21. Math Surprises Buffon's Needle simulation and a surprising demonstration of Barbier's theorem about shapes of constant width http://www.cut-the-knot.com/ctk/August2001.html

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Cut The Knot! An interactive column using Java applets by Alex Bogomolny Math Surprises: An Example August 2001 Compte de Buffon (1707-1788) in the 18 th century posed and solved the very first problem of geometric probability. A needle of a given length L is tossed on a wooden floor with evenly spaced cracks, distance D apart. What is the probability of the needle hitting a crack? The answer he discovered with the help of integral calculus is given by the simple formula [ Beckmann Eves Kasner Paulos ... Stein P = 2L/ p D With P approximated by the ratio of hits to the total number of tosses, the formula offers a way of evaluating p , an observation that eventually led Pierre Simon Laplace (1749-1827) to propose a method, known today as the Monte Carlo Method, for numerical evaluation of various quantities by realizing appropriate random events. History records several names of people who applied the method manually to approximate p . A Captain Fox [ Beckmann , p. 77] mentions Wolf from Zurich (1850) who obtained

22. Karsten Grosse-Brauckmann: Research Differential geometry, especially surfaces of constant mean curvature. http://www.math.uni-bonn.de/people/kgb/Research/research.html

www.math.uni-bonn.de/people/kgb/research.html K. Grosse-Brauckmann: Research Projects Much of my research is devoted to constant mean curvature (cmc) surfaces, in particular the construction of examples. Constant mean curvature surfaces appear in nature, in particular when the area of an interface is minimized under a volume constraint. Soap bubbles are the most popular example: The photos show Tom Noddy at the International Congress 1998 (courtesy of J. Sullivan ). Mathematicians have used the following methods to construct constant mean curvature surfaces: Kapouleas produced surfaces close to some degenerate well known surfaces with a singular perturbation approach; Pinkall, Sterling, and many others found tori as solutions of an integrable system (a more general approach by Dorfmeister, Pedit and Wu remains to be exploited); and the Lawson-Karcher conjugate cousin method yields sufficiently symmetric surfaces. Moduli Spaces of Embedded Constant Mean Curvature Surfaces with Finite Topology In this current project, which is joint with

23. 112 Pieces Of Pi Images and illustrations created by using the digits of the circle constant. http://www.antigravitypress.com/Math/pi/

While studying Pi with Gillian, Gareth, and Zaamen, my math group from Tracy's class at Metropolitan Learning Center, I started to generate images with the digits of Pi. Four examples are presented here. In this version, a color value is assigned to each of the digits 0-9 to make this pretty picture. Thanks to David Blatner for his book and website The Joy of Pi for 112 digits of Pi. Now, would anyone like more Pi

24. Mathcad Library: Constants References for Euler s constant, g. RM Young, Euler s constant, math. DW Sweeney, On the computation of Euler s constant, math. Comp. http://www.mathcad.com/library/Constants/eulerrefs.htm

Well-Known Constants Pythagoras' Golden mean Natural log Archimedes' ... Home by Steven Finch Mathsoft Engineering and Education, Inc. References for Euler's Constant, g R. M. Young, Euler's constant, Math. Gazette v. 75, n. 472 (1991) 187-190. R. P. Boas, Partial sums of infinite series, and how they grow, Amer. Math. Monthly MR 55 #13118 D. E. Knuth, Euler's constant to 1271 places, Math. Comp. MR 26 #5763 J. M. Borwein and P. B. Borwein, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity , Wiley, 1987; MR 99h:11147 D. W. Sweeney, On the computation of Euler's constant, Math. Comp. 17 (1963) 170-178; corrigenda 17 (1963) 488; MR 28 #3522 R. P. Brent, Computation of the regular continued fraction for Euler's constant, Math. Comp. MR 55 #9490 R. P. Brent and E. M. McMillan, Some new algorithms for high-precision computation of Euler's constant, Math. Comp. MR 82g:10002 D. W. DeTemple, A quicker convergence to Euler's constant, Amer. Math. Monthly MR 94e:11146 J. Nunemacher, On computing Euler's constant, Math. Mag.

