Circle Basics: Radius, Diameter, Circumference

Geometry · Axiom Academy

LESSON Circle Basics: Radius, Diameter, Circumference The three measurements every circle carries — radius, diameter, and circumference — shown as the motion that links them through π. Pin one end at the center O and the other on the edge: that segment is the radius r, and it has the same length in every direction. Extend it straight through the center to the far edge and you've drawn the diameter d — two radii laid end to end, so the diameter is always exactly twice the radius. The radius reaches from center to edge The diameter is twice the radius 2. Circumference: The Distance Around The circumference C is how far it is around the circle. Roll the circle along a straight line for exactly one turn and the path it covers IS the circumference — and that length always comes out to π times the diameter. You can write it from the radius or from the diameter; they're the same statement. Why π? Take the diameter and step it off around the circle's edge. It fits three whole times , with a little left over — about 0.14159… of a diameter more. That ratio of circumference to diameter is the same for every circle, and we call it π. Its decimal digits never end and never settle into a repeating pattern. The same value for every circle — large or small, the ratio C/d is always π. 3.14 for quick work, or the fraction 22/7 when you need one. π = C ÷ d, which rearranges into C = πd — the circumference formula. 4. Example: Finding Circumference

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