Why can't we divide by zero?

"The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction."


http://www.math.utah.edu/~pa/math/0by0.html

The Secret Lives of Numbers

"The authors conducted an exhaustive empirical study, with the aid of custom software, public search engines and powerful statistical techniques, in order to determine the relative popularity of every integer between 0 and one million. The resulting information exhibits an extraordinary variety of patterns which reflect and refract our culture, our minds, and our bodies.

For example, certain numbers, such as 212, 486, 911, 1040, 1492, 1776, 68040, or 90210, occur more frequently than their neighbors because they are used to denominate the phone numbers, tax forms, computer chips, famous dates, or television programs that figure prominently in our culture. Regular periodicities in the data, located at multiples and powers of ten, mirror our cognitive preference for round numbers in our biologically-driven base-10 numbering system. Certain numbers, such as 12345 or 8888, appear to be more popular simply because they are easier to remember."

 http://www.flong.com/projects/slon/

Dictionary of Algorithms and Data Structures

"This is a dictionary of algorithms, algorithmic techniques, data structures, archetypal problems, and related definitions. Algorithms include common functions, such as Ackermann's function. Problems include traveling salesman and Byzantine generals. Some entries have links to implementations and more information. Index pages list entries by area and by type."


http://www.nist.gov/dads/

Mathway: Step-by-Step Math Problem Solver

http://www.mathway.com/

New Math

http://www.pontydysgu.org/2008/06/new-math/

The top ten things that math probability says about the real world

"Every academic discipline has its own peculiarities, and let me start by pointing out a peculiarity that my own topic (math probability) inherits from its parent mathematics. Just about every University offers an undergraduate course in math probability, and as a student in such a course what you actually do is about 100 homework problem of this kind. The top ones are ``just math" without any attempt at a real-world explanation, and the bottom two are weird made-up stories (poisonous mushrooms and car mufflers) referring to real-world items but not attempting to be empirically realistic. If you come from say Medieval History, you might think I've chosen some extreme example, but (alas!) different textbooks differ only in the the relative proportions of these two genres."

http://www.stat.berkeley.edu/~aldous/Top_Ten/talk.html

One - A Poem

One
A Poem


A Raven

Midnights so dreary, tired and weary,
Silently pondering volumes extolling all by-now obsolete lore.
During my rather long nap - the weirdest tap!
An ominous vibrating sound disturbing my chamber's antedoor.
"This", I whispered quietly, "I ignore".

http://users.aol.com/s6sj7gt/cadtext.htm

Pi Day

"Pi, Greek letter (π), is the symbol for the ratio of the circumference of a circle to its diameter. Pi = 3.1415926535... Pi Day is celebrated by math enthusiasts around the world on March 14th. "

http://www.piday.org/

i10k - Converting the first 10,000 digits of pi into a musical sequence

http://avoision.com/experiments/pi10k/index.php

The Grammy in Mathematics

"Mathematician nominated for award for restoring the only known recording of a live Woody Guthrie performance"

http://www.sciencenews.org/articles/20080209/mathtrek.asp

Great Minds in Mathematics

"A civilization is like a great river flowing through time, nourished and strengthened by many rich tributaries from other cultures. Let us project our imagination backward to a few thousand years. We are invited by the mathematics society of Greece, the birthplace of many mythical gods. We ask them a simple question: "Who created mathematics?" They respond "Mathematics begins with this half-mythical figure of Pythagoras. Science Begins with him. Western philosophy begins with him. He is even the first to use the word mathematike. Before him there was only mathemata, which meant knowledge or learning in general." "

http://www.mcs.csueastbay.edu/%7Emalek/Mathlinks/Minds/Minds1.html

Music: a Mathematical Offering

Why do rhythms and melodies, which are composed of sound, resemble the feelings, while this is not the case for tastes, colours or smells? Can it be because they are mo-
tions, as actions are also motions? Energy itself belongs to feeling and creates feeling. But tastes and colours do not act in the same way.

Aristotle, Prob. xix. 29

http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html

GNU Octave

" GNU Octave is a high-level language, primarily intended for numerical computations. It provides a convenient command line interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with Matlab. It may also be used as a batch-oriented language."

http://www.gnu.org/software/octave/

Open source software package takes aim at high-cost math programs

"A new open source mathematics program is looking to push aside commercial software commonly used in mathematics education, in large government laboratories and in math-intensive research."

http://www.networkworld.com/community/node/22768

http://www.sagemath.org/

Harvard scientists predict the future of the past tense

"Lieberman and Michel's group computed the "half-lives" of the surviving irregular verbs to predict how long they will take to regularize. The most common ones, such as "be" and "think," have such long half-lives (38,800 years and 14,400 years, respectively) that they will effectively never become regular. Irregular verbs with lower frequencies of use -- such as "shrive" and "smite," with half-lives of 300 and 700 years, respectively -- are much more likely to succumb to regularization."

http://www.sciencecodex.com/harvard_scientists_predict_the_future_of_the_past_tense

How to use a slide rule

See how calculations used to be done before the days of electronic calculators. Find out about an important piece of engineering history. All pieces of the slide rule are draggable.

An Intuitive Explanation of Fourier Theory

Fourier theory is pretty complicated mathematically. But there are some beautifully simple holistic concepts behind Fourier theory which are relatively easy to explain intuitively. There are other sites on the web that can give you the mathematical formulation of the Fourier transform. I will present only the basic intuitive insights here, as applied to spatial imagery.

http://sharp.bu.edu/%7Eslehar/fourier/fourier.html

Favorite Math Jokes

A farmer discovered his horse was extraordinarily intelligent. You could ask it an arithmetic problem, and it would tap out the answer with a hoof. Researchers were fascinated and tested the horse. They discovered the horse understood algebra, Euclidean geometry, calculus, and even group theory. However, when they gave the horse problems with Cartesian coordinates, it just stood there dumbly, like any horse. This was quite surprising, given how intelligent the horse was otherwise. They brought in an expert who examined the situation and explained the problem: "Of course the horse cannot understand any Cartesian coordinates you show it. You are putting Descartes before the horse."

http://edp.org/mathjoke.htm

Software for Algebra and Geometry Experimentation

SAGE is free open source math software that supports research and teaching in algebra, geometry, number theory, cryptography, numerical computation, and related areas. Both the SAGE development model and the technology in SAGE itself is distinguished by an extremely strong emphasis on openness, community, cooperation, and collaboration: we are building the car, not reinventing the wheel. Our overall goal is to create a viable free open source alternative to the commercial programs Magma, Maple, Mathematica, and MATLAB.

http://modular.math.washington.edu/sage/

Euler's Beautiful Equation

"Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth." —Benjamin Pierce, a Harvard mathematician, after proving Euler's equation, e^iπ = –1, in a 19th-century lecture.

http://blog.sciencenews.org/mathtrek/2007/04/eulers_beautiful_equation.html