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Wrapping a Rope around the Earth Puzzle

Suppose Poindexter takes a very long rope and wraps it around the equator of the Earth. Assume he has just the right length that makes this work without any slack. Suppose Alistair then comes along and adds 10 feet of rope to the length and the tiny bit of slack is used to have the rope uniformly hover just ever so slightly above the ground. How high off the ground is that rope?

Let's answer this puzzle in one fell swoop for ALL planets, not matter their size, and answer it for cubical planets and triangular planets as well!

This seemingly straightforward activity leads to astoundingly surprising discoveries. For starters, patterns, no matter how compelling they may seem, need not always be true! This puzzle proves this.

In the late 1800s French mathematician Bertrand proposed a disturbing paradox which seems to lead one to think that one third equals one half which equals one quarter. It shook the foundations of probability theory.

Let's examine - and explain - the paradox!

Here's a cute, but disturbing, geometric interpretation of two famous series in mathematics: the harmonic series (which sums to an infinite value) and the Basel series (which sums to a finite value). Put the two together and ... WHOA!

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.