25. Math Forum: Ask Dr. Math FAQ: About Pi Explains what the constant is and a brief history. Includes resource links. http://mathforum.org/dr.math/faq/faq.pi.html

Ask Dr. Math: FAQ A bout Pi Dr. Math FAQ Classic Problems Formulas Search Dr. Math ... Dr. Math Home What is pi ( )? Who first used pi? How do you find its value? What is it for? How many digits is it? By definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it. For the sake of usefulness people often need to approximate pi. For many purposes you can use 3.14159, which is really pretty good, but if you want a better approximation you can use a computer to get it. Here's pi to many more digits: 3.14159265358979323846. The area of a circle is pi times the square of the length of the radius, or "pi r squared": A = pi*r^2 A very brief history of pi Pi is a very old number. We know that the Egyptians and the Babylonians knew about the existence of the constant ratio pi, although they didn't know its value nearly as well as we do today. They had figured out that it was a little bigger than 3; the Babylonians had an approximation of 3 1/8 (3.125), and the Egyptians had a somewhat worse approximation of 4*(8/9)^2 (about 3.160484), which is slightly less accurate and much harder to work with. For more, see A History of Pi by Petr Beckman (Dorset Press).

26. RealCities.com | 08/28/2002 | Overall SAT Scores Remain Constant; Math Up Slight Overall SAT scores remain constant; math up slightly, verbal down Gaston Caperton, the College Board president, noted math scores have increased by 15 points over the past 10 years http://www.tallahassee.com/mld/tallahassee/3947876.htm

Search: Articles-last 7 days Articles-older than 7 days The Web for News Business Sports Entertainment ... Homes var request_url = escape(document.location.href); var request_domain = ".tallahassee.com"; Jobs Search List Cars ... Weather Tallahassee Miami Tampa Local Events Yellow Pages Discussion Boards AP HEADLINES Updated Sunday, Jun 06, 2004 Reagan Honed Message, Skills in Calif. - 02:53 AM EDT Roadside Bomb Kills 2 Soldiers in Iraq - 02:50 AM EDT Landslide Buries Part of Village in China - 02:47 AM EDT 1999 Reagan Biography Sparked Controversy - 02:47 AM EDT Former President Ronald Reagan Dies at 93 - 02:42 AM EDT MORE Great schools Before choosing a place to live, do your homework! Review public, private and charter school performance before you decide. Search schools Back to Home Sunday, Jun 06, 2004 email this print this Posted on Wed, Aug. 28, 2002 Overall SAT scores remain constant; math up slightly, verbal down By STEVE GIEGERICH Associated Press SAT scores for the high school class of 2002 were even with last year's graduates, as a two-point increase in math proficiency was offset by a two-point decrease on the language portion of the college entrance test. Figures released Tuesday by the College Board, the New York-based nonprofit which owns the SAT, reflect a cumulative score of 1,020 - identical to the average achieved by the class of 2001.

27. Mathematical Constants Subject Re How did we come by e? From Matthew P Wiener Date 1998/08/12 Newsgroups sci.math http://pauillac.inria.fr/algo/bsolve/constant/e/wiener.html

Mathematical Constants by Steven R. Finch Clay Mathematics Institute Book Fellow My website is smaller than it once was. Please visit again, however, since new materials will continue to appear occasionally. It's best to look ahead to the future and not to dwell on the past. * My book Mathematical Constants is now available for online purchase from Cambridge University Press (in the United Kingdom and in North America ). It is far more encompassing and detailed than my website ever was. It is also lovingly edited and beautifully produced - many thanks to Cambridge! - please support us in our publishing venture. Thank you. (If you wish, see the front cover and some reviews Here are errata and addenda to the book (last updated 5/25/2004), as well sample essays from the book about integer compositions optimal stopping and Reuleaux triangles . Here also are recent supplementary materials, organized by topic: Number Theory and Combinatorics Bipartite, k-colorable and k-colored graphs Transitive relations, topologies and partial orders Series-parallel networks Multiples and divisors ... Two asymptotic series (in progress) Shapes of binary trees Tauberian constants Integer partitions Planar graph growth constants Class number theory Inequalities and Approximation Hardy-Littlewood maximal inequalities Bessel function zeroes Nash's inequality Uncertainty inequalities Constant of interpolation Real and Complex Analysis Radii in geometric function theory Numerical radii of linear operators Probability and Stochastic Processes

28. RealCities.com | 08/28/2002 | Overall SAT Scores Remain Constant; Math Up Slight Overall SAT scores remain constant; math up slightly, verbal down Gaston Caperton, the College Board president, noted math scores have increased by 15 points over the past 10 years http://www.ledger-enquirer.com/mld/ledgerenquirer/3947876.htm

