Visit the Tim's Toy Shop, at
https://www.grand-illusions.com/
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This simple little experiment shows something that we find quite profound.
Create a random pattern of dots on an A4 sheet of paper, and then make an identical copy of the dots on a sheet of acetate. It is important to make sure you are using an acetate that is designed to work in a photocopier!
Place the acetate on top of the sheet of paper, and align the two sets of dots.
Then. move the top sheet slightly, giving it a slight rotation. Immediately a circular pattern appears, around the point of rotation. It works the other way, in that if the acetate sheet has been placed randomly on the top of paper in such a way that the dots are not aligned, and a circle of dots appears, place your finger tip in the centre of the circle and rotate the acetate sheet in order to move it into perfect alignment.
Tim then goes on to show other experiments when the acetate size is made slightly bigger or slightly smaller than the paper sheet.