac

\prod_ ^  \frac   = \prod_ ^  \frac   \cdot \frac   = \frac

1995 Bailey-Borwein-Plouffe !algorithm:

- \frac - \frac - \frac - \frac \right

An integral formula from calculus (see also Error function and Normal !distribution)::

\in t_? ^  e^ \,dx = \sqrt

Basel problem, first solved by Leonhard EulerEuler (see also Riemann zeta !function)::

\zeta(2 )? = \frac   + \frac   + \frac   + \frac   + \cdots = \frac  !

\zet a(4)=? \frac   + \frac   + \frac   + \frac   + \cdots = \frac

:and generally, !

\zeta(2n)

? is a rational multiple of

\pi^

for positive integer n

Gamma function evaluated at 1/2::

\Gamma\left( \right)=\sqrt

Stirling's approximation::

n! \sim \sqrt  \left(\frac  \right)^n

Euler's identity (called by Richard Feynman "the most remarkable formula in !mathematics")::

Property of Euler's totient function (see also Farey sequence)::

\sum_ ^  \phi (k) \sim 3 n^2 / \pi^2

Area of one quarter of the unit circle::

\int_0^1 \sqrt \,dx =

An application of the residue theorem:

\oint\frac  =2\pi i ,

:where the path of integration is a circle around the origin, traversed in the standard (anti-clockwise) direction.

Continued fractions - π has many continued fractions representations, including::

\frac   = 1 + \frac       }}}}}

(Other representations are available at functions.wolfram.com - The Wolfram Functions Site.)

Number theory - Some results from number theory:

The probability that two randomly chosen integers are coprime is !6/π² .

The probability that a randomly chosen integer is square-free is !6/π² .

The meanaverage number of ways to write a positive integer as the sum of two perfect squares (order matters) is π/4.

The product of !(1-1/p² )? over the primes, ''p'', is !6/π² .

? \prod_ } \left(1-\frac     \right) = \frac

Here, "probability", "average", and "random" are taken in a limiting sense, e.g. we consider the probability for the set of integers , and then take the limit (mathematics)limit as ''N'' approaches infinity.The remarkable fact (note the order to which the number approaches an integer) that:

e^ } = !262537412640768743.99999999999 925007...

or? equivalently,:

e^ } = !640320^3+743.99999999999925007 ...

? can be explained by the theory of complex multiplication.

Dynamical systems and ergodic theory - Consider the recurrence relation:

x_  = 4 x_i (1 - x_i) \,

Then for almost everywherealmost every initial value ''x''₀ in the unit interval 0,1,:

\lim_  \frac   \sum_ ^  \sqrt  = \frac

This recurrence relation is the logistic map with parameter ''r'' = 4, known from dynamical systems theory. See also: ergodic theory.

Physics - The number π appears routinely in equations describing fundamental principles of the universe, due in no small part to its relationship to the nature of the circle and, correspondingly, spherical coordinate systems.

The cosmological constant::

\Lambda = 8\pi G} \over

Einstein's field equation of general relativity::

R_  -   R \over 2} + \Lambda g_  =   T_

Coulomb's law for the electric force::

F = \frac

Permeability (electromagnetism)Magnetic permeability of free space::

\mu_0 = 4 \pi \times 10^ \,\mathrm \,

Probability and statistics - In probability and statistics, there are many probability distributiondistributions whose formulae contain π, including:

probability density function (pdf) for the normal distribution with mean μ and standard deviation σ::

f(x) =   }\,e^

pdf for the (standard) Cauchy distribution::

f(x) = \frac

Note that since

\int_ ^  f(x)\,dx = 1

, for any pdf ''f''(''x''), the above formulae can be used to produce other integral formulas for π.An interesting empirical approximation of π is based on Buffon's needle problem. Consider dropping a needle of length ''L'' repeatedly on a surface containing parallel lines drawn ''S'' units apart (with ''S'' > ''L''). If the needle is dropped ''n'' times and ''x'' of those times it comes to rest crossing a line (''x'' > 0), then one may approximate π using::

\pi \approx \frac

History of π - ''Main article: History of Pi''.π has been known in some form since antiquity. References to measurements of a circular basin in the Bible give a corresponding value of 3 for π: "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about." — 1 Kings 7:23; KJV. Nehemiah, a Late Antiquitylate antique Jewish rabbi and mathematician explained this apparent lack of precision in π, by considering the thickness of the basin, and assuming that the thirty cubits was the inner circumference, while the ten cubits was the diameter of the outside of the basin.

