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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 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?
Egyptian Fractions
David Eppstein has collected and implemented several algorithms for constructing Egyptian fractions and includes some other notes and WWW links on the subject.
Egyptian mathematics Discussion of the Egyptian number system.
Egyptian Multiplication Jim Loy discusses the method that Eqyptians used to multiply two numbers.
Egyptian Numerals
Discussion of the Egyptian number system including pi.
Favorite Mathematical Constants
All numbers are not created equal; that certain constants appear at all and then echo throughout mathematics, in seemingly independent ways, is a source of fascination. Just as physical constants provide "boundary conditions" for the physical universe, mathematical constants somehow characterize the structure of mathematics.
Fermat Project
Images used in a popularized introduction to Fermat's Last Theorem, a famous recently solved problem in number theory. Three dimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical ideas involved. The second half of the film makes a transition to show a remarkable family of four dimensional surfaces related to Fermat's theorem, and projects them to three dimensions for display using standard rendering and shading techniques.
The Fibonacci Numbers
This page is a directory of material related to the Fibonacci numbers.
Fun with PI
This page contains some methods to calculate PI to a lot of decimals. It also contains some programs you can use to try it yourself, all of these programs were written and tested on my home LINUX-system. I used one of the programs on this page to calculate 100 decimals of PI. (It took 12 hours on my Pentium-60!) If you are really interested, you can get the file that contains all the decimals here.
The Great Internet Mersenne Prime Search
Join over 6000 of your fellow number theory enthusiasts in the search for new Mersenne primes. The Great Internet Mersenne Prime Search (GIMPS) harnesses the power of thousands of small computers like yours to solve the seemingly intractable problem of finding HUGE prime numbers.
Inverse Symbolic Calculator
The ISC is the Inverse Symbolic Calculator, a set of programs and specialized tables of mathematical constants dedicated to the identification of real numbers. It also serves as a way to produce identities with functions and real numbers. It is one of the main projects presently ongoing at the CECM.
Irrationality proofs
Proofs that e, log(2) and pi are irrational are given.
Largest Known Primes
This page from the University of Tennessee, Martin, contains links to other sites containing information on prime numbers and also contains information on finding large primes and how to prove such numbers are prime.
Marin Mersenne
Luther Welsh has collected biographies and other information about Marin Mersenne
and his work including many links to other WWW sites which information on Mersenne Primes. He has also collected a bibliography on Mersenne Numbers & Primes.
Math Pages - Number Theory Section
This site contains over 300 short articles on a variety of mathematical topics, including number theory, etc. This section has articles on Limit Cycles of xy (mod x+y), Squares in Arithmetic Progression (mod p), etc.
Mathematical constants and computation
This site contains information on the computation and the algorithms 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 the Mayans' counting system.
The Miraculous Bailey-Borwein-Plouffe Pi Algorithm
David Bailey, Peter Borwein and Simon Plouffe have recently computed the ten billionth digit in the hexadecimal expansion of pi. They utilized an astonishing formula which enables one to calculate the dth digit of pi without being forced to calculate all the preceding d-1 digits.
Number-Theoretic Hacks
David Eppstein has implemented a number of simple number-theoretic algorithms for his own amusement, and provide them here on the net. Topics include Egyptian Fractions, J.H.Conway's "nimber" arithmetic, C++ fast algorithm for computing 2-adic inverse, C program for rational approximation of real numbers, etc.
Number theory: Perfect, amicable and sociable numbers.
Information on numbers given in title together with lists of these numbers. Also included is a bibliography on amicable pairs and some information on aliquot cycles.
Numbers from 1 to 10 in Over 2000 Languages einn, tveir, thrr, fjriri, ... (Old Norse for 1, 2, 3,...) etc.
This is a mock-up of an interactive display that will be used to test the concept (and level of interest in) a number museum. Includes information on various topics as perfect numbers, prime numbers, Pythagorean triples, pi, and Fermat's Last Theorem.
