Everyone can do geometry. From primary school onward, we draw lines, triangles and circles. This is only natural: shapes are all around us. Like a botanist in the garden of mathematics, a geometer seeks to understand, study and classify these shapes. In this quest, geometers use a variety of tools. One of them is algebra.
Equations for shapes
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Although a line can easily be drawn with a ruler, the points on it can also readily be identified using an equation of the form y = ax + b. Given a value of x, solving the equation gives a unique y, and the point with coordinates (x, y) lies on the line.
A circle can be treated in the same way. Every point in the plane with coordinates (x, y) satisfying the equation *x 2 + *y 2 – 1 = 0 lies on the circle with center O (0, 0) and radius 1.
