A line, or a pancake?
From equations to geometry. The next three lessons belong to the most perfect shape — and right at the start we will clear up words the whole class mixes up.
A circumference is only a line — the outline your compasses draw. Like a hoop.
A circle (the disc) is the whole pancake — the circumference and everything inside. Like a pancake.
When you paint a fence around a round flower bed, you are dealing with a circumference. When you sow grass on the whole bed, you are dealing with a disc. Perimeter belongs to the circumference, area to the disc — that is why the difference matters.
More words today: centre (the point in the middle), radius r (the distance from the centre to the line), diameter d (across the whole circle through the centre). We have d = 2r — the diameter is double the radius. This one equals sign is what you will need all the time today.
And get out the compasses. Geometry is learned by hand.
Adam and Tereza are planning a round flower bed in the school garden. Tereza sticks a peg in the ground, ties a 1-metre string to it and ties a drawing peg to the other end. She walks around the centre and a perfect circumference stays in the soil. “The string is the radius,” she says. Adam measures the distance through the centre: 2 metres. “And this is the diameter — twice as much.” Then they argue how much fence to buy and how much grass seed. Tereza: “The fence is a circumference. The grass is a disc. Two different questions — and the next two lessons will answer them.”
Hold the compasses by the head at the top, not by the legs. Stick the needle, tilt slightly in the direction of turning and turn in one stroke. A wobbly circumference = holding by the legs.
A dictionary of the circle and drawing
Centre S — the point from which every point on the circumference is equally far. That is the whole definition of a circumference: the set of points at the same distance from the centre.
Radius r — the distance from the centre to the circumference. In a circumference you can draw infinitely many, all the same length.
Diameter d — a line through the centre from edge to edge. d = 2r. The other way r = d/2. The diameter is the longest distance that fits into the circle.
Chord — a line joining two points of the circumference that does not have to go through the centre. The diameter is the longest possible chord.
Notation: a circumference k with centre S and radius 3 cm is written k(S; 3 cm).
Drawing a circumference k(S; 3 cm):
- Mark point S with a cross.
- Open the compasses to 3 cm — measure on a ruler from the needle to the pencil.
- Needle into S, one smooth stroke.
Check the opening: draw a radius and measure it. Compasses like to loosen while drawing — check the opening after finishing too.
Example 1: from radius to diameter and back
A round paddling pool has radius r = 1.2 m. What is its diameter?
d = 2r = 2 · 1.2 = 2.4 m.
And the other way: a pizza has diameter 32 cm. What is the radius?
r = d/2 = 32 : 2 = 16 cm.
Simple, but it is the most common conversion in the whole chapter. Formulae in the next lessons sometimes want r, sometimes d — and you must be able to switch without hesitating.
Example 2: will a table fit through a door?
A round table top has radius 55 cm. The door is 100 cm wide. Will the top go through sideways?
The widest place of the top is the diameter: d = 2 · 55 = 110 cm.
110 cm > 100 cm — sideways it will not go. (Diagonally luckily yes, but that is another problem.)
The lesson: when you ask “will a round thing fit?”, compare the diameter, not the radius. The radius would trick you here — 55 < 100 looks hopeful, but it is only half the truth.
Example 3: draw and label
Task: draw a circumference k(S; 4 cm) and mark in it a radius, a diameter and one chord.
Method: a cross for S, compasses open to 4 cm, one stroke.
Radius: a line from S to any point on the circumference. Label r.
Diameter: put a ruler to S, extend to both sides of the circumference. Label d. Measure: it must be 8 cm — that is a check that the compasses held.
Chord: join two points of the circumference off the centre. It will be shorter than 8 cm — always.
A disc and a circumference are not the same word for one thing. Circumference = a line (perimeter), disc = an area (area). Tests catch people on this: “the area of a circumference” is a trick — a line has no area.
Practice: now you do it 🎲
Now try it for real. You will see all the questions at once, like on paper. 开始 with ten. When it goes well, add more.
Perimeter belongs to the circumference (the line). Calculate with π ≈ 3.14.
On paper
Today you draw. Compasses, a ruler, a sharpened pencil.
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Draw a circumference k(S; 3 cm). Mark and label radius r and diameter d. Measure d and check that it is 6 cm.
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Into the same circumference draw two different chords and measure them. Write why none can be longer than the diameter.
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Find three round things at home (a mug, a plate, a coin), measure their diameter with a ruler and calculate the radius. Write it in a table.
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Draw two circumferences with the same centre: k(S; 2 cm) and k(S; 4 cm). Colour the area between them — that is what a ring looks like, say a running track around a pitch.
Now you 💪
- I know a circumference is a line and a disc is an area.
- I can convert radius to diameter and back: d = 2r.
- I draw a circumference from the notation k(S; 3 cm) in one stroke.
Done when: You have drawn circumferences with a labelled radius, diameter and chord, a table of three measured objects, and one ring.
What to take from this lesson
- Circumference = a line (a hoop), disc = an area (a pancake).
- Radius r is from the centre to the edge, diameter d across the whole centre: d = 2r.
- The diameter is the longest chord and the widest place of the circle.
- Notation k(S; 3 cm): centre S, radius 3 cm.
- Perimeter will belong to the circumference, area to the disc — that comes right in the next lesson.
© 2026 Ing. Martin Polak / AlgoRhino · 内容使用条款