What We Did in Atlanta This Winter

From the Mathematical Association of America (MAA) winter meetings in Atlanta—There was a wonderful minicourse on the legendary Swiss German mathematician Leonhard Euler, presented by William W. Dunham of Muhlenberg College and C. Edward Sandifer of Western Connecticut State University. Euler’s 300th birthday will be commemorated in the summer of 2007 with a reality tour of Berlin and St. Petersburg, where Euler did most of his work. Some of our favorite nuggets we didn’t know before:

(1) The sum of the squares of the sides of a quadrilateral are equal to the sum of the squares of the diagonals plus the square of the segment connecting the midpoints of the diagonals (which shrinks to zero in the case of a parallelogram).
(2) Pi = 20arctan(1/7) + 8arctan(3/79)
(3) 1/3 + 1/7 + 1/8 + 1/15 + 1/24 + 1/26 + . . . = 1
(4) Euler discovered the largest perfect number, 2^30 (2^31 -1), a record which stood over 100 years
(5) Venus passes in front of sun twice every 120 years, with those two alignments separated by eight years. This discovery led to an international cooperative movement to calculate the distance to the sun.
(6) A proof that e^ix = cosx + isinx Start with the integral of 1/sqr(1+z^2) dz = ln (z + sqr(1+z^2), replace z with iy and dz = idy; a couple of steps later, replace y with sinx, dy with cosxdx

. . . . A fabulous exhibit of original M.C. Escher woodcarvings went largely unnoticed by the visiting mathematicians in Atlanta, largely because gallery owner Skot Foreman (is he aware of the significance of his name???) did not know a potential gold mine of buyers was just minutes away. We picked up a videotape and a 2004 calendar!