Hi I'm Henry Segerman, and this is an impossible triangle in real life.
And well here it is. I can take this screwdriver and poke through the hole in the triangle,
and as you can see it all looks reasonable. Usually this design is drawn in 2D,
looking something like this. It's often called the "Penrose triangle", named after mathematician
Roger Penrose and his father Lionel Penrose. As is often the case however, it was first
discovered by someone else: artist Oscar Reutersvärd.
So what makes this design impossible?
We see three apparently flat faces of some three-dimensional object,
and then the problem is how close different parts of the object are to where the viewer is.
So this face here turns a corner and it sort of covers up part of this face here. And so that
means that this thing must be in front of this thing. Well we continue on around: this face turns
a corner here and covers up part of this face back here. So that means that this thing has to be in
front of this thing. And we continue on around: this turns a corner here and is covering up part
of this face in here, and so that means that this bit has to be in front of this bit. And so
as we've gone around the triangle, we keep moving further and further away from the camera, so that
means in particular that this bit here has to be further back than itself. And that's impossible.
So this real life impossible triangle must be cheating somehow.
This model designed by someone called tato_713 shows one way to cheat.
Here the faces are not flat. This means that the faces can be in front of each other at
the corners in the right way, but then they can bend backwards to get into the correct
position at the next corner. So that we don't move backwards overall as we go around the triangle.
However you can kind of tell from the lighting that the faces aren't flat. If we can't fake flat
faces then, well, the faces better be flat. Now there is an easy way to make something
that looks like this and that has all of its faces flat, but you're not going to like it.
You can just draw the design on a flat piece of paper and be done with it.
But then we aren't really talking about a 3D object and the different faces wouldn't be
lit differently. You have to draw a line to show the difference between this face and this face.
So if we want flat faces, and we want the faces to point in different directions so that they
can be lit differently, we have to give up on the faces meeting properly at the edges.
That's what's going on with this design. And well, it turns out that there's more
to getting the lighting even than just having flat faces.
The faces here tilt past each other, and when they do you can see the shadows changing.
So this doesn't work well either: you can tell when the faces aren't meeting properly.
Okay so if the faces have to be flat and they have to meet each other properly, what do you do?
Well all you can do is have them mostly meet properly, and not draw attention to the place
where they don't meet properly - which is here.
In this design the faces do get closer to you as we go around the triangle,
except that there's one pair of apparently neighboring
faces - this face and this face - which are not actually neighboring.
With the camera in the perfect position and lighting carefully chosen, it's pretty difficult
to see where the cheating is. Right now I've got a soft light shining from above in this direction.
However, if I turn on this hard light shining more from the left and I turn off the overhead light,
you can see that there's this edge on the side which is really standing out. What's happening
here is that the light's coming in here and it's sort of diffusing a little bit through
the face which is on the side here, and it's lighting up what you see from the front here.
And of course it shouldn't do - it should be shadowed by this bit back here which,
well it doesn't because they're not actually in the same place, and so this destroys the illusion.
All right, that's my fake impossible triangle. Thanks for watching!