Tomorrow, 2/7, is the day we celebrate e-day, in honor of the number e≈2.7182…. And celebrate we do: there are decorations, and e-related foods (browniEs, e-clairs, pi(e), etc.) and an e-day quiz. So it’s a big deal around here. And sometimes dangerous.
The date was February 7, 2005. The time was 5:00am. I’d gotten up early to cook, and this year decided to try a recipe that involved baking the brownies, then putting white chocolate chips and crushed candy canes on top. I placed the whole pan under the broiler for a few minutes for the chips to soften before spreading them around. And I’m sure all would have gone well if TwoPi hadn’t asked from the dining room, “Hey, are there any nonzero integers a, b, and c such that ?” Naturally I started to work on that question, and forgot all about the brownies.
Until the fire alarm went off.
The candy canes had caught on fire, and the entire pan was in flames (see the evidence in the picture above). We got to try out the fire extinguisher, and managed to get everything under control with only one lost pan of food.
Then TwoPi found a solution to the problem while I cleaned up. It looks like there are an infinite number of answers: if you rearrange the terms you find
By setting equal to 1, the term simplifies to and on a calculator or spreadsheet you can quickly scan through values of c that lead to that term having an integer cube root. For example, . Presumably there are other solutions if is set equal to a different integer. Hmmm….something for the e-day quiz.