Fibonacci numbers and the golden section in nature, art, geometry, architecture, music and even for calculating pi! Puzzles and investigations.

Fibonacci numbers and the golden section in nature, art, geometry, architecture, music and even for calculating pi! Puzzles and investigations.

This website aims to show that there are many constants in mathematics other than just e and pi!

The Natural Logarithmic Base It is not known who first determined We see in this limit the outcome of a fierce tug-of-war. On one side, the exponent explodes to infinity. On the other side, 1+x rushes toward the multiplicative identity 1. It's interesting that the additive equivalent of the above limit is trivial. A geometric characterization of e is as follows: e is the unique positive root x ...

The Golden Mean We start with a problem in aesthetics. Consider the following line segment _________________________________ What is the most pleasing division of this line segment into two parts Some people might say at the halfway point: _________________.________________ Others might say at the one-quarter or three-quarters point. The correct answer is, however, none of these, and is found ...

Archimedes' Constant Much more scholarly expositions concerning are available, for example, references . Our treatment of this, the most famous of the transcendental constants, is necessarily incomplete. The area enclosed by a circle of radius 1 is while its circumference is The formula for A is based on the definition of area in terms of a Riemann integral, i.e., a limit of Riemann sums. The ...

This website aims to show that there are many constants in mathematics other than just e and pi!

Ask Dr. Math Middle School Archive Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ TOPICS This page: pi Search Dr. Math See also the Dr. Math FAQ: Pi = 3.14159... Internet Library: pi T2T FAQ: pi day MIDDLE SCHOOL About Math Algebra equations factoring expressions graphing equations Arithmetic division exponents factorials factoring numbers ...

A history of Pi A chronology of Pi History Topics Index A little known verse of the Bible reads 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 about. (I Kings 7, 23) The same verse can be found in II Chronicles 4, 2. It occurs in a list of specifications for the great temple ...

The Book * The Author * The Digits * Pi Links * Pi Facts * The Quote The number Pi is Year 2000 Compliant ...

The open source project for calculating Pi.

The Phi-Nest information on the Golden Section, Divine Proportion, Fibonacci series and phi.

666 - THE MARK OF THE BEAST

Detailed overview of the nature of Pi.

Welcome to THE SOCIETY 47 is the quintessential random number. Many have noticed. Many have wondered: why Many more have wondered: so what The 47 society is dedicated to exploring the phenomenon that is 47. Take your time, explore the mystery of 47: thumb through our SEARCHABLE ARCHIVES, PROVOCATIVE LINKS, and IMAGE GALLERY. Draw your own conclusions and share your views: enter our CHAT ROOM ...

Logical and cosmological implications of the concept of infinity ...

In-depth information and mathematical formulas concerning Phi.

Illustrative overview of the concept of infinity.

PRIME NRICH PLUS Coding theory: the first 50 years Mathematics, marriage and finding somewhere to eat Dynamic programming: an introduction Decoding a war time diary The life and numbers of Fibonacci Student interview - Sarah Hudson Career profile - Helen Hewson Recent NRICH Articles Pushing back Pi Cosmos launch The Higher Education Maths Course List for 1998 Primes update: success again! Recent ...

Highly detailed information about the base of the natural logarithm, or e.

Brun's Constant Brun's constant is defined to be the sum of the reciprocals of all twin primes: Note that the prime 5 is taken twice (some authors don't do this). If this series was divergent, then a proof of the Twin Prime Conjecture would follow immediately. Brun proved, however, that the series is convergent and thus B is finite . Brun's result demonstrates the scarcity of twin primes ...

Heilbronn Triangle Constants The nth Heilbronn triangle constant is the smallest number for which the following holds. Given any arrangement of n points in the unit square, there is at least one triangle, formed by three of the points, with an area not exceeding . Goldberg considered the exact values of the first several Heilbronn constants, including and made several conjectures. Yang, Zhang & ...

Googolplex Funny and Imagination-provoking , said the critics once upon a time, and awarded me the Top 5% icon you see here, for being among the top 5 percent of all sites on the Internet. That was in 1995, and all links to their own pages are broken now, but that certificate was never revoked, so I think I can still wear it with pride. But I'm afraid that since their comment on my page has ...

Warning: 666 Is Coming ...

Detailed explanation of the golden mean, or phi.

