Parallel Lines and Similar Figures

You might wonder at some point what parallel lines were used for. To cut wooden planks and stone bricks? To partition dough in equal sizes for cooking pizza? To make rulers and hammers and other tools?

Well, as it turns out, all of the above and more. Before the times table was organised neatly by John Leslie (yes, he's the Scottish mathematician & physicist who recommended the times table to schools) it was not easy memorising the times table when it went all the way up to 99 x 99.

Simply put, learning multiplication before we had proper schools teaching us the proper method was very hard. So people needed easy ways to do calculations that didn't require too much memory work.

Enter the Mesolabe Compass - A wonderful method used by Hippocrates of Chios.

Yeah, parallel lines were used to do calculations quickly for, say, store owners who had to calculate how much grain they were selling, and the worth of their goods. (Fun trivia, Hippocrates of Chios used to be a merchant, then he lost his wares and became a mathematician in Athens instead.)

As a bonus, he was incidentally using his compass on circles one day and discovered the interesting property between the 1:x triangle and the x:x² triangle. You can indeed find square roots by cleverly using Thales' theorem and similar triangles together.

The lesson here, is to be creative with the way you approach Maths. Who knows? You just might find something that's never been seen or used before.