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The angles of an equilateral triangle

From: Designs dekeConstructed: Animating a Mind-Bending Illusion

Video: The angles of an equilateral triangle

Now, one of the first things that we need to do is create this central guideline,

The angles of an equilateral triangle

Now, one of the first things that we need to do is create this central guideline, that's running through the triangle, and it's here to describe the motion of the ball. And this guideline is going to help us position the ball in the proper five locations, which is really important because every single one of these positions right here one, two, four, and five need to be in a straight line with each other. And then these guys right here two, three, and four. They need to be positioned around the corners of an equilateral triangle.

So, they need to be aligned with each other as well. Which means we need to understand the angles of the edges that we're working with. Which, not surprisingly perhaps, is the topic of this movie. So, I'll go ahead and switch over to this demo file right here. And even though we have an impossible triangle this the upright version of the triangle as you may recall. It is equilateral and all that means is that it has three equal sides, and the angles of those sides are these right here, at least were illustrator is concerned.

This is how it measures angles. So, this edge right there is horizontal, and therefore zero degrees. This next edge over on the left hand side is angled at 60 degrees. And the right hand edge is angled at 120 degrees. And to see how that manifests itself inside of Illustrator, I'm going to go ahead and select the line tool. And I'm just going to click somewhere inside, let's say, this first angles layer. So, I'll go ahead and select it there in the layers panel and then click. And I'll set the link to 100 pixels and the angle to 60 degrees, and then I'll go ahead and click Okay, and you can see, especially if I increase the line width here a little bit.

And I'll press the v key to get my black aero tool. See if I drag this guy over, that its angle exactly matches the edge of our original upright triangle. Now, where the angles become important for us. Is in terms of motion. So, lets say I need to extend the length of a line segment, which is something that we'll need to do in the very next movie. Then I need to know what extending in a 60 degree direction even means. Which is why I have this layer right here called first directions, I'll go ahead and turn it on and these arrows indicate the movement associated with each one of these angles.

So, if you move something 60 degrees, you're moving it up and to the right. If you move it 120, you're moving it up and to the left. And if you move it 0 degrees, you're moving it straight over to the right. Now, everything changes when we rotate the triangle. So, I'm going to go ahead and turn these layers off, and turn on this one called Sideways, which represents the current state of our impossible triangle. It's still equilateral. Every single one of the edges is the same length, but now its angles have shifted. So, what used to be the horizontal edge is now vertical at 90 degrees.

And we've also got a 150 degree edge, as well as a 210 degree edge. That's the same, by the way, as an angle of negative 150 degrees. At least where motion is concerned. So, let's say I want to move something down, and to the left. Why then I'll go ahead and turn on my second directions layer right here, and you can see this arrow is a direction that's associated with 210 degrees, or negative 150 degrees. Meanwhile if you move something 90 degrees, your moving it straight up.

And if you move a point positive 150 degrees, then you're sending it up and to the left like so. Now the most important motion for us is going to be this one down here, down and to the left. So, just remember it's going to be 210 degrees, or negative 150. And we'll see what that looks like in the very next movie.

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