This is a fun and clever idea: convert the decimal expansion of Pi into base 27 and name the “digits” A, B, C, D, … . This creates a way to decode numbers into words and phrases (the ‘0’ digit is interpreted to be a space, or a punctuation mark).
With this in place, you you can search for your name (or any phrase) in the infinite expansion of Pi!
http://www.dr-mikes-maths.com/pisearch.html
This will certainly excite all those cosmological conspiracy theorists out there!
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This is a collection of around 200 free online math books.
http://planetmath.org/?op=mscbrowse&from=books
It seems like many of these are pretty advanced, but it’s nice to know that when you are ready to learn about Geometrodynamics and Nontrigonometric Fourier Analysis, the resources are out there.
Could this be yet another nail in the coffin of textbook publishers? Let’s cross our fingers.
This is a wonderful demonstration of the scale of the universe.
http://primaxstudio.com/stuff/scale_of_universe/
By zooming in and out, you travel through space-time comparing and contrasting objects with magnitudes on the order of galaxies, planets, humans, atoms, and strings. A really creative and beautiful application.
This is a brilliant video introduction to the fine mathematical art of doodling.
http://www.youtube.com/watch?v=heKK95DAKms
This video–one of several from vi hart–is an engaging, witty, and serious look at the mathematics one can explore just by doodling and playing around with a few basic ideas. Sophisticated concepts in graph theory and knot theory spring up from some very simple, and very beautiful, sketches.
The creator of the videos is a bit hard on math teachers in her narration; apparently she’s had some bad ones. The snarkiness definintely adds character to the videos, but it’s a bit excessive at times.
I’m sure it isn’t easy making innovative, mind-opening videos like this, but it isn’t easy teaching a class full of doodling students, either!
This is the arithmetic portion of the MIT Entrance exam from 1869:
http://libraries.mit.edu/archives/exhibits/exam/arithmetic.html
Since it’s hosted by the MIT libraries website, I assume it’s authentic. I wonder if examinees were allowed to use graphing calculators on this exam?
Be sure to check out the English section also. I hope you know who Count Bismark is!