Circles
A
circle is defined as the set of points that lie at an equal distance, the radius r, from a central point P, and is one of the primitive elements taken for granted in Euclid’s axioms. The closed curve through all the outer points is the circle’s circumference, and the length of circumference C is linked to the radius r by the equation C = 2πr, while the area A of the circle is defined by another equation, A = πr2. In this way, the circle inevitably leads to one of the two great constants of mathematics, π (see page 40). The circle also defines other curves, lines, and areas. An arc is a limited part of the circumference, while a sector is a region of the circle bounded by two radii and an arc. A chord is a straight line across the circle between two points on its circumference, and a segment is an area within the circle bounded by the circumference and a chord. A secant is an extended chord—a straight line cutting the circle at two points—while a tangent is a straight line that touches the circle at a single point.