Overview of the concept of Pi.

Biography and links to information about Archimedes.

Information about the meaning, context, and existence of the concept of infinity.

Ramanujan, Modular Equations, and Approximations to Pi or How to compute One Billion Digits of Pi*** D.H. Bailey NASA Ames Research Center Moffett Field CA 94035 J.M. Borwein and P.B. Borwein Math Dept., Simon Fraser Univ. Burnaby, B.C. V5A 1S6 Canada Mathactivated text Other available formats Related links Author biographies Abstract: This article will follow up one small thread of Ramanujan's ...

World ranking list for people who like to memorize pi and want to see where in the world of memorizers they stand ...

Counting to Infinity The symbol, , has been around for more than two thousand years. The Romans used it to represent 1000, a BIG number to them. About 1650 the English mathematician, John Wallis, proposed that stand for INFINITY, and that stuck. The concept of infinity has tantalized and sometimes troubled mankind even longer. Zeno of Elea (495 BC -425 BC ), an early Greek thinker, is remembered ...

Phi: That Golden Number by Mark Freitag Most people are familiar with the number Pi, since it is one of the most ubiquitous irrational numbers known to man. But, there is another irrational number that has the same propensity for popping up and is not as well known as Pi. This wonderful number is Phi, and it has a tendency to turn up in a great number of places, a few of which will be discussed ...

666, The Number of the Beast Rev 13:16 And he causeth all, both small and great, rich and poor, free and bond, to receive a mark in their right hand, or in their foreheads: Rev 13:17 And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name. Rev 13:18 Here is wisdom. Let him that hath understanding count the number of the beast: for it is ...

Math Forum || K-12 Math Puzzles || Problems of the Week || Student Center For many years mathematicians, scientists, engineers and others interested in mathematics have played year games via e-mail and in newsgroups. We don't always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many ...

FIBONACCI Numbers Formulae You have reached the web pages of RAJESH RAM (maths@nivedh.com). This page contains some of the results that I have found on Fibonacci Numbers. Click here for a Text Version of this page. Click here for my mathematics home page Other Pages : PELL Numbers Formulae , Sums of Powers, FIBONACCI Numbers Formulae, TRIANGLE Numbers that are Perfect Squares, Sums of Cubes, ...

Article about the concept of infinity.

The Number of the Beast Mike Keith The number 666, first made famous by the Book of Revelation (chapter 13, verse 18), has also been studied by mathematicians because of its many interesting properties. Here is a compendium of mathematical facts about the number 666. Most of the well-known chestnuts are included, but many are relatively new and have not been published elsewhere. The number 666 ...

A Common Book of 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679... The mysterious and wonderful is reduced to a gargle that helps computing machines clear their throats. -- Philip J. Davis In recent years, the computation of the expansion of has assumed the role of a standard test of computer integrity. -- David H. Bailey It requires a mere ...

Famous quoatations, essays, thoughts about Pi, in Spanish.

A fascinating article that explains Pi and different ways of calculating Pi!

Golden Rectangle ...

Fibonacci and Lucas Factorizations Below are tables of known factorizations of Fibonacci numbers, Fn, and Lucas numbers, Ln, for n Small tables of Fibonacci factorizations n n (144K) Small tables of Lucas factorizations n n (136K) The first composite holes are at F851 and L842. Composite factors are indicated by (C) following the factor. The compact big tables Format of tables Fibonacci (223K) ...

A Math Forum Project Math Forum || K-12 Math Puzzles || Problems of the Week || Student Center For many years mathematicians, scientists, engineers and others interested in mathematics have played year games via e-mail and in newsgroups. We don't always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to ...

The One and Only 1 Page Funded in part by The Digits Project Artwork provided by Tom Brinck The digit 1 has been called The loneliest number, yet many organizations, including sports teams, companies and countries take pride in calling themselves Number 1. This page, part of The Digits Project, is dedicated to the investigation, analysis, and discussion of the paradoxical digit 1. CONSPIRACY ...

Mathematical problems and expressions involving fibonacci numbers.

Detailed overview of the concept of infinity, with associated mathematical formulas and expressions.

JVS and HLY proudly present: The Magic PIWORLD, the PIPHONIE, PISIGN, PICTURE GALLERY and much more Pi stuff ...

