Category Archives: Playing With Light

Playing with light, part two

Consider a second pyramid.

Second pyramid
Second pyramid

There are twelve shadings of this pyramid.

Shading Thirteen
Shading Thirteen
Shading Fourteen
Shading Fourteen
Shading Fifteen
Shading Fifteen
Shading Sixteen
Shading Sixteen
Shading Seventeen
Shading Seventeen
Shading Eighteen
Shading Eighteen
Shading Nineteen
Shading Nineteen
Shading Twenty
Shading Twenty
Shading Twenty-one
Shading Twenty-one
Shading Twenty-two
Shading Twenty-two
Shading Twenty-three
Shading Twenty-three
Shading Twenty-four
Shading Twenty-four

Consider combining the two pyramids in a single square.

Two Pyramids
Two Pyramids

If there are twelve ways to shade each of these pyramids, there are 144 different ways to shade them both.

Playing with light, part one

Imagine a triangle drawn within a square.

1st triangle
Triangle-in-square

Now, group four squares into a block.

Triangle-in-square block
Triangle-in-square block

Not very exciting, is it?

Now add three converging lines to the interior of the triangle. The flat triangle becomes a three-sided pyramid.

Pyramid-in-square block
Pyramid-in-square block

Now, let’s play with the light.

This pattern of pyramids implies a light source that shines on all faces at once.

Pyramid plane
Pyramid plane

If we imagine lowering the light source, then only one face at a time is lit, casting the other two faces in shadow. When the light source hits a face full on, the other two faces are in complete shadow. When the light source hits a face toward one end or the other, the neighboring face is in partial shadow, and the third face is in complete shadow. When the light source hits two faces at once, the third face is in complete shadow.

There are twelve different shadings for this one pyramid.

Twelve o'clock shadows
Shading One
Shading Two
Shading Two
Shading Three
Shading Three
Shading Four
Shading Four
Shading Five
Shading Five
Shading Six
Shading Six
Shading Seven
Shading Seven
Shading Eight
Shading Eight
Shading Nine
Shading Nine
Shading Ten
Shading Ten
Shading Eleven
Shading Eleven
Shading Twelve
Shading Twelve