Cycling + Me
I LOVE road biking. For 2014, I have two cycling goals.
1) I am going to ride my bike 500 miles in one month (I am thinking of trying this in May).
2) I am going to ride a century, 100 miles in one day (most likely not in May).
Because I have a passion for cycling and math, I thought that in addition to sharing these goals on my blog I should share a some things I love about cycling and present a mathematical perspective about cycling.
Cycling + Cognition
There are many reasons to love cycling and one reason is the cognitive benefits to cycling. Research has shown that activities, such as cycling, lessen depression and anxiety (Read this). I even read an article this past fall about how cycling helped lessen the effects of Parkinson's disease. Some articles even claim that cyclists are "smarter" because of their routine exercise (Look here). It makes sense why people say these things… with cycling or any other cardiovascular activity, you are increasing your blood flow and the oxygen to your brain. However, I honestly don't love cycling because I read these types of articles. I have read many of these types of articles because I can tell when I have been cycling and when I have not been cycling. I can testify that I am a happier person when I am moving on my bike and when I finish a long ride. There is something special about cycling and that is not captured in these studies. On my bike I feel like I get mental alone time (even if I am riding with others). As I am riding, I get an energizing peace and that allows me think time I feel super productive. Honestly, it may take a few hours out of my day to ride 50 miles, but I never feel like that time or those miles are wasted. There is something incredibly special about riding for 20 - 50 miles that words can not describe.
Cycling + Catenaries
Most bikes have wheels that are in the shape of a circle, which is convenient for the often smooth planes we ride on. However, what if your bike had square wheels? What kind of surface would your bike need to in order to ride smoothly? This short YouTube video below shows the type of surface that a square wheeled bike would need in order to ride smoothly.
As you can see, the square-wheeled bike needs an inverted catenary curve in order to ride smoothy. A catenary curve is traditionally described as a "hanging chain" between two posts or I like to point to the St. Louis Arch. Catenary curves can be mathematical described with a hyperbolic cosine curve (cosh).
The square wheeled bike presents an awesome mathematical adventure down catenary curve lane. But, imagine all of the other mathematical possibilities with this cycling consideration! If you want an inverted cycloid or want a path with adjoining triangles, what kinds of wheels would you need? Or, consider, what surface would you need for a triangular wheel? Well, it turns out that triangular wheels do not work well. However a cardioid wheel could work with the appropriate surface [I will leave these investigations to the reader for mathematical exercise, haha].
And, let me know if you want to take a mathematical field trip with me. I have never been to the Museum of Math and there are square wheeled bikes are on exhibit at the Museum of Math.