Numerical approximations of π - Due to the transcendental nature of π, there are no closed expressions for the number in terms of algebraic numbers and functions. Therefore numerical calculations must use approximations of π. For many purposes, 3.14 or 22/7 is close enough, although engineers often use 3.1416 (5 significant figures) or 3.14159 (6 significant figures) for more accuracy. The approximations 22/7 and 355/113, with 3 and 7 significant figures respectively, are obtained from the simple continued fraction expansion of π.An Egyptian scribe named Ahmes wrote the oldest known text to give an approximate value for π. The Moscow and Rhind Mathematical PapyriRhind Mathematical Papyrus dates from the Ancient EgyptEgyptian Second Intermediate Period—though Ahmes stated that he copied a Middle Kingdom of EgyptMiddle Kingdom papyrus—and describes the value in such a way that the result obtained comes out to 256 divided by 81 or 3.160.The Chinese mathematician Liu Hui computed π to 3.141014 (good to three decimal places) in AD 263 and suggested that 3.14 was a good approximation.The Indian mathematician and astronomer Aryabhata gave an accurate approximation for π. He wrote "Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given." In other words (4+100)×8 + 62000 is the circumference of a circle with diameter 20000. This provides a value of π = 62832/20000 = 3.1416, correct when rounded off to four decimal places.The Chinese mathematician and astronomer Zu Chongzhi computed π to 3.1415926 to 3.1415927 and gave two approximations of π 355/113 and 22/7 in the 5th century.The Iranian mathematician and astronomer, Ghyath ad-din Jamshid Kashani, 1350-1439, computed π to 9 digits in the base of 60, which is equivalent to 16 decimal digits as::2 π = 6.2831853071795865The German mathematician Ludolph van Ceulen (''circa'' 1600) computed the first 35 decimals. He was so proud of this accomplishment that he had them inscribed on his tomb stonetombstone. The Slovene mathematician Jurij Vega in 1789 calculated the first 140 decimal places for π of which the first 137 were correct and held the world record for 52 years until 1841, when William Rutherford calculated 208 decimal places of which the first 152 were correct. Vega improved John Machin's formula from 1706 and his method is still mentioned today.None of the formulas given above can serve as an efficient way of approximating π. For fast calculations, one may use formulas such as John_MachinMachin's::

\frac   = 4 \arctan\frac   - \arctan\frac

together with the Taylor series expansion of the function arctan(''x''). This formula is most easily verified using polar coordinates of complex numbers, starting with !:

(5+i)^4\cdot(-239 +i)=-114244-114244i.Hitachi supercomputer with 1 terabyte of main memory, which carries out 2 trillion operations per second, nearly twice as many as the computer used for the previous record (206 billion digits). The following Machin-like formulas were used for this:: \frac   = 12 \arctan\frac   + 32 \arctan\frac   - 5 \arctan\frac   + 12 \arctan\frac :K. Takano (1982).: \frac   = 44 \arctan\frac   + 7 \arctan\frac   - 12 \arctan\frac   + 24 \arctan\frac :F. C. W. Störmer (1896).These approximations have so many digits that they are no longer of any practical use, except for testing new supercomputers and (obviously) for establishing new π calculation records.In 1996, David H. Bailey, Peter Borwein and Simon Plouffe published a paper on a new formula for π as an infinite series:: \pi = \sum_ ^  \frac  \left( \frac   - \frac   - \frac   - \frac  \right) This formula permits one to easily compute the ''k''

^th Binary numeral systembinary or hexadecimal digit of π, without having to compute the preceding ''k'' − 1 digits. nersc.gov - Bailey's website contains the derivation as well as implementations in various programming languageprogramming languages. The PiHex project computed 64-bits around the quadrillionth bit of π (which turns out to be 0).Other formulas that have been used to compute estimates of π include::

\frac  =\sum_ ^\infty\frac  =1+\frac  \left(1+\frac  \left(1+\frac  \left(1+\frac  !(1+...)\right)\right)\right)&l t;/math>:Isaac? Newton Newton.: \frac   = \frac }  \sum^\infty_  \frac  } :Ramanujan.This converges extraordinarily rapidly. Ramanujan's work is the basis for the fastest algorithms used, as of the turn of the millennium, to calculate π.: \frac   = 12 \sum^\infty_  \frac  } :David Chudnovsky (mathematician) David Chudnovsky and Gregory Chudnovsky.: = 20 \arctan\frac   + 8 \arctan\frac :Euler.On computers running Microsoft Windows Operating_system OS, the program PiFast can be used to quickly calculate a large amount of digits. The largest number of digits of π calculated on a home computer, 25,000,000,000, was calculated with PiFast in 17 days.

