Welcome to the College Mathline Blog
This blog accompanies the College Mathline television program produced by Palomar College.
Here you can post a question for us or a comment about the show. You can also find information on our "real world" applications of mathematics.
Wednesday, April 30, 2008
A cycloid is the curve formed by a fixed point on the edge of a wheel as the wheel rotates along the ground. The curve is given by the parametric equations
x = r (t - sin t),
y = r (1 - cos t)
where r is the radius of the wheel. If you take one arch of the graph and turn it upside down it forms a ramp with a special property: it is the fastest path for a ball rolling down from one point to another. A second interesting fact: if you do have a ramp in this shape, no matter where you start a ball rolling, it will always take the same amount of time to reach the bottom. The cool photo is from illum on Flickr.
Note that our contest is still open!
Wikipedia entry for cycloid
YouTube video of a marble rolling down a cycloid ramp
Wednesday, April 23, 2008
We have a new contest for you:
If you were to write the numbers 1, 2, 3, 4, ... up to 100,000, how many zeros would you write?
We received some incorrect answers during the program today (hint: the number of zeros is a lot higher than 11,000 or 11,111) so the contest is still open. If you figure it out, don't post an answer here! Be the first one to call us live next Wednesday to claim the prize. (1-888-762-1489 is the toll-free number.)
This week we looked how strong a dam must be to hold back the water in a lake.It turns out that the force exerted on the dam doesn't depend on how much water is in the lake, but rather just on the depth of the water. It is tricky to calculate the total force on a dam however because the water pressure is different at different depths. So the bottom of the dam will experience a lot more force than the top. You can estimate the total force by considering horizontal sections of the dam separately, and if you want to be more accurate, calculus can get you to the precise value.
Wednesday, April 9, 2008
Today we looked at some of the mathematics of the Gateway Arch in St. Louis, Missouri. The shape of the arch follows an inverted catenary, a shape naturally formed by a hanging chain or cable. The monument was designed from an equation based on a hyperbolic cosine function.
Links for this week: