 How Long Is A Year?  Jim Loy
The exact length of a year, and how to figure it out using the earth, the sun, and the stars, with two observations on consecutive nights.
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 How To Be A Little Gauss  Jim Loy
There is a story about Carl Friedrich Gauss. Supposedly, when he was a little boy, his teacher asked the class to add up the numbers one through a hundred (1+2+3 etc., all the way up to 100)... To the teacher's annoyance, little Gauss came up with the
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 How to Compute One Billion Digits of Pi (Organic Mathematics Proceedings)  D. H. Bailey, J. M. Borwein, P. B. Borwein
Ramanujan, Modular Equations, and Approximations to Pi  Bailey, Borwein and Borwein. Abstract: This article follows up one small thread of Ramanujan's work which has found a modern computational context, namely, one of his approaches to approximating
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 How to Compute Planetary Positions  Paul Schlyter
A description of how to compute the positions for the sun and moon and the major planets, as well as for comets and minor planets, from a set of orbital elements. The algorithms have been simplified as much as possible while still keeping a fairly good
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 How to Correctly View a Flatland Painting  Mark Schlatter
A paper with Java illustrations: Given a two dimensional painting of a three dimensional object, you can use geometry to find the ideal viewing locationthe position where the image appears most three dimensional. This site reviews that geometry (using
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 How to Fix an Election  Ivars Peterson (MathTrek)
Voting sounds like a simple matter. Just pick a candidate, then count the ballots and announce the tally. When there are three or more candidates (or choices), however, the results may not actually reflect the true preferences of the voters.
Suppose
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 How To Get Into the Newspapers  Keith Devlin (Devlin's Angle)
A lecture to Devlin's readers with good advice on how to write math clearly enough and other important things to do to get an article published in the newspapers.
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 How to Lace Like an Ace (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
One of your sneakers has a broken shoelace. You want to replace it, but the only laces you have around are much shorter. Is there a way to lace your shoes so that you can use the shorter laces? There are three common ways to lace shoes: American (or standard)
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 How to Play Fair With Loaded Dice (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: For some reason you need a standard fair die (with the numbers from 1 to 6 on the six faces). All you have is an unfair "loaded" die. How can you use the loaded die to fairly choose random numbers from 1 to 6? ... Roll the die
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 How to sell soap  Keith Devlin (Devlin's Angle)
Humorous takeoff on scriptwriting a series on two families: the Points and the Lines...
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 Howto Series  ERIC/AE; Bruce Thompson, Texas A&M Univ.
This is a set of online, fulltext books and booklets addressing practical evaluation, research, measurement, and statistical issues. The series started as a joint project of ERIC/AE and Bruce Thompson, Texas A&M University. We have since added other
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 How to Split Your Vote (Math Chat)  Frank Morgan, MAA Online
Answer to the Challenge: Suppose all that any voter in the U.S. cares about is that different parties control the Presidency and the Congress. If there is no communication, how should each voter vote?
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 Humanity's Life Span (Math Chat)  Frank Morgan, MAA Online
Challenge: Estimate the life span of the human race. Answer: Al Zimmermann says with 80% confidence that we have between 100,000 and 10 million years to go.
Perhaps another million years is the best guess. (By comparison, the dinosaurs reigned for over
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 Hungarian Central Statistical Office (HCSO)
Introduction to and history of the Hungarian Central Statistical Office; Hungary in figures; important yearly data and most recent statistics; glossary of statistical definitions; catalog of publications; professional and scientific institutes; and detailed
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 HungHsi Wu's Home Page  HungHsi Wu
Articles on the Common Core Mathematics Standards (CCSS) and math education in general, such as "The impact of Common Core Standards on the mathematics education of teachers," "Bringing the Common Core State Mathematics Standards to Life" (published in
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 Hunting e  Ivars Peterson (MathTrek)
Lagging far behind in the celebrity sweepstakes is the number known as e. Carried to 20 decimal places, e is 2.71828 18284 59045 23536. Only 50,000,817 of its decimal digits have been computed so far  though there are unconfirmed reports that 1 billion
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 Hypatia  Taylor, Dawson; Dept, of Computer Science, Queen Mary & Westfield College, East End, London, UK
Hypatia is a searchable directory of research workers in Computer Science and Pure Mathematics, and a library of their papers. Contents: New papers, people, places and papers, bibliographies, useful links, Hypatia of Alexandria. Authors can be found by
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 Hyperspace  International Society on General Relativity and Gravitation, QMW, University of London
A set of hypertextbased services for general relativity research from the QMW Relativity group (Queen Mary and Westfield College, Univ. of London). Software for finding GR (e)mail addresses; GR News Archive; Our GR related FTP archives; Preprint searches
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 The Ideal Voting System (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: What is the shortest line segment fencing off prescribed area 0 < A < 1 in a unit square? (What about the leastarea piece of plane dividing off prescribed volume 0 < V < 1 in a unit cube? What about a 4D cube?) ...assume
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 Identical Calendars for 2000 (Math Chat)  Frank Morgan, MAA Online
For programming into the VCR on January 1st for correct day and date, what years in the 1900s have the same calendar as the year 2000? An identical calendar must, like 2000, be a leap year starting on a Saturday. Leap years occur every four years, and
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 Identities for Linear Recurring Sequences  Kevin Brown
There are several methods for computing the Nth term (mod M) of a
linear recurring sequence of order d in log_2(N) steps, but most
such methods require d^2 full multiplications (mod M) per step.
The algorithm described below requires only d(d+1)/2
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 Ido Efrat
A mathematics professor at Ben Gurion University of the Negev in Israel. Site includes the syllabi for current courses and a list of Efrat's publications in abstract algebra, especially group theory. Some articles may be downloaded in PDF or DVI format.
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 IFS (Iterated Function Systems) for 2D and 3D Visualization  Craig M. Wittenbrink
Using fractal interpolation to graphically represent two and threedimensional scalar data: download article in PDF or PostScript format, and view related images.
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 If You Build It, Will They Come? Participant Involvement in Digital Libraries  Giersch, Klotz, McMartin, Muramatsu, Renninger, Shumar, and Weimar
A paper concerning a workshop involving representatives from several digital libraries with user participation. The workshop explored the ways users participate in digital libraries, and methods of studying these participants' interactions.
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 Illinois Mathematics Association of Community Colleges (IMACC)
A searchable site that offers online versions of AMATYC publications, including "Crossroads in Mathematics: AMATYC Standards," "The AMATYC position on Adjunct Faculty," and local publications, including "Illinois Mathematics and Computer Science Articulation
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 The Illustrative Mathematics Project
Providing guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience with the Common Core State Standards, and by publishing other tools
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 Image Coding Using Fractals  Signal and Image Processing Group, University of Bath
Graphs show how image compression using fractals compares to other methods. Also includes comparison pictures and a list of articles on fractal compression, some of which may be downloaded in gzipped PostScript format.
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 Image Coding Using Wavelets  Signal and Image Processing Group, University of Bath
Read the article "What makes a good orthonormal wavelet for image compression?" Download other wavelet articles in PDF or PostScript format. Visit the Wavelet Warehouse, a repository of wavelet filters (biorthogonal and orthonormal) to download and
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 Image Compression  from DCT to Wavelets: A Review  Subhasis Saha
An article published in ACM Crossroads, the student magazine of the Association for Computing Machinery, about how recent growth in dataintensive multimediabased Web applications has not only sustained the need for more efficient ways to encode signals
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 Images Created by Man & Chaos  Alan Beck
Some personal observations on fractal art and artists. "...the fractal artist does not create but explores, does not manufacture but discovers. Instead of being repelled by computers, such adventurers revel in them, as European mariners of old rejoiced
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 Imaginary Numbers  Jim Loy
A brief essay on imaginary numbers. An imaginary number is a real number times the positive square root of 1. The positive square root of 1 is usually called i. It is not an integer, it is not real. It is the answer to the question, "What number squared
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 Immersed in Klein Bottles  Ivars Peterson (MathTrek)
"Need a zerovolume bottle? Searching for a onesided surface? Want the ultimate in nonorientability?" The intriguing subject of these cryptic entreaties is a bizarre mathematical object known as a Klein bottle, discovered in 1882 by German mathematician
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 The impact of dynamic geometry software on learning  Bryan Dye; MathsNet
A paper that aims to measure the impact of use of dynamic geometry software on learning via the Internet; to compare various software packages, for example: Geometer's sketchpad, Cinderella, and CabriGeometre; and to measure the impact of "home learning"
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 The Impact of the Math Forum's Problem(s) of the Week on Students' Mathematical Thinking  K. Ann Renninger, Laura Farra, and Claire FeldmanRiordan
Article in PDF format. Presented at the International Conference of the Learning Sciences 2000.
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 Implementing Curriculum, Instruction and Assessment Standards in Mathematics (NCREL)  Cathy Cook; Pathways to School Improvement
From Critical issues in mathematics. National educational standards are being developed in nearly all subject areas. The National Council of Teachers of Mathematics has recently developed standards for mathematics; its Curriculum and Evaluation Standards
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 Implications Rules  Alan Selby
Implication Rules: two puzzles that show the difference between one and twoway implication rules. Mastering the difference is a simple, first step, in rule and patternbased thought, needed to precisely read rules, definitions and statements in all
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 Impossible World  Vlad Alexeev
About impossible figures in art. These figures can be painted on paper but cannot be represented in space. There are many artworks by M.C. Escher, Jos de Mey, Sandro del Prete and many other artists. Also, you can view animations and read articles about
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 Impressions from ICME9  Cut the Knot!, Alexander Bogomolny
Statistics on attendance (by country) at the International Congress on Mathematics Education held in Tokyo, Japan in August, and impressions of talks on the state of mathematics education in the year 2000. According to Mogens Niss (Denmark) who gave the
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 InCharge Education Foundation  InCharge Education Foundation, Inc.
The nonprofit InCharge Education Foundation promotes financial wellness by offering data, information, research, and education on the behaviors and issues facing average individuals and families on consumer credit, money management, and financial wellbeing
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 The Incredible Pi Code  Ivars Peterson (MathTrek)
Researchers have expended a great deal of effort computing as many of the digits of pi as computer technology and mathematical methods allow. Last year, Yasumasa Kanada of the University of Tokyo calculated pi to 206,158,430,000 decimal digits. A high
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 The Independent Set Algorithm  Ashay Dharwadker
A polynomialtime algorithm for finding maximal independent sets in a graph with new bounds on Ramsey numbers.
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 Index Using Mathematics Subject Classification (MSC)  Dave Rusin; The Mathematical Atlas
The index pages at this site are organized according to the Mathematics Subject Classification (MSC) scheme. (This is the scheme developed by the American Mathematical Society and Zentralblatt für Mathematik.) General headings include Foundations;
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 Indian numerals  MacTutor Math History Archives
Linked essay on the method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value), which emerged in India. With references and other related web sites.
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 The Indian Sulbasutras  MacTutor Math History Archives
Linked essay on the Sulbasutras, appendices to the Vedas that contain all that is known of Vedic mathematics, and give rules for constructing altars. (The Vedic people entered India about 1500 BC from the region that today is Iran. The word Vedic describes
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 Individual Differences and the United States Education System  Douglas Trelfa
An overview of ability grouping and tracking in the United States, from The Educational System in the United States: Case Study Findings, March 1999. A discussion of the diversity of beliefs found regarding the question of how to deal effectively and
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 The Inertia Tensor and After Dinner Tricks  Steve Drasco
In PDF format, a paper introducing momentum, angular momentum, the inertia tensor, and principle axes and stable/unstable rotations.
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 The Infinitude Of Primes  Jim Loy
A prime number (such as 2 or 3 or 5) is a natural number (positive whole number) which is only divisible by itself and one (and no other natural number). This short essay explains Euclid's proof that there are infinitely many prime numbers.
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 Infinity  MacTutor Math History Archives
Linked essay on the mathematical, philosophical, and religious aspects of infinity. With references and other related web sites.
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 Infinity: You Can't Get There From Here!  B. Sidney Smith; Math Academy Online/Platonic Realms
A "minitext" offering a concise introduction to the concept of infinity. Includes historical background, Cantor's set theory, and an introductory discussion of cardinality, as well as suggested reading.
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 Information and Communication, Circuits  Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to information and communication, circuits, which includes questions of particular interest to algebraists, especially coding theory (related to linear algebra and finite groups) and encryption (related
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