Welcome to About BIG NUMBERS Explore the world of big numbers. Discover how big and how small our world is. How big is a zillion How small is a quadrillion Numbers and science. From the atom to the universe. Sun and sand and water and air. And more. Continue ...

The Zero Home Page Not enough attention has been paid to the digit zero in the course of history. It was the last of the decimal digits to be established in Western systems, but it has so many strong effects on our lives. Where would we be without zeros In big trouble... In our paychecks, zeros are critical. We all like to see lots of zeros lined up on a check. Speaking of lines, there would be ...

Welcome to Pi Memorama! -- a place for pi-memorizing enthusiasts everywhere. What What can you do here Download free pi software (for the Mac), read and submit reasons for memorizing pi, and learn a memory system -- and thanks to the privacy of the internet, you can do it all without wearing any pants. Why Why memorize pi Read why people do it, and submit your own reasons. How There's a ...

Home - Yahoo! - Help Ask Yahoo! Wednesday, December 1, 1999 Ask a Question Previous Question Who or what is a Mercator Next Question What is the weather like on Io Learn something new every day. Add Ask Yahoo! to My Yahoo! Dear Yahoo! What is the Golden Ratio and what significance does it have Kevin St. Louis, Missouri Dear Kevin: We suspected that the Golden Ratio was somehow connected to ...

Navigation Panel: Up | Down to First Subsection | Forward (skipping subsections) | Graphical Version | PostScript version | U of T Math Network Home University of Toronto Mathematics Network Answers and Explanations Is there really such a thing as infinity It's a tough question, because the word infinity can mean different things in different contexts. In mathematics, whether or not a certain ...

The concept of pi refers to the constant ratio of the diameter:circumference of any circle; irrespective of the number of degrees contained within that circle.

The Golden Ratio and The Fibonacci Numbers The Golden Ratio ( ) is an irrational number with several curious properties. It can be defined as that number which is equal to its own reciprocal plus one: = 1/ + 1. Multiplying both sides of this same equation by the Golden Ratio we derive the interesting property that the square of the Golden Ratio is equal to the simple number itself plus one: 2 = ...

Nove Tessaa Nau Dyevit Ah-hop IIIIIIIII Neuf Jiu Nine Devet Neun Kilenc Nueve Kyu Na Tesha Nio Dokuz Chin Nine Nou 9 Hut Nio Yhdeksan No Iwa Ni VIIII Dziewiec Noua Siyam Nove IX Ni Dokuz Negen Kyu Noy Ah-hop Na While the original intention was for this page to be about the digit 9, the material strays to the number and word nine -- oh, well. September or November Tom asked me to mention that ...

Four 4 is a number, a word or symbol used to designate quantities or, by extension, entities having quantitylike properties. Rational Numbers The simplest numbers are the natural numbers, 1, 2, 3, ..., used in counting; they are also called the whole numbers, positive integers, or positive rational integers. The natural numbers are closed with respect to addition and multiplication; that is, the ...

The constant e and its computation e = 2.71828182845904523536028747135266249775724709369995... (Click here for a Postscript version of this page.) eip+1=0 , all analysis lies here - Felix Klein (1849-1925). Gentlemen, we have not the slightest idea what this equation means, but we may be sure that it means something very important (to his students about the formula i-i = ep. - Benjamin Peirce ...

Welcome to the e Home Page You are visitor number to Euler's Number home page as of 10/17/95. For some fun try these links: e to 100, 000 decimal places. Top ln(e^10) reasons why e is better than pi. e to 2, 000, 000+ decimal places. Join 15 the digit club or view who has already joined. Fun facts and intersting things about e. Back to my home page. ...

Detailed mathematical explanations of countable and uncountable infinity, the principle of induction, and the real number system.

Square root of 2 The square root of 2 is very important number in mathematics. However it is generally overshadowed by other interesting quantities like PI. While PI is the circumference of a unit circle, the square root of 2 is the diagonal of a unit square. The square root of 2 is, of course, related to PI as that sqrt(2)=2sin(PI/4). Fortunately, it is much easier to compute the numeric value ...

The Verbose Pi Page ...

Zero in Four Dimensions: Historical, Psychological, Cultural, and Logical Perspectives Hossein Arsham University of Baltimore, Baltimore, Maryland, 21201, USA harsham@ubmail.ubalt.edu Contents: 1. Introduction 2. Historical Perspective 3. Psychological Perspective 4. Cultural Perspective 5. Logical Perspective 6. Concluding Remarks 7. Notes, Further Readings, and References Introduction The ...

