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Frequently Asked Questions

How do you use geometry to perform arithmetic calculations?


René Descartes (1596-1650) the French philosopher and mathematician added many great ideas to the world of mathematics, but perhaps one of his greatest contributions was Cartesian geometry. Simple in essence, it has built a bridge between the world of geometry, number, and algebra. He was able to demonstrate that the four basic arithmetical operations are possible using geometrical constructions. Addition and subtraction are clearly trivial, but the other two can be demonstrated as follows.

Let us begin with the problem of multiplying two numbers. We start by constructing two lengths equal to the factors, a and b.

By marking a length of one unit along the base line and doubling that length we can use parallel lines, and in fact similar triangles, to produce the length 2a.

And so it is possible to produce the length ab.

Of course the reverse can be applied to divide two numbers.