Search: Articles-last 7 days Articles-older than 7 days The Web for News Business Sports Entertainment ... Homes var request_url = escape(document.location.href); var request_domain = ".ledger-enquirer.com"; Jobs Search List Cars ... Weather Columbus Macon Washington DC Local Events Yellow Pages Discussion Boards SPECIAL SECTIONS Active Times Gateway Gazette Going Places Golf Guide ... Back to Home Sunday, Jun 06, 2004 email this print this Posted on Wed, Aug. 28, 2002 Overall SAT scores remain constant; math up slightly, verbal down By STEVE GIEGERICH Associated Press SAT scores for the high school class of 2002 were even with last year's graduates, as a two-point increase in math proficiency was offset by a two-point decrease on the language portion of the college entrance test. Figures released Tuesday by the College Board, the New York-based nonprofit which owns the SAT, reflect a cumulative score of 1,020 - identical to the average achieved by the class of 2001. Test-takers averaged 504 on the verbal segment of the test and 516 on the math section. Gaston Caperton, the College Board president, noted math scores have increased by 15 points over the past 10 years, and attributed the gain to a renewed emphasis on mathematics in the nation's high schools. The College Board said 45 percent of this year's high school seniors took precalculus, compared to 12 percent in 1992.

29. EXSLT - Math:constant - Implementer Page Version 1 Status implemented User Page index.html XML Definition math.constant.xml Function Package math.constant.zip. Function Syntax. http://www.exslt.org/math/functions/constant/math.constant.html

EXSLT math constant - Implementer Page User Page How To Downloads Modules Dates and Times Dynamic Common Functions ... Contact Version: Status: implemented User Page: index.html XML Definition: math.constant.xml Function Package: math.constant.zip Function Syntax number math:constant string number Template Syntax math:constant string number The math:constant function returns the specified constant to a set precision. The possible constants are: PI E An implementation of this extension function in the EXSLT math namespace must conform to the behaviour described in this document. Implementations Built-in support for math:constant is available in the following XSLT processors: Processor Processor Version Implemented Version 4XSLT, from 4Suite. libxslt from Daniel Veillard et al. The following implementations of math:constant are available: Language Implemented Version Creator Date Download XSLT Template James Fuller math.constant.template.xsl Javascript ... math.constant.function.xsl Change History Submitted: Creator: James Fuller http://www.ruminate.co.uk

30. Is The Speed Of Light Constant? Original by Philip Gibbs 1996. Is The Speed of Light constant? This quantity is also referred to as c. Is c, the speed of light in vacuum, constant? http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.htm

[Physics FAQ] Updated 1997 by Steve Carlip. Original by Philip Gibbs 1996. Is The Speed of Light Constant? There are a number of senses to the meaning of this question and so there are a number of different answers. Firstly . . . Does the speed of light change in air or water? Yes. Light is slowed down in transparent media such as air, water and glass. The ratio by which it is slowed is called the refractive index of the medium and is always greater than one. This was discovered by Jean Foucault in 1850. When people talk about "the speed of light" in a general context, they usually mean the speed of light in a vacuum. This quantity is also referred to as c Is c , the speed of light in vacuum, constant? At the 1983 Conference Generale des Poids et Mesures , the following SI (Systeme International) definition of the metre was adopted: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is

31. On-line Month. Comm. May-2002. Cydonia Math-constant. By Angel Garcia Online month. comm. may-2002. Cydonia math-constant. by Angel Garcia. Subject On-line month. comm. may-2002. Cydonia math-constant. http://mathforum.org/epigone/sci.math.num-analysis/streldplimpshah

On-line month. comm. may-2002. Cydonia math-constant. by Angel Garcia reply to this message post a message on a new topic Back to sci.math.num-analysis Subject: On-line month. comm. may-2002. Cydonia math-constant. Author: bp887@FreeNet.Carleton.CA Organization: The National Capital FreeNet Date: 25 May 2002 13:26:57 GMT Cydonia was primarily designed as Monument to Mathematics; to plainly say how old martian civilization was, by displaying 'irrational conundrums' which cannot be derived except by extremely long experience with computer-science: probably multi-million years collecting data from recreational mathematics. The three most fundamental 'irrational' math. constants are associated in Cydonia with a string of conundrums in chained trivial Geometry. No current terrestrial experts can come close to such cydonian conundrums with current experience in computer science: http://www.geocities.com/Eureka/Concourse/9460/may02.html and also in my URL down below. Angel, secretary of Universitas Americae (UNIAM). His proof of ETI at Cydonia and index of book "TETET-98: Generacion del Hombre en Marte" by Prof. Dr. D.G. Lahoz (leader on ETI and Cosmogony) can be studied at URL: http://www.ncf.carleton.ca/~bp887

32. Math Tools Discussion Subject math fact memorization .constant time delay? Author jhays. Date Nov 19, 2003. I have students in the 8th and 9th grade http://mathforum.org/mathtools/discuss.html?do=r&msg=_____round-43.2.1.2

