Quite Basic -- Sieve of Eratosthenes

A BASIC programming website that uses the Sieve of Eratosthenes as an example.

Gallery of Illustrations

An interesting website that has plenty of mathematical illustrations.

Number Puzzles

Found some great number puzzles on the Internet.

Bridges
Dominosa
Light-up
Loop
Nonograms
Nurikabe
Shikaku
Sudoku

Drunk Men Work Here

This is a very interesting website. Problems 170 and 129 are a couple of great logic games.

Security Codes

I was entering the four-digit security code to our house, and I realized that it doesn't end with an ENTER (E) key to accept it. The problem with that is you can keep pressing numbers until the right combination is found. Since most keypads use all ten digits (0-9), the total number of combinations should be $10^n$. However, it is the ENTER key that makes it so difficult.

Let D equal the number of digits for the security code. Let K equal the number of digits on the keypad.

For a binary keypad (0, 1) and a three-digit code, our set consists of (000E, 001E, 010E, 011E, 100E, 101E, 110E, 111E). Thus, we have at most $2^3 \times (3+1)$ possible keys to enter, where the plus one is for the ENTER key. Generally speaking, we'd have $K^D \times (D+1)$ possible keys to enter.

Without the ENTER key, we could keep pressing the keypad until all combinations have formed. The minimum number of keys required would be $K^D + D$.

So for a binary keypad, we'd have:

D	String	Keys (wo/ E)	Keys (w/ E)
1	01	2	4
2	00110	5	12
3	0001110100	10	32
4	0000111100101101000	19	80
5	000001111100010010101110110011010000	36	192

Thus, one only needs to know the string concatenations to be able to guess the right combination if no ENTER or code-stopper key is required.

Update: See De Bruijn Sequence and ProjectEuler #265 for a related problem.

Cinderella

Experience Geometry on your desktop and on the web. Easily create startling geometric constructions! Starting from simple triangle relations, continuing with trigonometric theorems up to fractals and transformation groups Cinderella lets you create and manipulate visualizations in an intuitive, yet powerful way.

Click here for more information.

Wolfram Mathematica Online Integrator

This online integrator from Wolfram is actually pretty cool.

Worldmapper

Worldmapper is a collection of world maps, where territories are re-sized on each map according to the subject of interest.

How online games are solving uncomputable problems

Online games that tap your brainpower without you noticing can crack problems that have defeated the most powerful computers, says Lewis Dartnell. Get involved with distributed computing with these online games and downloads.

Click here for more information.

The Eyeballing Game

The Eyeball website gives you some mathematical figures and asks you to eyeball them correctly. I scored a 5.92 on my first try.

Just scored 3.13 on my second try.

More games at the Games for the Brain website.

Titanic Primes Raced to Win $100,000 Research Award

Researchers have discovered the two largest known prime numbers, a whopping 12,978,189 and 11,185,272 digits long, as part of a 12 year old, world-wide volunteer computing project, the Great Internet Mersenne Prime Search ("GIMPS"). The primes can be written shorthand as 2^43,112,609-1 and 2^37,156,667-1. The larger number qualifies for a $100,000 research award, most of which GIMPS will donate to the University of California, Los Angeles (UCLA), and to charity.

Click here for more information.

F#

I'm learning F#, Microsoft's latest functional programming language for the .NET family. Very nice and interesting. I recommend buying these books on it: F# for Scientists, Foundations of F#, and Expert F#.

Proof of the Existence of God

Click here for the explanation.

Lucy Pringle's Crop Circle Photograph Library

Latest crop circle found in England. Original article here.

XKCD Cartoon - Purity

WorldWide Telescope

The WorldWide Telescope (WWT) is a Web 2.0 visualization software environment that enables your computer to function as a virtual telescope—bringing together imagery from the best ground and space-based telescopes in the world for a seamless exploration of the universe.

Processing

Processing is an open source programming language and environment for people who want to program images, animation, and interactions. It is used by students, artists, designers, researchers, and hobbyists for learning, prototyping, and production. It is created to teach fundamentals of computer programming within a visual context and to serve as a software sketchbook and professional production tool. Processing is developed by artists and designers as an alternative to proprietary software tools in the same domain.

There's also a Javascript version of the code.

OpenVisuals

OpenVisual is a visualization that is created using Processing and OpenVisuals API, which makes it possible to use with any datasets on this website. Visualization artists can use these datasets to build a visualization. Once they upload the visualization to this website, it can also be used to visualize any other dataset on this website through OpenVisuals API.

Glimpses Of A New Mathematical World

A new mathematical object was revealed yesterday during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics.

Click here for more information.

Building a 5-ton mechanical calculator... from 19th-century plans

Starting in May, many will have the opportunity to see for themselves how they did computing the old-fashioned way: with lots of gears, a big crank and some muscle.

The Computer History Museum, in Mountain View, Calif., will unveil a new construction, the first in the United States, of the 19th century British mathematician Charles Babbage’s Difference Engine No. 2, an improved version of his earlier mechanical digital calculator.

Click here for more information.