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Road biking, dirt road riding on Frankenbike, tandem riding, group riding, time trialing, randonneuring - I love to ride, and I love to write. As I've traveled along on two wheels, I've learned one thing: Expect Adventure. Join me on the journey!

Betty Jean Jordan

Sunday, April 26, 2020

Asymptotes and Cream Filling

Several of my recent off-road rides have been rather math-y.  That's a good thing.  In addition to cycling, one of my favorite things is math.

Asymptotes

A week or so ago, I was doing a typical after-work dirt road ride.  I was mainly out there to enjoy the evening and get a good workout; I wasn't looking to set any race records.  In the last few miles, I noticed that my average speed was 13.8 mph.  That's not bad for one of my mixed surface rides.  Dirt road rides are significantly slower than paved road rides.

It occurred to me that it would be cool if I could finish my ride with an average of 14 mph.  However, I doubted I could ride fast enough for the remaining short distance to bring my average up that high.  Nevertheless, I kept up a steady tempo.  A few moments later, I checked my speed and noted that I was riding 14 mph.  Even if I kept up that pace forever, much less the remaining distance to my house, I would only asymptotically approach an average speed of 14 mph.

At least I came up with the name of my rock band if I ever have one: The Asymptotes.

Cream Filling

When I was little, my cycling consisted largely of riding to the cul-de-sac, which was only a block away.  There was little traffic in our suburban neighborhood - plenty safe.  I'd ride back and forth to the cul-de-sac and around and around it.  That sounds boring now, but it was lots of fun back then.

A few days ago I took my mountain bike back to the trails in the Oconee National Forest in south Jasper County.  I planned to ride while Robert hiked and did a little trail maintenance.  It had rained a few days earlier, making several of the trails pretty mucky.  I stayed on the River Trail, which was mostly dry, paralleling the Ocmulgee River.  I rode back and forth, back and forth.  It was like the adult version of riding my bike back and forth to the cul-de-sac when I was a kid.

The non-mucky portion of the River Trail that I rode was about 3/4 mile long.  Back and forth, back and forth.  I rode it pretty fast for me on a mountain bike because this is the least technical part of the trail system in the Oconee National Forest in Jasper County.  Also, it was a beautiful afternoon, and I got to be right next to the river.



It reminded me of the cream filling in an Oreo cookie, which is the best part.  The chocolate cookies are just meh.  Then I thought about Little Debbie Oatmeal Creme Pies (OCPs).  They have much more cream filling than Oreos, and the cream filling delivery vehicle is far superior.  But just how much more cream filling are we talking about?  Time to do some calculations.

Assume that Oreos and OCPs have the same thickness of cream filling, approximately 1/8 inch, and that for each treat the filling covers the same area as the delivery vehicle (meh chocolate cookies and pretty good oatmeal cookie-like things, respectively).  Therefore, the difference in cream filling volume depends on the different diameters.  According to an ABC News story on The Google, an Oreo has a diameter of 1 3/4 inches.  The diameter of an OCP is more elusive.

I found a recipe for OCP tiramisu in which whole OCPs are layered with creamy tiramisu filling in stemless wine glasses.  (Sounds good except that tiramisu has coffee in it - yuck!)  I have some stemless wine glasses and measured their diameter.  The largest OCP that could fit in there whole, perhaps with some careful bending to keep it intact, is 2 1/2 inches.

Additional research showed that a box of 12 OCPs has dimensions of 4.12 x 4.50 x 12.00 inches.  Assuming three layers of four OCPs in the box, each OCP would have to have a diameter slightly less than 12/4, or slightly less than 3.  Therefore, my assumption of an OCP having a diameter of 2 1/2 inches is probably about right.  (Ideally, I would go to a store that sells individually wrapped OCPs and take a measurement, but that's not practical during these shelter-in-place times.)  Now we're ready to calculate the volumes of cream filling:

Oreo: volume = pi x r^2 x h = 3.14159 x (1.75 / 2)^2 x 1/8 = 0.30 in^3 cream filling

OCP: volume = pi x r^2 x h = 3.14159 x (2.5 / 2)^2 x 1/8 = 0.61 in^3 cream filling

Therefore, an OCP is already more than twice as good as an Oreo, even before accounting for an OCP's vastly superior cream filling delivery vehicle.

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