Miscellaneous formulas - In radixbase 60, π can be approximated to eight significant figures as:

3 + \frac   + \frac   + \frac

In addition, the following expressions can be used to estimate π

accurate to 9 !digits::

(63/25)((1 7+15\sqrt? !5)/(7+15\sqrt5))

< li> accurate to 17 digits::

3 + \frac

accurate to 3 digits::

\sqrt  + \sqrt

:Karl Popper conjectured that Plato knew this expression; that he believed it to be exactly π; and that this is responsible for some of Plato's confidence in the omnicompetence of mathematical geometry — and Plato's repeated discussion of right triangles which are either isosceles or halves of equilateral triangles.

Less accurate approximations - In 1897, a physician and amateur mathematician from Indiana named Edward J. Goodwin believed that the transcendental numbertranscendental value of π was wrong. He proposed a bill to Indiana Representative T. I. Record which expressed the "new mathematical truth" in several ways:The ratio of the diameter of a circle to its circumference is 5/4 to 4.'' (π = 3.2)The ratio of the length of a 90 degree arc to the length of a segment connecting the arc's two endpoints is 8 to 7.'' (π ≈ 3.23...)The area of a circle equals the area of a square whose side is 1/4 the circumference of the circle.'' (π = 4)It has been found that a circular area is to the square on a line equal to the quadrant of the circumference, as the area of an equilateral rectangle is to the square on one side.'' (π ≈ 9.24 if ''rectangle'' is emended to ''triangle''; if not, as above.)The bill also recites Goodwin's previous accomplishments: "his solutions of the trisection of the angle, doubling the cube and - the value of π having been already accepted as contributions to science by the American Mathematical Monthly....And be it remembered that these noted problems had been long since given up by scientific bodies as unsolvable mysteries and above man's ability to comprehend." These false claims are typical of a mathematical crank (person)crank. The claims trisection of an angle and the doubling of the cube are particularly widespread in crank literature.The Indiana Assembly referred the bill to the Committee on Swamp Lands, which Petr Beckmann has seen as symbolic. It was transferred to the Committee on Education, which reported favorably, and the bill passed unanimously. One argument used was that Goodwin had copyrighted his discovery, and proposed to let the State use it in the public schools for free. As this debate concluded, Professor C. A. Waldo arrived in Indianapolis to secure the annual appropriation for the Indiana Academy of Sciences. An assemblyman handed him the bill, offering to introduce him to the genius who wrote it. He declined, saying that he already knew as many crazy people as he cared to. The Indiana Senate had not yet finally passed the bill (which they had referred to the Committee on Temperance), and Professor Waldo coached enough Senators overnight that they postponed the bill indefinitely. faqs.jmas.co.jp - source

Open questions - The most pressing open question about π is whether it is a normal number -- whether any digit block occurs in the expansion of π just as often as one would statistically expect if the digits had been produced completely "randomly". This must be true in any base, not just in base 10. Current knowledge in this direction is very weak; e.g., it is not even known which of the digits 0,…,9 occur infinitely often in the decimal expansion of π.Bailey and Crandall showed in 2000 that the existence of the above mentioned Bailey-Borwein-Plouffe formula and similar formulas imply that the normality in base 2 of π and various other constants can be reduced to a plausible conjecture of chaos theory. See Bailey's above mentioned web site for details.It is also unknown whether π and E (mathematical constant)''e'' are algebraically independent, i.e. whether there is a polynomial relation between π and ''e'' with rational coefficients.John Harrison, (1693–1776) (of Longitude fame), devised a meantone temperament musical tuning system derived from π. This Lucy Tuning system (due to the unique mathematical properties of π), can map all musical intervals, harmony and harmonics. This suggests that musical harmonics beat, and that using π could provide a more precise model for the analysis of both musical and other harmonics in vibrating systems.

