TeXclip

TeXclip is the web application for people who prefer TeX than PowerPoint's equation editor.

Wikisky

Okay, this is not a math post per se, but who doesn't like astronomy? Wikisky can show you the stars above a given location at a certain time. Pan, zoom, browse and explore the night sky using a Google-Earth-like interface.

Mathematics in Movies

This site offers some clips of the mathematical scenes from different movies and TV shows. I hghly recommending watching Sneakers (1992), A Beautiful Mind (2001) and Proof (2005).

Goldbach Conjecture: Proved?

The Goldbach Conjecture states that all positive, even integers ≥ 4 can be expressed as the sum of two primes.

Several papers have recently surfaced at arXiv.org claiming to have proved this. However, none of these methods have been verified yet.

• A Proof of Goldbach Conjecture


• From the Goldbach Conjecture to the Theorem

Fibonacci Sequence

In a book completed in the year 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?

The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.

Fibonacci numbers come up surprisingly often in nature, from the number of petals in various flowers to the number of scales along a spiral row in a pine cone. They also arise in computer science, especially in sorting or organizing data.

Amazingly, the ratios of successive terms of the Fibonacci sequence get closer and closer to a specific number, often called the golden ratio. It can be calculated as $\frac(1 + \sqrt5)(2)$, or 1.6180339887…. For instance, the ratio 55/34 is 1.617647…, and the next ratio, 89/55, is 1.6181818….


Fibonacci's immortal rabbit problem. A red rectangle designates a newborn pair, which doesn't produce offspring until the second month.

Proof Without Words

1³ + 2³ + … + n³ = (1 + 2 … + n)².
Mathematically, $\sum_{i=1}^{n} i^3 = (\sum_{i=1}^{n} i)^2$.

Proof Without Words

Area(Parallelogram) = ad - bc.

Proof Without Words

Law of Cosines: $\a^2 +b^2 - 2ab\cos\theta = c^2$.

Proof Without Words

1 + 4 + 9 + … + n² = n(n + 1)(2n + 1)/6.
Mathematically, $\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}$.

Scaling and Counting Concepts

Secret Worlds: The Universe Within (Powers of 10) shows you the scale of the universe and the microscopic world.

The MegaPenny Project helps you to visualize large numbers.

A Dot for Every Second in the Day

Very interesting website that shows you how things are scaled. Similar to Starship Dimensions.

Famous Unsolved Codes and Ciphers

This site contains an unofficial list of well-known unsolved codes and ciphers. A couple of the better-known unsolved ancient historical scripts are also thrown in, since they tend to come up during any discussion of unsolved codes.

Proof Without Words

$AB + AX = AD$.

XML MAIDEN Project

More Cascading Style Sheets (CSS) to help you create better looking math sites.

Indian American Mathematician is Awarded the Abel Prize

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2007 to Srinivasa S.R. Varadhan, Courant Institute of Mathematical Sciences, New York. He receives the prize “for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviation”.

Click here for more information.

MIT OpenCourseWare

MIT recently started offering its entire learning curriculum for free to anyone. Click here for their math portal.

Proof Without Words

Pythagorean Theorem: For a right triangle with legs a and b and hypotenuse c,
$a^2 + b^2 = c^2$.

Proof Without Words

The area of a regular dodecagon is 3R².

Proof Without Words

1/4 + (1/4)² + (1/4)³ + … = 1/3.
Mathematically, $\sum_{i=1}^{\infty} \frac{1}{4^i} = \frac{1}{3}$.

Proof Without Words

1 + 2 + 3 + … n = n(n + 1)/2.
Mathematically, $\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$.