Depth 1 · 84 s
Three and a bit
Roll a circle out flat and lay its diameter along it - 3 times and a bit. That bit is the same for every circle. A hexagon shows why it's more than 3, and the number is pi, about 3.14.
About this video
Wrap a string once round a tin can and lay it out straight. How many times does the can's width fit along it? This animation rolls a circle once along the ground so that its way round, its circumference, lies out flat. Then it lays the diameter, the way across, along it: once, twice, three times, and a little bit is left over.
Do it with a coin, a plate or a bicycle wheel and the answer is the same: the way round divided by the way across is always about 3.14. To see why it is more than 3, the video draws a hexagon inside a circle. The hexagon is made of six triangles with equal sides, so each side is exactly one radius long, and its way round is six radii, which is three diameters. The circle bulges out past every side, so it is a little longer than 3 diameters. About 2,200 years ago Archimedes used polygons with more and more sides, up to 96, to squeeze the number between 3.140 and 3.143.
This number is called pi and written π. Its digits, 3.14159265358979..., never end and never repeat: π is an irrational number. For every circle, the circumference is π times the diameter, so a bicycle wheel 66 cm across travels about 3.14 × 66 = 207 cm, just over 2 metres, each time it turns. This video goes with the Pi: Once Round the Circle lesson of Geometry Level 1 on Knaph.
This video shows depth 1 of Pi (π).
Learn Pi (π)Transcript
- 0:00Wrap a string once round a can. How many widths fit along it?
- 0:07Roll the circle out flat. Now lay its diameter along it. One, two, three.
- 0:19Three diameters, and a little bit more.
- 0:24A coin, a plate, a wheel. Small or big, the answer is always the same. About three point one four.
- 0:34Why more than three? Draw a hexagon inside. Each side is exactly one radius.
- 0:42Six radii make three diameters.
- 0:44But the circle bulges out. So it's a bit more.
- 0:48Archimedes used more and more sides, up to ninety-six. Pi is between three point one four zero and three point one four three.
- 0:58This number is called pi. Its digits never end, and never repeat.
- 1:06Way round equals pi times way across. A wheel sixty-six centimetres across rolls about two hundred and seven centimetres each turn.
- 1:16Every circle, small or big, is pi times its width round.