# algebra

## Perfect Shuffles

We know from the Fun Fact Seven Shuffles that 7 random riffle shuffles are enough to make almost every configuration equally likely...

## Quick Square Roots

Here’s a very quick way to generate the square root of N. Let A0=N. Then generate a sequence of numbers A1, A2,...

## Mug Trick

Take a mug that has a handle, and fill it with coffee. Hold the mug in your hand. Now, without...

## Chords of a Unit Circle

Take N equidistant points on the unit circle. Pick one of those points, then draw chords from it to all...

## 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...

## Squaring Numbers between 40 and 60

Here’s a quick way to square numbers between 40 and 60. You know the squares of 40, 50, and 60,...

## Multiplying Complementary Pairs

Quick! What’s 23 x 27? 621 There’s a trick to doing this quickly. Can you see a pattern in these...

## Visual Multiplication with Lines

Here’s a way to multiply numbers visually! Suppose you want to multiply 22 by 13. Draw 2 lines slanted upward...