33. GSL-- Pre-0.5 - Math/constant.hh File Reference Author Christian Holm Date Wed Mar 12 152419 2003. include gsl/gsl_math.h . Include dependency graph for math/constant.hh Namespaces. namespace, gslmm. http://cholm.home.cern.ch/cholm/misc/gslmm/math_2constant_8hh.html

Examples Modules Namespaces Hierarchy ... GSL homepage constant.hh File Reference Detailed Description Mathematical constants. Author: Christian Holm Date: Wed Mar 12 15:24:19 2003 Include dependency graph for math/constant.hh: Namespaces namespace gslmm Top of page Last update Wed Jun 2 13:52:32 2004 Christian Holm Created by DoxyGen 1.3.7

34. GSL-- Pre-0.5 - Gslmm::constant Struct Reference constants. include gslmm/math/constant.hh The documentation for this struct was generated from the following file math/constant.hh. Top http://cholm.home.cern.ch/cholm/misc/gslmm/structgslmm_1_1constant.html

Examples Modules Namespaces Hierarchy ... GSL homepage gslmm::constant Struct Reference Physical Constants Collaboration diagram for gslmm::constant: legend List of all members. Detailed Description Mathematical contants. Static Public Attributes const double e const double const double const double const double const double const double pi const double const double const double const double const double const double const double const double const double const double euler const double const double const double Member Data Documentation const double gslmm::constant::e [static] The base of exponentials, const double gslmm::constant::euler [static] Euler's static constant, const double gslmm::constant::half_of_pi [static] divided by two, const double gslmm::constant::log10_of_e [static] The base-10 logarithm of e, const double gslmm::constant::log2_of_e [static] The base-2 logarithm of e, const double gslmm::constant::log_of_10 [static] The natural logarithm of ten, const double gslmm::constant::log_of_2 [static] The natural logarithm of two, const double gslmm::constant::log_of_pi [static] The natural logarithm of const double gslmm::constant::minus_infinity [static] Positive infinity

35. 1 Introduction 10 RP Brent, Computation of the regular continued fraction for Euler s constant, math. 34, p. 305312. 13 RM Young, Euler s constant, math. http://numbers.computation.free.fr/Constants/Gamma/gamma.html

The Euler constant : g g (Postcript version of this page : gamma.ps , pdf version : gamma.pdf . Versions of Formulas on the Euler constant are also available : gammaFormulas.ps gammaFormulas.pdf Introduction Euler's Constant was first introduced by Leonhard Euler (1707-1783) in 1734 as g lim n n log(n) It is also known as the Euler-Mascheroni constant . According to Glaisher [ ], the use of the symbol g is probably due to the geometer Lorenzo Mascheroni (1750-1800) who used it in 1790 while Euler used the letter C. The constant g is deeply related to the Gamma function G (x) thanks to the Weierstrass formula G (x) =xexp( g x) x n exp x n This identity entails the relation G g It is not known if g is an irrational or a transcendental number. The question of its irrationality has challenged mathematicians since Euler and remains a famous unresolved problem. By computing a large number of digits of g and using continued fraction expansion, it has been shown that if g is a rational number p/q then the denominator q must have at least 242080 digits. Even if g is less famous than the constants p and e, it deserves a great attention since it plays an important role in

36. E -- From MathWorld search. Bailey, D. H. Numerical Results on the Transcendence of constants Involving , e, and Euler s constant. math. Comput. 50, 275281, 1988. http://mathworld.wolfram.com/e.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Number Theory Constants e e The constant e is base of the natural logarithm , whose symbol honors Euler This means that e is the unique number with the property that the area of the region bounded by the hyperbola the x -axis , and the vertical lines x = 1 and x = e is 1. In other words, With the possible exception of e is the most important constant in mathematics since it appears in myriad mathematical contexts involving limits and derivatives . The numerical value of e is (Sloane's e can be defined by the limit (illustrated above), or by the infinite series as first published by Newton (1669; reprinted in Whitehead 1968, p. 225). e also has a surprising connection with the product-of-primes primorial function, and is given by the unusual limit (Brothers and Knox 1998).

