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

Let’s Weave a Celtic Knot! Found knots

I found a Celtic knot in a coloring book.

I copied and enlarged it to fit a sheet of paper. There are two cords in this knot. I made five copies and cut out the outlines of the cords.

Cord outlines
Cord outlines
Cord outlines
Cord outlines

I glued the lighter outlines to the darker outlines. For one outline, I put a spot of glue at the spot where the outline is under the other one. For the other outline, I cut open the spaces where the outline is under the other one.

Glued or cut cord outlines
Glued or cut cord outlines

I used the fifth copy as a placement guide. I positioned one outline on the guide, then put the other on top of it, gluing the two outlines together.

Glued outlines
Glued outlines

Slide the cut ends under the other outline, and the knot is complete.

Complete knot
Complete knot

 

Let’s Weave a Celtic Knot! D11D

Download and print three copies of D11D. This knot is similar to B11B.

D11D
D11D

Determine the outline of the cords in the knot. The cords may cross over themselves, forming loops in the outline. Color or decorate the separate cords as you wish. Leave one copy blank.

Three copies
Three copies

Cut out the cord outlines.

Cord outlines
Cord outlines

The two cord outlines in this knot are identical. The cords cross over themselves to form three loops (one is very small). Along each loop, two parallel lines indicate where the other cord crosses over it. For each loop, cut open one (and only one) of these spaces.

Use the third printed knot as a placement guide. Look at the end of the knot closest to you to determine which outline goes on top of the other. Look for the first crossing of the two outlines. Place the cut outlines in position on the guide.

Layered Outlines
Layered Outlines

Working from the bottom up, either slide cut ends under or bring cord outline to the front, until you reach the top.

Completed Knot
Completed Knot