Descartes' Coordinates — Plot a Treasure Map and Draw with Numbers

In 1637 Rene Descartes labelled the flat plane with two number lines, so that every point became a pair of numbers and every equation became a curve. Algebra and geometry, separate for 2,000 years, became one. You will plot with it.

On card, rule a grid and draw two number lines crossing at the middle: the horizontal x-axis and the vertical y-axis, meeting at the origin (0, 0). Number the lines both ways from the centre.

Plot a few points by their coordinates: (3, 2) means three right and two up. Join a list of points to draw a shape. Then try equations: mark several points where y = 2x + 1 and see they line up straight; mark points three units from the origin and watch a circle appear. For fun, hide a 'treasure' and give a friend only its coordinates to find it.

What your grid unlocks. (1) Every point is a pair of numbers and every equation is a shape -- a line, a parabola, a circle -- so geometry becomes something you can CALCULATE. (2) The distance between two points is Pythagoras in disguise. (3) Once shapes were equations, Newton and Leibniz could build calculus on top a generation later, and physics could write motion and forces as formulas. (4) Every graph you read, every pixel on a screen, every GPS position and every 3D game world rests on Descartes' simple idea that a point is just a list of numbers.