Welcome to Spring!
Our "knowledge app" site demonstrations.wolfram.com was completely redesigned to use the inline Mathematica 8 or free Wolfram Player plug-in rather than having to open a separate window (alongside various other changes).
This apparently small plug-in change makes a big usability difference and by the same token, it changed the site workflow quite a bit. It also required the latest version of Player--just releasing too--and itself quite a feat of engineering.
Division by Zero has an exploration of Albrecht Dürer’s ruler and compass constructions.
These constructions are definitely Geogebra-worthy.
Brent Yorgey at Math Less Traveled has a great exploration of Triangunit divisors and quadratic reciprocity. Brent tackles a challenging problem. The Math is not trivial but Brent makes it accessible.
Pat Ballew writes about Gauss and Constructable Polygons.
+plus magazine picks holes in mathematics in an article about Godel's incompleteness and followup work on the subject:
The logician Kurt Gödel proved in the 1930s that if you set out proper rules for mathematics, excluding leaps of faith or intuition as admissible moves, you lose the ability to decide whether certain statements are true or false. And this isn't because you chose the wrong rules: for any set of rules, as long as they're strong enough to make sense of whole number arithmetic, there will be statements you can't prove or refute.
Hat tip to Shecky.
CTK Insights has a nice exploration: The 1089 Prediction Trick and Beyond.
A second nice article at CTK Insights is: How to Make Your Own Divisibility Criteria. It's a very concise explanation of how to come up with your own rule for divisibility by, say, 19.
As the final food-for-Math thought of the week, check out Alasdair's musings on the quadratic and cubic formulas. There are some nice simplifications of these formulas for students struggling to memorize them, not that I recommend memorizing.