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Ball Physics

Circle Illusion

Balls slide back and forth on straight lines, yet together they seem to form a rolling circle.

About

Circle Illusion is a calm visual demonstration with soft piano notes. Inside a large ring, coloured lines are added through the centre one at a time, a new one every three seconds. On each line a single glowing ball moves straight back and forth, fastest in the middle and slowest at the ends, a smooth motion known as simple harmonic motion.

No ball ever leaves its own straight line, yet because each one is timed slightly later than the one before, together they appear to form a smaller circle rolling around inside the big ring. The effect grows clearer as lines are added, and after about 45 seconds there are 16 distinct rainbow-coloured lines. Each time a ball touches the outer ring it plays a piano note, building a gently repeating melody. There are no controls: tap or click once to enable sound, then just watch.

How to Play

  1. Tap or click the screen once to turn on sound.
  2. Sit back and watch; there are no other controls.
  3. Follow a single ball and notice that it only moves along its own line.
  4. Then look at all the balls together to see the rolling circle.

Tips

  • Cover all but one ball with your finger: on its own, each ball just slides back and forth in a straight line.
  • The hidden circle is half the width of the outer ring and always touches its edge as it rolls.
  • After the first 16 lines, new lines run along the same diameters and their balls sit exactly on top of the earlier ones, so the shape stays the same while colours and notes layer up.
  • Each line has its own note, so the melody follows the order in which the balls reach the ring.

Details

Category
Ball Physics
Layout
square

A circle that is not there

Circle Illusion is a calm visual demonstration. Inside a large ring, coloured lines are added through the centre, a new one every three seconds. On each line a single glowing ball moves straight back and forth, and no ball ever leaves its own line.

Yet when you look at all the balls together, they seem to form a smaller circle rolling around the inside of the big ring. The circle is not drawn anywhere. It exists only in the way your eyes group the moving points.

The idea behind it

Each ball moves in simple harmonic motion, the same smooth back-and-forth motion as a weight on a spring or a pendulum: fastest in the middle of the line and slowest at the ends. Each ball is timed slightly later than the one before, and that small delay is what makes the group appear to rotate.

This is a known geometric effect, where a circle rolling inside a circle of twice its size traces straight lines along diameters. The hidden circle here is half the width of the outer ring and always touches its edge as it rolls.

How to watch it

Try covering all but one ball with your finger. On its own, each ball just slides along a straight line. Then uncover the others one at a time and notice when the circle appears. After about 45 seconds there are 16 distinct rainbow-coloured lines, and the effect is at its clearest.

Every time a ball touches the outer ring, it plays a piano note, so the motion also builds a gentle repeating melody. Tap or click once to enable sound, then just watch.

Frequently asked questions

Are the balls really moving in a circle?
No. Each ball moves only along its own straight line. The circle is an illusion created by their timing.
How many lines are there?
A new line is added every three seconds, up to 16 distinct lines. After that, new lines run along the same diameters.
Are there any controls?
No. Tap or click once to turn on sound, then watch.

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