Mathman strikes again. Here’s a nifty picture I have borrowed from Cracked.com. The text, by Cracked user RainbowCrash, says, “Manhole covers are round so that they cannot possibly fall through their own holes. Any shape other than a circle would be able to fit through in at least one way.” Curiously, RainbowCrash’s profile advertises, “I’m not stupid anymore!” So let’s help him out here. There are shapes, other than a circle, that meet this definition. The requirement, when generalized, is that it must be a curve of constant width. Wolfram defines this as “Curves which, when rotated in a square,

# Tag: mathematics

## And Behind Door #3…

I am in Atlanta right now and tomorrow morning I am giving a talk on the SMBC cartoon, “An Ethical Trilemma”: Saturday Morning Breakfast Cereal – An Ethical Trilemma No Description Despite the punchline, “So far, no ethicists are impressed with the Monty Hall Trolley Problem,” I am impressed with the problem. It represents a much more interesting problem than the comic gives it credit for. You can check out my slides here: This is an embedded Microsoft Office presentation, powered by Office Online. Also, as an aside, this is my first presentation since going to work for the Johns

## So I Am Not Teaching Calculus After All

Well, no sooner had I posted my note about teaching calculus again this fall when UMUC changed my schedule. This is not unusual for me (though I may be unusual in this regard at UMUC, it’s a bit unclear). I occasionally end up getting put in other classes than planned at the last minute. Part of this stems from the fact I have taught almost the entire undergraduate mathematics curriculum, and part of it is I just don’t mind the challenge of something good new. This fall, I will be teaching MATH 115 Precalculus. I have taught precalc several times

## NaN versus NA in R

R has two different ways of representing missing data and understanding each is important for the user. NaN means “not a number” and it means there is a result, but it cannot be represented in the computer. The second, NA, explains that the data is just missing for unknown reasons. These appear at different times when working with R and each has different implications. NaN is distinct from NA. NaN implies a result that cannot be calculated for whatever reason, or is not a floating point number. Some calculations that lead to NaN, other than , are attempting to take

## You Can Do Anything as a Math Major

This article on stemjobs.com popped up on Facebook the other day. What Can You Do With a Math Degree Besides Teach? Some students fall in love with math. They admire the order, the adherence to hard and clear rules and the complex beauty that the discipline brings. But many of those interested in math are loath to teach. Yet, they are unclear on what other career paths are available to them. That’s a legitimate question. Most of us only encounter math teachers and never see what good mathematics is beyond that. But there are a lot of options option to

## Euler Method in R for the Initial Value Problem

During differentiation, the value of whatever vertical shift is present is lost as a result of the elimination of the constant term, which has a derivative of 0. We normally acknowledge this when integrating a function by adding a constant, the constant of integration, to an indefinite integral. This is sometimes a nonissue since, if finding the value of a definite integral, the constant terms cancel and the constant of integration is unnecessary. For ordinary differential equations, them there is no convenient cancellation, leading to the initial value problem. The initial value problem provides a value of , where is