Classes started last week, but that’s not the real start of the semester. No, the real start of the semester is when Problem of the Week returns. Which means the semester starts today!
The theme for the term is “False Proofs.” By this I mean proofs that seem superficially convincing, but lead to an obviously absurd conclusion. Your task as the problem solver is to locate the exact moment when everything goes off the rails. Our problem for this first week is a classic of the genre, in which we, ahem, prove that an elephant weighs the same as a sly. As we go along we shall see that it is possible to construct a triangle with two right angles, that the hypotenuse of a right triangle is always the same length as one of its legs, and multiple proofs that 2=1. Good times!
Feel free to post explanations and comments below. As always, do not worry that my students are going to read the blog and thereby be able to cheat. This is not a formal assignment for them, and they receive no extra credit for participating. It’s a fairly small group of students who participate in this, and they are not the types looking to take the easy way out. There’s a five dollar gift card to Starbucks on the line, for one lucky winner, but as one of my grumpier students pointed out to me today, that’s barely enough for one drink.
from ScienceBlogs http://ift.tt/1g6vwIo
Classes started last week, but that’s not the real start of the semester. No, the real start of the semester is when Problem of the Week returns. Which means the semester starts today!
The theme for the term is “False Proofs.” By this I mean proofs that seem superficially convincing, but lead to an obviously absurd conclusion. Your task as the problem solver is to locate the exact moment when everything goes off the rails. Our problem for this first week is a classic of the genre, in which we, ahem, prove that an elephant weighs the same as a sly. As we go along we shall see that it is possible to construct a triangle with two right angles, that the hypotenuse of a right triangle is always the same length as one of its legs, and multiple proofs that 2=1. Good times!
Feel free to post explanations and comments below. As always, do not worry that my students are going to read the blog and thereby be able to cheat. This is not a formal assignment for them, and they receive no extra credit for participating. It’s a fairly small group of students who participate in this, and they are not the types looking to take the easy way out. There’s a five dollar gift card to Starbucks on the line, for one lucky winner, but as one of my grumpier students pointed out to me today, that’s barely enough for one drink.
from ScienceBlogs http://ift.tt/1g6vwIo
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