It’s an Illusion, Part 4 – Planes Cross Through Each Other

2 Intersecting Planes

The concept is simple enough, in theory, and provable mathematically.  Planes exist, and they can intersect, or cross through, one another.  To understand how this works you have to know that planes are two dimensional surfaces (they have height and width, but not depth), and that they are flat and level.  They can also be any shape (square, rectangular, triangular, circular, oval, etc) and any size.

Any planes that are not parallel to one another cross.  They can cross each other along a line (a sheaf of planes), or through a point (a bundle of planes). As different planes cross they create interesting patterns and shapes.

3 Intersecting Planes

Imagine what we might create if we could actually use intersecting planes.  Escher imagined, as you can see in “Intersecting Planes”, birds and fish on different planes and those planes passing through each other.  And so have others – creating the illusion of intersecting planes has become popular in origami.  It’s fascinating to watch Tung Ken Lam create a shape that shows what several intersecting planes might look like.

But it’s still just an illusion.  For now, anyway.

Images:

M. C. Escher, Intersecting Planes.

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