Circles, Measured
A circle has no sides to add up, so measuring one needs a different idea entirely. This track starts with the parts — the radius and diameter that describe a circle from its centre, and the chords, arcs, sectors and segments that name the pieces of it — then turns to measurement. The distance round the rim turns out to be π times the distance across, whatever the size, and the only real decision in using that is whether the number you were handed is the width or half of it. The next tutorial goes back to where π itself comes from: not a rule anyone chose but the result of measuring any circle two ways and dividing, which gives the same answer every time because all circles are scaled copies of one another. The track finishes by taking the rim apart, since an arc is simply the same fraction of the circumference as its angle is of a full turn.
CodePLU Goal
Upgrading Human Mental Models
Learn how to think in Workflows
What Are the Radius and Diameter of a Circle?
A circle has no sides to measure, so everything is measured from its centre instead. The radius reaches out to the edge, the diameter crosses the whole way through, and telling them apart is what every circle calculation depends on. Place each name on a real circle in an interactive playground.
What Are a Chord, an Arc, a Sector and a Segment?
Once a circle has a centre and a radius, the rest of its vocabulary describes pieces: a straight cut across it, a stretch of its edge, a wedge from the middle and the cap left over. Place all four on real circles in an interactive playground.
What Is the Circumference of a Circle?
The circumference is the distance all the way round a circle, and it is always π times the diameter — a little over three diameters, whatever the size. The only decision is whether you were given the diameter or the radius. Practise both in an interactive playground.
Where Does Pi Come From?
π is not a rule someone invented; it is what you get when you measure round a circle and across it and divide. Every circle gives the same answer, which is why one number works for all of them. Use it in reverse to find a circle's width in an interactive playground.
How Long Is an Arc?
An arc is part of a circle's rim, and its length is that same fraction of the whole circumference. Find the fraction from the angle at the centre, then apply it — two steps, no new formula to learn. Practise on six sectors in an interactive playground.