due 4apr
square:  c=16
              ratio of c:d  :  4:1
             verification: c=(pi)d
                                16=(4)4

triangle: 12:4=3
hexagon:ratio:3

To expand on this idea, are there non-euclidean spheres?

The reason there are only 3 shapes that tesselate is they are the only shapes whose interior angle measures divide evenly into 360.

due Feb 19
If you go down the triangle and take the sums of each row, the sum will double each time. If a row is made into a single number by using each number in the row as a digit of the number (carrying over when a number in the triangle has more than one digit), the number is equal to 11 to the nth power when n is the number of the row. I thought the hockey stick pattern is cool. If you go from the edge of the triangle, go inward and downward diagonally as far as you want, and then go outward and downward diagonally one number, the number you end with is the sum of all the numbers you hit before you changed direction. That's a terrible explanation. And supposedly if you fill in all the odd numbers, you get the Sierpinski triangle.

Math humor, due Jan 17

Q: What is the definition of a polar bear? A: A rectangular bear after a coordinate transformation
Q: Why are you drumming on your algebra book with two big sticks? A: Because we are studying log rhythms.
Teacher: Your behavior reminds me of square root of 2. Student: Why? Teacher: Because its’ completely irrational.
Q: How is an artificial christmas tree like the fourth root of -68? A: Neither has real roots.
Son: "My math teacher is crazy". Mother: "Why?" Son: "Yesterday she told us that five is 4+1; today she is telling us that five is 3 + 2."
Q: Why did the chicken cross the mobius strip? A: To get to the same side. Q: Why did I divide sin by tan? A: Just cos.
Q: What do you call a number that can't keep still? A: A roamin' numeral.

Yeah. Pretty bad. And you might have heard this one; it's not really a math joke, but I like it:Four Friends Four friends have been doing really well in their algebra class: they have been getting top grades for their homework and on the midterm. So, when it's time for the final, they decide not to study on the weekend before, but to drive to another friend's birthday party in another city - even though the exam is scheduled for Monday morning. As it happens, they drink too much at the party, and on Monday morning, they are all hung over and oversleep. When they finally arrive on campus, the exam is already over. They go to the professor's office and offer him an explanation: "We went to our friend's birthday party, and when we were driving back home very early on Monday morning, we suddenly had a flat tire. We had no spare one, and since we were driving on backroads, it took hours until we got help." The professor nods sympathetically and says: "I see that it was not your fault. I will allow you to make up for the missed exam tomorrow morning." When they arrive early on Tuesday morning, the students are put by the professor in a large lecture hall and are seated so far apart from each other that, even if they tried, they would have no chance to cheat. The exam booklets are already in place, and confidently, the students start writing. The first question - five points out of one hundred - is a simple exercise in algebra, and all four finish it within ten minutes. When the first of them has completed the problem, he turns over the page of the exam booklet and reads on the next one: Problem 2 (95 points out of 100): Which tire went flat? 

source: http://www.jokes4us.com/miscellaneousjokes/mathjokes/algebrajokes.html