The nature of π - In non-Euclidean geometry the sum of the angles of a triangle (geometry)triangle may be more or less than π radians, and the ratio of a circle's circumference to its diameter may also differ from π. This does not change the definition of π, but it does affect many formulae in which π appears. So, in particular, π is not affected by the shape of the universe; it is not a physical constant but a mathematical constant defined independently of any physical measurements. The reason it occurs so often in physics is simply because it's convenient in many physical models. For example, consider Coulomb's law :

F = \frac   \frac

. Here, !4''πr''²? is just the surface area of sphere of radius ''r''. In this form, it is a convenient way of describing the inverse square relationship of the force at a distance ''r'' from a point source. It would of course be possible to describe this law in other, but less convenient ways, or in some cases more convenient. If Planck charge is used, it can be written as:

F = \frac

and thus eliminate the need for π.

Fictional references -

''Contact (novel)Contact'' -- Carl SaganCarl Sagan's science fiction work. Sagan contemplates the possibility of finding a signature embedded in the Positional notationbase-11 expansion of Pi by the creators of the universe.

''Pi (film)π (film)'' -- On the relationship between numbers and nature: finding one without being a numerologist.

''Time's Eye'' -- science fiction by Arthur C. Clarke and Stephen Baxter. In a world restructured by alien forces, a spherical device is observed whose circumference to diameter ratio appears to be an exact integer 3 across all planes. It is the first book in The Time Odyssey series.

''The Simpsons'' -- "Pi is exactly 3!" was an announcement used by Professor Frink to gain the full attention of a hall full of scientists.

''Going Postal'' -- fantasy novel by Terry Pratchett. Famous inventor Bloody Stupid Johnson invents an organ/mail sorter that contains a wheel for which pi is exactly 3. This "New Pie" starts a chain of events that leads to the failure of the Ankh-Morpork Post Office (and possibly the destruction of the Universe all in one go.)

π culture - There is an entire field of humorous yet serious study that involves the use of mnemonic techniques to remember the digits of π, which is known as piphilology. See :q:English_mnemonics#PiPi mnemonics for examples.March 14 (3/14 in US date format) marks Pi Day which is celebrated by many lovers of π. On July 22, Pi Approximation Day is celebrated (22/7 - in European date format - is a popular approximation of π).In the early hours of Saturday 2 July, 2005, a JapanJapanese mental health counsellor, Akira Haraguchi, 59, managed to recite π's first 83,431 decimal places from memory, thus breaking the standing world record news.bbc.co.uk.355/113 (~3.1415929) is sometimes jokingly referred to as "not π, but an incredible simulation!"

See also -

List of topics related to pi

Pi (letter)Greek letter pi

Calculus

Geometry

Trigonometric function

Pi through experiment

Lindemann-Weierstrass theoremProof that π is transcendental

Proof that 22 over 7 exceeds πA simple proof that 22/7 exceeds π

Feynman point

Pi Day

Lucy Tuning

Cadaeic Cadenza

References -

Petr Beckmann, ''A History of Pi''

External links -

Digit resources -

gutenberg.net - Project Gutenberg E-Text containing a million digits of Pi

!3.1415926535897932384626433832 795028841971693993751058209749 44592.com - Pi to a million places

solidz.com - Archives of Pi calculated to 1,000,000 or 10,000,000 places.

pisearch.de.vu - Search π – search and print π's digits (up to 3.2 billion places)

super-computing.org - Statistics about the first 1.2 trillion digits of Pi

3.14.maxg.org - A banner of approximately 220 million digits of pi

Calculation -

projectpi.sourceforge.net - Calculating Pi: The open source project for calculating Pi.

backpi.sourceforge.net - Background Pi: An open source project for calculating Pi over many computers. (Inspired by "Calulating Pi", Above)

!numbers.computation.free.fr - PiFast: a fast program for calculating Pi with a large number of digits

cecm.sfu.ca - PiHex Project

!files.extremeoverclocking.com< /a> - Super Pi: Another program to calculate Pi to the 33.55 millionth digit. Also used a benchmark

pislice.com - PiSlice: A distributed computing project to calculate Pi

wikisource:Calculating the digits of piCalculating the digits of π using generalised continued fractions - open source Python programming languagePython code

General -

!www-history.mcs.st-andrews.ac. uk - J J O'Connor and E F Robertson: ''A history of Pi''. Mac Tutor project

!machination.mysite.freeserve.c om - A collection of Machin-type formulas for Pi

lrz-muenchen.de - A proof that Pi Is Irrational

joyofpi.com - PiFacts-Record Broken

joyofpi.com - The Joy of Pi-About the Book

mathworld.wolfram.com - From the Wolfram Mathematics site lots of formulae for π

pisymphony.com - Pi Symphony : An orchestral work by Lars Erickson based on the digits of pi and 'e'.