37. Euler-Mascheroni Constant -- From MathWorld Bailey, D. H. Numerical Results on the Transcendence of constants Involving , e, and Euler s constant. math. Comput. Young, R. M. Euler s constant. math. http://mathworld.wolfram.com/Euler-MascheroniConstant.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Mathematical Problems Unsolved Problems ... Stingley Euler-Mascheroni Constant The Euler-Mascheroni constant, denoted (or sometimes C ), is defined by the series where is a harmonic number (Graham et al. 1994, p. 278; originally due to Euler). has the numerical value (Sloane's ), and is implemented in Mathematica as EulerGamma The Euler-Mascheroni constant was denoted and calculated to 16 digits by Euler in 1781. It is therefore sometimes known as Euler's constant. No quadratically converging algorithm for computing is known (Bailey 1988). X. Gourdon and P. Demichel computed a record 108 million digits of in October 1999 (Gourdon and Sebah). It is not known if this constant is irrational , let alone transcendental (Wells 1986, p. 28). The famous English mathematician

38. Colby Community College Mathematics Department Information And Math Tables, Form GAMMA constant. gamma = = 0.5772156649 0153286061 Summary A collection of math related tables, facts, information and formulas http://colbycc.edu/www/math/constants/gamma.htm

GAMMA Constant gamma = = lim ( 1 + 1/2 + 1/3 + 1/4 + ... + 1/n - ln(n) ) = 0.5772156649... e ^-x ln x dx (see Gamma Function Summary: A collection of math related tables, facts, information and formulas ... with the main title and index page located at: http://www.colbycc.org/www/math/math.htm . These pages are maintained by Colby Community College and the Colby Community College Mathematics Department. If you have any comments, suggestions or a page that you've constructed (that you believe would be valuable and appropriate to include on/in/at our math site), please contact our CCC Math Department Faculty Page Keywords: Mathematics, Mathematic, Mathematical, Math, Mathematically, Reference, Table, Tables, Formula, Formulas, Fact, Facts, Information, Data, Computation, Computational, Algebra, Geometry, Trigonometry, Trig, Analysis, Calculus, Calc, Addition, Subtraction, Multiplication, Division, Powers, Roots, Exponents, Identities, Chart, Graph, List, Java, On-line, Games, Puzzles, Listing, Equations, Equation, Graphs, Graph, Conversions, Convert, Number, Numerical, Factorial, Sequence, Series, Conic, Integral, Differential, Mensuration, Measure, Function, Statistics, Stat, Math Reference.

39. Mathematics Archives - Numbers for the computation of various numbers including pi, e, log(2), the square root of 2, Euler s constant gamma and Apery s constant. Mayan math, Information on http://archives.math.utk.edu/subjects/numbers.html

Numbers Facts about the number 17: 17 in history, computing, astronomy, etc. The 47 Society The 47 Society is an international interest-group that follows the occurence and recurrence of the quintessential random number: 47. Many suspect that the coinciential nature of 47 carries some mystical, metaphysical and/or scientific significance. What is special about the number 73939133? Aesthetics of the Prime Sequence Hear and see the prime numbers! A Common Book of p The number p has been the subject of a great deal of mathematical (and popular) folklore. It's been worshipped, maligned, and misunderstood. Overestimated, underestimated, and legislated. Of interest to scholars, crackpots, and everyday people. Continued Fractions A senior Honor's Project at Calvin College by Adam Van Tuyl which gives the history, theory, applications and bibliography on the thery of continued fractions. In the section on applications there are a number of interactive programs that convert rationals (or quadratic irrationals) into a simple continued fraction, as well as the converse. Data Powers of Ten A petabyte?

40. Mathematics Archives - Topics In Mathematics - Number Theory Number Theory Section of sci.math FAQ ADD. On a Generalized FermatWiles Equation ADD. KEYWORDS Landau-Ramanujan constant, mathcad, abc-conjecture; http://archives.math.utk.edu/topics/numberTheory.html

Topics in Mathematics Number Theory Absolute Primes ADD. KEYWORDS: Article, Repunits SOURCE: Arkadii Slinko, University of Auckland and Mathematics Olympiad Learning Centre TECHNOLOGY: Adobe Acrobat Reader Aesthetics of the Prime Sequence Algorithmic Number Theory - Bibliography AMS - Fermat's Last Theorem ADD. KEYWORDS: Number theory, Fermat's Last Theorem, History, Reports, Articles AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases Arithmetic properties of Binomial Coefficients ADD. KEYWORDS: Elementary Number Theory, Lucas' Theorem, Pascal's triangle via cellular automata, Bernoulli numbers and polynomials, Theorems of Morley and Emma Lehmer and their generalizations, Some useful p-adic numbers Bernoulli (Beta) and Integer Part Sequences ADD. KEYWORDS: Article SOURCE: Rod Nillsen, Keith Tognetti and Graham Winley, University of Wollongong TECHNOLOGY: Adobe PDF, Postscript and DVI readers

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