![]() ![]() If I slice this, the right angle (not any right angle - 90º -īut 'the right angle' - the proper angle. If I try to draw the plane - but you get the actual idea: This could be,Īnd alike I'm gonna draw the plane - yet maybe it won't be so obvious Right over here, like this, and then you slice this side Quite like that, now you slice this side, Like that, this back side that you can see, Right over there, like this, Imagine slicing this backside, we'll do it a little bit different - so imagine slicing the top, Think about it: How can you get a pentagonīy slicing a cube with a plane? All right, so here I go, this is how you can get a pentagonīy slicing a cube with a plane: Imagine slicing the top Some really interesting things: Can you get a pentagonīy slicing a cube with a plane? And I really want you to pause the videoĪnd think about it here, because that's such a fun thing. You can do an isosceles, you can do scalene triangles. So actually you're not gonna be able to do an obtuse triangle either. So you can't quite have an exactly a right angle,Īnd so since you can't get to 90º, sure enough you can't get near to 91º, Who'd still be less than 90º, you can approach 90º. Really, really close, like here, you would approach having a right angle,īut it wouldn't be quite a right angle: you'd still have these angles If you pushed this point up more,Īctually I'd do that in a different color, you were going to haveĪn isosceles triangle. On this space of the cube, that's gonna be an equilateral triangle. You could constructĪn equilateral triangle, so as long as this cut is the same lengthĪs this cut right over here, is the same length as that upper length, or the length that intersects I can keep drawing the plane, but I think you get the idea - this would be a triangle. You can cut this side over here, this side right over here, and this side right over here, and then, this is it - of course If you think you can figure it out, triangles are not so bad. But what about triangles?" Well, once again pause the video I can get a square, I can get a rectangle. "Ok, that's not so hard to digest, that if I intersect a plane with a cube, That magicians use to saw people in half, or pretend like they are - they give us the illusion of sawing people in half, it might look something like this. If you imagine the plane just like one of those huge blades Let me shade in the stuff, if you kind of view this, So it might look like this, and once again That I'm cutting with, and my cube is going to beĪ rectangle. That I'm actually cutting with, so the intersection of the plane That you are cutting with so, the intersection, let's see: This could be the plane Right over there, then the intersection of the plane I think you'd see where this is going, this side like that, and then you cut the bottom, You can actually cut like this: So, if you cut this side like this, and then cut that side like that, and then you cut this side like that That I'm talking about? Well for a rectangle On your own: How can you get these shapes How can you get that? And at any point, I encourage you: Pause the video and try to think about it ![]() ![]() So a square isĪ pretty straightforward thing to get, if you're doing a planar slice of a cube. it could look something like this.Īnd I can even color in the part of the plane that you couldĪctually see it the cube were opaque, if you couldn't see through it.īut if you could see through it you would see this dotted line,Īnd the plane would look like that. Let me see if I can do a decent,Īs you see you'd say a part of the plane, that is cutting this cube. ![]() So you can imagine a plane that did this, and if I wanna draw the broader plane, Of the glass cube, where you will see it, right over there, dotted line, and then it cuts this, right over here. We are to cut, just like this, the square is maybe the most obvious one, so it cuts the top right over there, it cuts the side, right over here, it cuts the side, I guess on the back To get the intersection of this cube, and that plane to be a square? We'll imagine that that plane So what am I talking about? Let's say we wanna deconstruct a square: How can we slice a cube with a plane Is explore the types of 2D shapes we can construct,īy taking planar slices of cubes. ![]()
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