Archive for April 3rd, 2011

The Winter Newsletter! Because winter is too long already.

April 3, 2011

The forecast this moment is predicting snow…SNOW!…and while it’s not going to be much, it looks like winter won’t end until we post our Winter Newsletter.  This issue is named The Chern Weekly Quarterly Whenever after Shiing-shen Chern (陳省身, Oct. 26, 1911—Dec. 3, 2004), who studied Differential Geometry (including, ummm, Chern classes in algebraic topology), was vice-president of the American Mathematical Society, and who founded the Mathematical Sciences Research Institute at Berkeley and the Nankai Institute for Mathematics.

This issue contains mostly department news and photos, but as always it contains a Sudoku and problems for your mathematical enjoyment!

Problem 5.2.1: Find the ratio of the areas of the circumcircles of a triangle and a square of equal perimeters.

Problem 5.2.2: In the figure at the right, ABCD is a rectangle, BE=BC, and AE is the diameter of the circle. What is relationship between BF and the original rectangle?

Problem 5.2.3: Using the digits 1-9 exactly once each, with only the operations +, —, ×, ÷, and/or exponentiation, write an expression that equals 2011. Now try it with the digits in order.

Problem 5.2.4: A box has three possible perimeters. Suppose box A has perimeters 12, 16, and 20, while box B has perimeters 12, 16, and 24. Which box has the greater volume?

You’re welcome to try your hand at these and post in the comments, for fame (of sorts, although referring to it as “famish” doesn’t make it sound very enticing at all) since we’ll happily acknowledge all who submit solutions in the next issue!  Which isn’t as much of a temptation as just solving for solving’s sake, but still, we do what we can.