What a circle is

People have drawn circles for a very long time: the cave paintings of Gudahandi in Odisha show circles, triangles and squares. Nature is full of them too: rings from a raindrop on water, the cut end of a stem, a sunflower's head, the full moon.

"Mark lots of dots, each exactly 3 cm from one point." As the dots fill in, they make a circle. That is the idea behind the definition: a circle is the set of all points of a plane at the same distance from a given point, the centre.

The words:

• a set of points that obey a rule is a locus, so a circle is the locus of points at a fixed distance from a point;
• that fixed distance is the radius (the spokes of a bicycle wheel are radii);
• a chord joins two points of the circle;
• a chord through the centre is a diameter, and it is the longest chord.

A circle is perfectly symmetric. Turn it by any angle and it looks the same: it has complete rotational symmetry. That is why a turning wheel always looks the same.

Fold a paper circle so the edge lies on itself. The crease is a line of reflection symmetry, and it is a diameter. Fold again along a different line: the two creases cross at the centre. That is how Jamuna finds it.