Detailed explanation of the number known as e, and links to associated resources.

Last updated March 27, 1996 1.61803398874989484820458683436563811772030917980576286213544862270526046281890 244970720720418939113748475408807538689175212663386222353693179318006076672635 443338908659593958290563832266131992829026788067520876689250171169620703222104 321626954862629631361443814975870122034080588795445474924618569536486444924104 ...

3.1415926535 ... History and Philosophy of Pi, Mathematics, Infinity, Mystery ...

Lengthy article about the concept of infinity, including a discussion of its history, Cantor's set theory, and cardinal numbers.

The Golden Ratio: A Golden Opportunity to Investigate Multiple Representations of a Problem Edwin M. Dickey College of Education University of South Carolina Copyright 1993, NCTM MATHEMATICS TEACHER October 1993 Teachers of algebra have spent adequate amounts of time teaching two major representations of mathematics: verbal and algebraic, but have spent too little time on two other critical ...

Inter.View to George Cardas - Cardas Cables by Lucio Cadeddu A brief introduction to Golden Ratio freely taken from Golden sections and sequences in an unstable problem by Lucio Cadeddu Golden Ratio is an easy concept of elementary geometry which has had, and still has, great relevance both in human designs and in Nature. Recently it has had wide application in HiFi Audio too. Let me write down ...

Mathematics, abstract math.NT/0006089 From: Greg Martin gerg@math.toronto.edu Date (v1): Mon, 12 Jun 2000 18:07:15 GMT (8kb) Date (revised v2): Fri, 17 Nov 2000 19:58:47 GMT (11kb) Absolutely Abnormal Numbers Authors: Greg Martin Comments: 9 pages. The details of the main construction have changed somewhat, though the method of proof is the same. The paper has been expanded a bit for clarity ...

Number Gossip Everything you always wanted to know about your favorite number, but were afraid to ask. Enter your number Index Definitions Other Links Enter your number Please enter a positive number less than 10000: Index abundant amicable apocalyptic powers aspiring automorphic(curious) cake Carmichael Catalan composite compositorial cube curious deficient even evil factorial Fibonacci lazy ...

Fibonacci Facts INFORMATION SHEET ON FIBONACCI NUMBERS The Fibonacci sequence first appeared as the solution to a problem in the Liber Abaci, a book written in 1202 by Leonardo Fibonacci of Pisa to introduce the Hindu-Arabic numerals used today to a Europe still using cumbersome Roman numerals. The original problem in the Liber Abaci asked how many pairs of rabbits can be generated from a single ...

Play the harmonics that you hear! Complete midi, fretting, scales, instructions.

A history of Zero Ancient Indian Mathematics index History Topics Index One of the commonest questions which the readers of this archive ask is: Who discovered zero Why then have we not written an article on zero as one of the first in the archive The reason is basically because of the difficulty of answering the question in a satisfactory form. If someone had come up with the concept of zero ...

666 The Number of the Beast A little archive of gleanings, theories and links relating to the most misunderstood number of all Direct to 666 Syndrome (updated) Every other year some doomsayer comes up with a new theory about the mark of the beast and the conspiracy to control the world through a computerised big brother system. The Bible reference to the mark and the number (Revelation 13:18) ...

Apery's Constant Apery's constant, , is defined to be the value of Riemann's zeta function when x=3. This designation of as Apery's constant is new but well-deserved. In 1979, Apery stunned the mathematical world with a miraculous proof that = 1.202056903... is irrational . We will return to this shortly; let us first discuss Riemann's function in a little more detail. The zeta function can be ...

The Arabic numeral system Arabic index History Topics Index The Indian numerals discussed in our article Indian numerals form the basis of the European number systems which are now widely used. However they were not transmitted directly from India to Europe but rather came first to the Arabic/Islamic peoples and from them to Europe. The story of this transmission is not, however, a simple one.

Indian numerals Ancient Indian Mathematics index History Topics Index It is worth beginning this article with the same quote from Laplace which we give in the article Overview of Indian mathematics. Laplace wrote:- The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple ...

Documentation of the significance and occurrence of the number 47 in Star Trek and its spinoffs.