The PI Page
What is a reasonable way to compute Pi?
PI Mathematics
PI Mathematics, a collaborative project, using the concept of PI as the focus, is a on the WWW. This multidisciplinary project which includes math, history, English and thinking skills is designed for fifth through eighth graders. It will allow students to discover the approximate value of PI, an irrational number, using measurement and reporting the data, applying formulas, problem solving and participating in a collaborative project utilizing Internet resources. Students will also explore the history of PI, using Internet references.
Plouffe's inverter
Table of current records for the computation of constants including pi, 1/pi, e, Catalan, Zeta(3), log(2), golden ratio, and the sqaure root of 2.
Prime Curios Have you met a nice number recently? We have! "Prime Curios!" is an exciting collection of prime number curiosities, integer wonders, amusing factorizations, and surprising trivia.
Prime k-tuplets
A prime k-tuplet is a sequence of consecutive prime numbers {p1, p2, ..., pk} such that, in some sense, pk - p1 is as small as possible.
Prime Numbers
These pages were written as an experiment to aid students to better understand proofs of theorems. From an email message: It seems to me that one of the main difficulties that students of (higher) matematics encounter stems from the insistence on getting all the logical prerequiesites set up before trying to explain anything interesting. (Of course, this style of presentation goes back at least as far as Euclid.) Hypertext should make it possible to explain the ideas behind a proof before writing down the proof formally, and it should also allow you to link to the lemmas so that they can be read only as needed when trying to understand more details in a proof.
The Prime Puzzles and Problems Connection
Our main purpose is to create an anthology of the most interesting problems & puzzles explicitly related to primes.
Pythagorean Triples
How to construct Pythagorean triples.
A Question of Numbers
An article in the January-February 1996 issue of the American Scientist.
Recreational Topics from the Theory of Numbers
Contains information on palindromic triangulars, palindromic squares, circular primes and palindromic primes.
RJN's More Digits of Irrational Numbers Page
The first 10 million(!) digits of e, the first 10 million digits of the square root of 2, etc.
Roman Numerals How do you add and divide with Roman numerals? Check out these pages.
Sci.Math FAQ - Sections on Numbers
Search In 10 Million Digits of Pi Page
This page provides you with a form to scan for an arbitrary decimal pattern in the first 10 million digits of PI.
Some numbers from Robert Joseph Harley
Includes the only known factor of the generalized Fermat number 10^1024+1, some small prime factors of googolplex+1, information on twin primes, sums-of-inverses-of-primes, etc.
The 3x+1 Problem and its Generalizations
A WWW version of Jeff Lagarias' paper which originally appeared in the American Mathematical Monthly (Volume 92, 1985, 3 - 23). Includes a number of Maple codes to illustrate the concepts.
Topics in Mathematics - Number Theory
This is the Number Theory section of the Mathematics Archives' Topics in Mathematics which contains links to various WWW sites which contain information about Number Theory.
Tout L'Univers de Pi et de Pi-Phénomènes!
This French site contains all the information which wyou will ever need to know about the number pi. The history, mathematicians who have used pi, formulas for pi, etc. are provided.
Useless Facts about Pi
If useless, why bother? But do check out this site!
Vampire Numbers No, it's not a joke. These sinister beasts really do lurk amongst millions of unsuspecting, innocent integers. However, their existence was not made public until 1995 when Clifford Pickover wrote a Brain Boggler for Discover magazine entitled "Interview with a Number." Since then, hundreds of people have been bitten by the vampire number.
When does 1 = 2?
Here are some examples from the newsgroup sci.math. Other examples are available from the University of Toronto.
A German website on prime numbers.
and other stories
Culturally, our discomfort with the concepts of zero (and infinite) is reflected in such humor as 2 plus 0 still equals 2, even for large values, and popular retorts of similar tone. See this site for similar statements about zero and infinity.