What Gives!

Now, you don't need to be a math major to conjecture that as we enter the winter, and it gets quite a bit colder, skirts should get longer, and as we move back into the spring and summer months, well then, at least there is a half-ways reasonable excuse for wearing short skirts (though modest is, at all points of the year, hottest, and I'm not refering to temperature). Yet, I am finding that skirts are actually shorter now than 2 months ago! The style goes something like this: wear black leggings that cover your whole leg, and then put the shortest possible skirt on which will, in theory, cover your behind, though it's all really quite optional in reality. This can be represented visually below:

An example of reasonable winter attire:

An example of unreasonable winter attire:

Would it be too cynical to point out that my classes are far easier to understand than my peers?

The Hailstone Sequence

So, here is the pretty picture I made today. An explentation is below, if so desired (but count yourself warned).

WARNING!!! MATHEMATICAL CONTENT!!!



The Hailstone sequence is the sequence defined as

If a(n-1) is odd, a(n)=3*a(n-1)+1, and
if a(n-1) is positive, a(n) = a(n-1)/2

Unfortunately I don't have subscripts at my disposal, so the function/sequence bleedover will have to suffice.

While it has yet to be proved, it is thought that the hailstone sequence converges to 1 for any starting number a(n). I was interested in the number of steps it took to reach one. For instance, starting number 2 obviously takes 1 step, and 4 takes 2. 3 takes 8 steps, while a starting number of 5 only takes 6. The graph then displays on the X-axis the starting number, and on the Y-axis the number of steps (for lack of a better word... perhaps "iterations"?) it takes to arive at one. I'll admit I stole the idea for such a graph from Wikipedia, but they only went up to 9,999, so I consider myself the victor, even more so if Excel could have more than 16384 columns, which my buddy pointed out is 2^14! He's a computer science major, so a more sophisticated graph may be forth coming.


On another note, a Saturday morning impromptu math class (a full 6 days of quality education for a 5 day price!) to learn about mathematical induction was scheduled. I am most excited!