A repunit is a whole number consisting of only 1’s, such as 1, 111, or 111111111. (It’s like a repeating unit.) These numbers have...

Continue reading...# easy

These fun facts are at the easy level.

## Sine of (1/55555….)

Take your calculator, and enter a number consisting of several 5’s, such as 5555555. Now take the reciprocal of this number. Now take the...

Continue reading...## Divisibility by Eleven

It is easy to tell that the following are multiples of 11: 22, 33, 44, 55, etc. But how about:...

Continue reading...## Behold! the Pythagorean Theorem

Figure 1 shows one of the simplest proofs of the Pythagorean Theorem. It is also perhaps the earliest recorded proof, known...

Continue reading...## Why Does 0.999… = 1?

Consider the real number that is represented by a zero and a decimal point, followed by a never-ending string of...

Continue reading...## Area of a Hyperbolic Wedge

The unit circle can be parametrized by (cos w, sin w). Given a point on it, the region cut out...

Continue reading...## tamreF’s Last Theorem

Here’s an amusing theorem that is very easy to prove, which we’ll call tamreF’s Last Theorem. In fact it is tamreF’s...

Continue reading...## Hugging the Equator

Suppose that you have a rope around the equator of a basketball. How much longer would you have to make...

Continue reading...## Gaps in Primes

We know there are infinitely many primes, so are many interesting questions you can ask about the distribution of primes, i.e., how...

Continue reading...## Football Field

Take a long rope, tie it to the bottom of the goal post at one end of a football field....

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