Question

Dear Mitch,

I am having a little trouble drawing a 3d pyramid. Every time I try I can't see the optical illusion even though everybody else in my family can, maybe because I'm only six-and-a-half-years-old, and everyone else in the family is older. But if you have any advice for drawing 3-d pyramids that could help, I would really like to try it.

Sincerely,
Thomas Reywas

Answer

Hi Thomas,

First, you should know something that a lot of people seem to NOT know, or forget: pyramids don't HAVE to have only three sides (not including the base, or bottom part). I think some people think that pyramids have three sides because all triangles have three sides, but pyramids can have 3 OR MORE sides, as long as each side is a triangle! (Again, I'm NOT counting the bottom as a ''side", because that bottom can have 3 sides OR any number of sides MORE THAN three. And most pyramids people see in books and other places have four sides (not including the bottom).

Anyway, there are two ways that people seem to want to draw them: They either want their drawing to look like a see-through pyramid, like it's made of glass, or they want it to look like a solid pyramid (that you cannot see through).

I think it's a little easier to draw a solid one, so I'll explain that one first.

AND...

I'm going to try to do it so simply and magically that you just have to follow two short sentences of instruction, and I won't even draw the picture for you so you can see the magic happen on your paper for yourself!

Okay:
STEP 1:

Draw a diamond shape, just like the red diamond on the Queen of diamonds, or the diamond on the four of diamonds, or the diamond from any other diamond-card from a deck of cards. So, what you have on your paper should look a little like a kite that got away from the string.

STEP 2:

Draw a straight line down the center of the diamond, connecting the top point to the bottom point. Then STOP!

Give your eye and mind a chance to adjust; sometimes it's good to look at something else for a minute or two.

Then look at your drawing. Notice anything?

(And if you really want to give it a 3-d look, take a pencil and try shading one side a little darker than the other, and then maybe give the whole pyramid a shadow going off to one side.)

Tell me how it looks after you try it!

OKAY, now, for the see-through pyramid, which is just a tiny bit trickier, try this method:

STEP 1:

Draw an ISOSCELES triangle. (If you can 't remember which one that is, look at the answer I gave a few weeks ago about triangles -- click here!)

STEP 2:

Draw a short straight line down from the top point and continue until you reach the middle of the open space inside the triangle. Do it slowly, and when you get halfway down the inside of the triangle, STOP.

STEP 3:

Go back to the bottom end of that short line you just drew and connect that point to the bottom LEFT corner of the isosceles triangle that you started with.

STEP 4:

Go back to the same point at the bottom end of the short line hanging straight down from the top, and this time moving in the opposite direction draw a short line connecting that point to the bottom RIGHT corner of the isosceles triangle you started with. So now you should have a giant upside-down Y cutting your triangle into three triangles.

Now, put down your pencil and take your eyes off the picture you just drew and look at something else for a moment or two.

Now go back to the drawing. Take a look at it. Notice anything?

--Mitch

P.S. Just remember that when it comes to pyramids, they always try to make a good point! (That's a little math joke!)