The Magic Of Math

The Magic of Math shows you not only the power, but also the beauty of mathematics, unlike you’ve ever seen it in school and with practical, real-world applications.

When Arthur was little he loved playing around with numbers. One day, when he tried to see which of the pairs of numbers that, when added together, equal 20, would give him the biggest number when multiplied, he noticed something.

Of course if you do this exercise and go through the pairs, like:

7 * 13 = 91

8 * 12 = 96

9 * 11 = 99

10 * 10 = 100

you’ll quickly see that 10 * 10 gives you the biggest result. But if you go back through those numbers and measure the distance of each to 100, something interesting emerges. For 100, the difference is 0, for 99 it’s 1, for 96 it’s 4 and for 91 it’s 9.

Put these in order: 0,1,4,9. Notice anything? These are the first few square numbers!

0² = 0

1² = 1

2² = 4

3² = 9

and so on. Once Arthur spotted this pattern, calculating any square number became a lot easier. For example, instead of trying to calculate 13 * 13 in your head, you can instead switch it to 10*16, which gives you an easy 160. Now all you have to do is add the square number of the difference to the original number. Both 10 and 16 are 3 away from 13, so if you add 3² = 9 to 160 you get the result: 169!

So 13 * 13 = 16 * 10 + 3² = 160 + 9 = 169. Neat, huh? Even better, this works for all square numbers.

Finding mathematical patterns will make your whole life a lot easier, so try to practice it whenever you get a chance.

This might only work among your slightly nerdier friends, but it’s also a great way to practice mental math. Have someone go through these five steps: Think of two numbers from 1 to 10. Add those together. Multiply by 10. Add the larger number of the two. Subtract the smaller number of the two. Have them tell you the result. Here’s how you can shock them by instantly telling them what their numbers were. Let’s say your friend’s number was 117. Take the last digit of the number and add it to the preceding number. In this case it’s 7 + 11 = 18. Divide by 2 to get the larger number. Here it’s 18 / 2 = 9. Subtract the last digit of their answer to get the smaller number. Here, it comes out to 9 – 7 = 2. Not sure…