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Maths of Planet Earth | Limitless Applications

A planet to discover Anamorphic_art_toy_by_OOZ_&_OZ. Myrna Hoffman

Published on June 18th, 2013 | by Jo

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Try this: Anamorphic art

You will need

  • A copy of the anamorphic grid [pdf, 29kB]Maths+Stats
  • A copy of the square grid [pdf, 20kB]
  • Pencils and textas
  • A roll of aluminium foil, or some reflective mylar film taped into a cylinder

What to do

  1. Make a picture by using the textas to colour boxes in the square grid. You could make a house, or a face, or just a pretty spiral of colours. Make sure you fill each box with only one colour – it will make the next step a lot easier.
  2. Examine your anamorphic grid. Note the grid has the same number and arrangement of boxes as the square grid, but the boxes have all been stretched. Look at the letters and numbers on the edges of the two grids – each box has its own address of one letter and one number.
  3. Look at box A1 on your square grid, then colour box A1 on the anamorphic grid the same colour. Do this for all the other boxes in the grid. Note that the letters go right to left on the anamorphic grid, and left to right on the square grid.
  4. Once you’ve finished colouring in, take the roll of aluminium foil out of its box. Stand the roll on its end, positioned on the cross in the middle of the anamorphic grid.
  5. Look at the reflection in the aluminium foil – can you see your original picture?

Maths.Stats4

What’s happening?

When you copied your picture from the square grid to the anamorphic grid, you stretched it and flipped it until it looked very different. Reflected in the curved surface of the aluminium foil, the stretched shape looks  normal.

When light hits a reflective surface, it bounces off at an angle. The angle between incoming light and the mirror’s surface is the same as the angle between mirror’s surface and the outgoing light. Think of a cricket ball bouncing off a pitch.

For a flat mirror, these bounces all line up, so the pattern of light heading towards the surface is the same as the pattern that leaves it. Curved mirrors have a changing surface, which means the pattern of light that leaves the mirror (and hits your eye) is not arranged in the same way as the light that hit it.

With a cylinder, the surface changes when you go around the cylinder, but not when you go up and down. Up and down lines in your picture stay straight in the anamorphic grid. Sideways lines have to curve on paper to look straight in the mirror.

Most surfaces around you are reflective. You can’t see your reflection in your shirt or the wall because its surface is like countless tiny curved mirrors, scattering light rather than reflecting the same incoming pattern.

More information

Anamorphic sculpture
Anamorphic art generator (program)
The maths of anamorphic art (pdf more advanced)

Photo credit: Basketball morph – Myrna Hoffman, Ooz & Oz

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