2 - Calculus for Climatologists—Solution

Summary

When Anne arrived at Thirsty's the following Friday afternoon, she saw that Len and Jason had gotten there before her and had chosen a quiet table near the windows. Len was slouched back in his chair, absorbed in the demanding task of cleaning his fingernails with the blunt end of a toothpick. Jason was systematically tearing a paper napkin into thin strips. As there was no food or drink on the table, they apparently had not yet been served.

Jason looked up. “What happened to you?” he asked, giving Anne a rather fierce look. “You're late.”

“I'm sorry,” replied Anne. “I wanted to type out the solution and print it before I came here, and the printer jammed, and it took about 20 minutes to get it cleared. Anyway,” she continued, opening her backpack and pulling out a sheaf of papers, “here it is.” She gave several sheets to each of the others.

Len stirred slightly. “So, you've actually got a solution? Good for you! What's the answer?”

“You were right, Len. Any great circle has to contain two antipodal points at the same temperature. I've got the proof right here.”

“You actually proved that?” exclaimed Jason. “This I've got to see. You know, you had the easy job—if I was going to prove that it it couldn't happen, I'd have had to have temperature readings from every single point on some great circle at the same instant of time, and there just isn't the available meteorological data to do that, and I bet there never will be!”