Quote:
Originally Posted by Paul Beardsley
I don't know if I'm confusing fact with fiction here, but I recently heard something about a student who used Eratosthenes' method of measuring the diameter of the Earth... and got an answer of 1.2 metres! If true, it sounds as if the student had the necessary maths skills, but not the commonsense to check for obvious errors.
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Ditto. I have classes work out the lunar distance using parallax, starting from the location of the lunar limb during a solar eclipse at various times done from our location, and the knowledge that the center of the umbra was at a certain place when we had greatest eclipse. One of the students didn't think anything was odd on finding that Moon was closer than Seattle. I mean, that's what the calculator said, so it must be right...
One aspect which I think operates here is also at work in Another Controversy Which I Will Not Name. For lots of students, they've almost never seen any math but trivial arithmetic impact their daily lives, so these sots of calculations have always been school assignments of the jump-through-hoops-for-a-grade variety. This suggests a certain lack of practice in estimation of physically reasonable outcomes. I start many of these same classes with Fermi's question about the likely number of piano tuners in New York City, to set the tone for estimating.