February 18, 2009, 2:51 pm

By Robert Talbert

Spreadsheets are one of the most underrated tools available for doing and learning mathematics, especially calculus. At my college we include spreadsheets as a central tool for our Calculus I course and use them every chance we get. But as with all technology, there is the possibility of encountering a seemingly inexplicable glitch when using them even in a very tame situation.

Here’s one I encountered this week when setting up a spreadsheet to do an average velocity/instantaneous velocity problem. We started with a falling object whose position from the start point at time *t* is given in the following table:

The eventual goal is to compute the average velocity from t=2 to t=3, then t=2.5 and t=3, then t=2.9 and t=3, and so on, finally estimating the instantaneous velocity right at t=3. Actually, this is where the glitches started. The “25″ in the third cell was supposed to be a “20″ …

Read More

August 28, 2008, 1:57 pm

By Robert Talbert

At the end of this post, I made a totally naive guess that the recently discovered candidate to be the \(M_{45}\), the 45th Mersenne prime, would have 10.5 million digits. There was absolutely no systematic basis for that guess, but I did suggest having an office pool for the number of digits, so what I lack in mathematical sophistication is made up for by my instinct for good nerd party games. On the other hand, Isabel at God Plays Dice predicted 14.5 million digits based on a number theoretic argument. Since I am merely a wannabe number theorist, I can’t compete with that sort of thing. But I *can* make up a mean Excel spreadsheet, so I figured I’d do a little data plotting and see what happened.

If you make a plot of the number of digits in \(M_n\), the nth Mersenne prime, going all the way back to antiquity, here’s what you get:

The horizontal axis is *n* and the vertical…

Read More