π is the ratio of any circle's circumference to its diameter, the same number for a coin and for a planet. From the radius alone you get the diameter (2r), the circumference (2πr) and the area (πr²).
Worked example · circle radius 2
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How to: Circles
- Everything about a circle follows from its radius.
- Diameter.
- Circumference.
- Area.
Questions people ask
Why does every triangle have angles adding to 180°?
Draw a line through one vertex parallel to the opposite side: the two alternate angles equal the other two angles of the triangle, and the three angles at the vertex lie on a straight line. That is Euclid's proof, and it is why the fact holds only on a flat plane.
When do I use the law of sines versus the law of cosines?
Cosines when you know three sides, or two sides and the angle between them. Sines when you know an angle and the side opposite it, plus one more piece.
What is the difference between area and perimeter?
Perimeter is the length of the boundary (one dimension, measured in metres); area is the amount of surface inside (two dimensions, square metres). Doubling every side doubles the perimeter but quadruples the area.
More in Geometry
TrianglesPythagorean theoremPolygonsSolidsCoordinate geometryEuclid's axioms and the structure of proofCongruent and similar trianglesCircle theoremsTransformations: translation, rotation, reflection, dilationSolid geometry: prisms, pyramids, spheres