A Page devoted to the poetry of mathematics, and the intrinsic beauty of our world.

It has become increasingly clear to me that, no matter the language you use to describe the patterns around us...beauty is beauty. Mathematics, poetry, art, and music are all basically the same endeavor. It has been extremely fulfilling to learn the language of Math, and I hope that a few out there have done the study necessary to understand some of what follows. Because it is possible to grow to adulthood and not necessarily learn this language, A lot of artistic expression has been passed by... So, to those who understand this language: I hope you find these particular poems as pretty as I have. To those who don't: I'm sorry that you've never had the chance to learn, and I hope some of my translation into "english" can help you, at least, appreciate these works of art to a lesser degree... >/< Sp!kY >\<

1) The first in my series of problems is the picture on the Right. Assuming that this square has been quartered infinitely, and the top left quarter of each of THOSE quarters is filled in, what fraction of the square winds up, as the light-purplish color, in the end? (college geometry, 1994, Musser and Trimpe, Prentice-Hall Inc)

2) Leonard Euler, who is sometimes referred to as the "Bach" of mathematics, proved the following equation. See if you can prove it as well.

Where, "e" is the irrational base of the natural logorithms, 2.71828... "i" is the square root of -1, and pi is 3.1459....