planetmath.org - PlanetMath: Pi

groups.yahoo.com - The pi-hacks Yahoo! Group

mathforum.org - Finding the value of Pi

cf.geocities.com - Proof that Pi exists

pi314.at - Friends of Pi Club ''(German and English)''

cut-the-knot.org - Determination of Pi

lucytune.co.uk - LucyTuning - musical tuning derived from Pi

dse.webonastick.com - The Pi Is Rational Page

Mnemonics -

users.aol.com - One of the more popular mnemonic devices for remembering pi

? cilea.it - Andreas P. Hatzipolakis: ''PiPhilology''. A site with hundreds of examples of π mnemonics

!startfromhere.freeserve.co.uk< /a> - Pi memorised as poetry

archivestowearpantsto.com - First fifty digits of Pi, memorised as a humorous song

bangalore.sancharnet.in - Phrase to easily remember upto 8 decimal places of the value of Pi (See Item #3 on page)

brianbondy.com - Free software to help memorise PiCategory:Transcendental numbersCategory:Mathematical constantsCategory:Famous numbers!3.1416Category:Pibg:Пиca:Nom bre? πda:Pi (tal)de:KreiszahlLink FAde et:Piials:Pies:Pi (geometría)eo:Pifa:عدد پیfi:Pii (vakio)fr:Pigl:Número piko:원주율id:Piis:Πit:Pi grecohe:פאיLink FAhe jv:Pilt:Pimr:'पाय' (π) अव्यय राशीnl:Pi !(wiskunde)ja:円周率pl:Pipt: Piru:Пиsco:Pisimple:Pisk:Lud olfovo? číslosl:Pisr:Пиsv:Pi (tal)th:ไพvi:Pitr:Pi sayısıuk:Число піzh:圓周率

Websites

Homotiller Media
Home page that accompanies 'zine of the same name. Music reviews, interviews, art, writing, things to see and do while documenting decline of the greatest nation in the world: The United States of America.
http://homotillermedia.com

Omniscient Investigations
Timely, thorough & cost-effective investigations doggedly pursued with intellectual rigor. Specializing in criminal defense, civil litigation and claims investigations. We also perform commercial & background investigations as well as process service. Covering all of Western New York State. Licensed, bonded & insured.
http://www.omniscientinvestigations.com/

Vincent Calvino P.I. Series by Christopher G. Moore
Intelligent and articulate, Moore offers a rich, passionate and original take on the private eye game [that] fans of the genre should definitely investigate, and that fans of foreign intrigue will definitely enjoy. --Kevin Burton Smith, January Magazine Christopher G. Moore's Vincent Clavino P.I. Series began with the first novel set in Bangkok Spirit House in 1992. The 3rd Calvino novel Zero Hour in Phnom Penh won the German Critics Award for Crime Fiction (Deutscher Krimi Preis) for best international crime fiction in 2004. The latest in this on-going series is Pattaya 24/7 (No. 8). Calvino novels have been translated into several languages, including French, German, Italian, Chinese, Japanese, Norwegian and Thai. Vincent Calvino is a likeable ex-lawyer from New York who's given up practice to turn P.I. in Southeast Asia, where he finds himself in the labyrinth of local politics, double-dealing and fleeting relationships. Unlike typical tough-guy sleuths, Calvino admits he would never survive without his guardian angel, his Shakespear-quoting and saxophone-playing buddy, Colonel Pratt, an honest and well-connected Thai cop who helps him find hidden forces, secret traps and ways to keep him alive in a foreign land. The Vincent Calvino P.I. series has drawn comparisons to literary masters. January Magazine said, Moore's work recalls the international 'entertainments' of Graham Greene or John le Carre, but the hard-bitten worldview and the cynical, bruised idealism of his battered hero is right out of Chandler. Japan Times described Calvino as: Hewn from the hard-boiled Dashiell Hammet/Raymond Chandler model, Calvino is a tough, somewhat tarnished hero with a heart of gold.
http://www.vincentcalvino.com/

Bible Numerics
The Study Bible Mathematics.Creation Evolution. The death blow to the Da Vinci Code
http://www.biblemaths.com/

CECM
Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
http://www.cecm.sfu.ca/

Groups, Algorithms and Programming
Group at the University of St. Andrews developing GAP, a free system for computational discrete algebra.
http://www-gap.dcs.st-and.ac.uk/

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