# An optical illusion

Here is a picture. What is odd about it?

Some suggestions:

• Look at each individual corner: does it look sensible? (I think they each do, more or less.)
• Look at each individual triangle, going round the sides clockwise or anticlockwise: does it look sensible? (I think not: each time I get to a corner I feel I have to change my previously assumed viewpoint, so each one ends up looking twisted despite the straight edges.)
• Look at pairs of triangles: red and green, then green and blue, then blue and red: are they interlinked or is one resting on another? (I think that once it is possible to ignore one triangle, it becomes possible to see that the other two are not interlinked as pairs, and that the red triangle rests on the green triangle, the green triangle rests on the blue triangle, and the blue triangle rests on the red triangle.)
• Look at the three triangles together: since no pair of triangles is interlinked, can the the three be unentangled? (I think it looks as if they cannot, which is indeed the case, but why not is harder)

The picture above is a combination of the two classic pictures below:

The first of these has three rings and is known as the Borromean Rings. Although they are interlinked as a triple, no pair of them is linked; remove one of them and the other two are not linked. They cannot actually be made as ordinary circular rings, though they can be made out of string or other shapes in three dimensions.

The second is designed to seem to be a three-dimensional triangle. Following the sides round (either clockwise or anti-clockwise) reveals the changing perpective and why this is known as the Impossible Triangle.

Do you think that the top picture works as an optical illusion? Or is it just too complex? Any comments would be welcome.

Here is another impossible picture using a similar structure:

The top of these three pictures intertwines two impossible rectangles to make a mysterious cross.

The second pretends to show how to construct an impossible rectangle by combining the optical illusion of a cricket wicket with its own rotation.

The third shows the intertwining of two elliptical shapes (which would requiring some bending in three dimensions to be possible).

Returning to triangles, here are two knots: a left-handed trefoil knot and a right-haded trefoil knot. Does either look better than the other?

© Henry Bottomley October 2001and June 2002. How about looking at circumnavigating a cube and a tetrahedron? Or the 216, 212, 22 or 8 browsersafe colours for web pages? Or Pythagoras's theorem in moving pictures? Or seven formulae for the area of a triangle? Or Medians and area bisectors of triangles? Or Java World Map Projections (including a triangular equal area projection).