Odds and Evens: Week of 3-10-08

Don't forget to submit your solution to the Mystery Mathematician of the Week! So far, one correct solution has been emailed to me. Remember to email me at "dmarain at gee-mail dot com." Slight hint: Our star this week delved into many areas of mathematics including those special types of equations we have been
discussing...

• Yes, Pi Day is coming. I hope to have something special up for that occasion. It would have been 'pi-fect' had our next Carnival of Mathematics coincided with that event, but I'll leave it to our crack math team out there to project in what year the next Pi Day will match with one of our Carnivals!
  
• Unfortunately I missed submitting to the perfect 28th edition of the Carnival over at Tyler and Foxy's Scientific and Mathematical Adventure Land. That title by itself should win an award!
• Have you been keeping up with the comment thread to our recent post regarding an integer parallelogram with sides of 39 and 25 and with a diagonal of 34? TC contributed a couple of beautiful variations, one of which was easily solved by Joshua. Joshua also gave a thorough solution to the original problem. Eric provided the theoretical background for solving these kinds of Diophantine equations. I figure if I compile Eric's comments for the past year, I would have one amazing textbook for algebraic number theory!
  
• Stay tuned for an investigation that builds on the integer parallelogram problem as mentioned in the comment section. This one involves finding a limited number of solutions to integer-sided triangles which have an angle of 60 degrees. Of course the trivial solution would be the equilateral triangle but we're looking for scalene triangles here. A little bit of trig and some algebra and geometry will be required. The general solution requires, you guessed it, Pell's equation, but we will not go there!