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Explain this to me ...

Martin

Martin

Active Member
I can't, for the life of me, figure this one out:

trigrid.gif


Good luck.

Cheers, Martin :cool:
 
Look at where the top of the triangle crosses the graph lines. It's pretty simple if you just pay attention. The area covered is exactly the same in both diagrams.
 
Sorry, just realised that you've put an image on which is blocked by the browser in my work. All I can see is a dot where the picture should be. :(
 
It's the one with the different shaped blocks that make up a triangle, and then when you rearrange them to not make a triangle there's a 'mysterious' gap.
 
Litany, if that's an explanation you've just given, I don't get it. Explain it to me, in detail.

They used the same 'pieces', and the area covere is exactly the same; how can there be an opening there then? Where is that opening in the top one?

Cheers, Martin :cool:
 
As I can't see it I can only guess it's something that I seen recently. If it's two right angled triangles, then the missing area is due to the angle of the hypotenuse. Neither are a straight line. The hypotenuse of the full triangle actually contains an obtuse angle while the triangle with the missing piece has a reflex angle.
 
Don't think of it as a triangle then. Think of it as a rectangle, only not all the pieces are coloured in and made into segments. Everything is still covering the same area, they're just in different places. The bottom shape isn't a triangle, I think that's an important thing to remember as you look at it.

The intersection across the grid is higher for the sloping line, so it's cutting deeper into the square, so that's where your blank square at the bottom is coming from. I can't explain it more technically than that, I haven't done maths for years, and pure maths completely messed up my head and made my attempts to explain anything worthless. There's probably someone here who can explain it much better than me.
 
As I can't see it I can only guess it's something that I seen recently. If it's two right angled triangles, then the missing area is due to the angle of the hypotenuse. Neither are a straight line. The hypotenuse of the full triangle actually contains an obtuse angle while the triangle with the missing piece has a reflex angle.
Click to expand...

The intersection across the grid is higher for the sloping line, so it's cutting deeper into the square, so that's where your blank square at the bottom is coming from. I can't explain it more technically than that, I haven't done maths for years, and pure maths completely messed up my head and made my attempts to explain anything worthless. There's probably someone here who can explain it much better than me.
Click to expand...

Another way to think of it is like lenses. One hypotenuse is concave, the other convex.
Click to expand...

Yeah. Uh huh.

*nods sagely*

Cheers, Martin :cool:
 
Mile-O-Phile said:
Then clean up the mess after your information triggered lobotamy. :eek:
Click to expand...


Look everybody, Mile-O tried to make a funny.

There may be hope for him yet. :)

RaVeN
 
How about this then? The shapes are cut in such a way that you can't rearrange them in the way shown to make the same triangle. You can't make a triangle at all. It's like tangrams. They only fit together in a certain way. The shape that's closest to a triangle, looks like it's the same triangle, only it's got this gap in it.

So look at the slant of the shape. Compare each square with the original triangle and you'll see it cuts through the vertical line in a higher position than did the original. It's not the same triangle fitting in the same area, it's a different shape entirely, but because the area of that little square is spread out across the whole of the slope it's not as obvious to the eye.
 
Mile-O-Phile said:
Go on, say it: they tesselate :)
Click to expand...

Noooooooo! You'll never make me say it.

How about everyone prints out the original triangle and then rearranges the bits, then we'll reconvene after a short break for naps.
 
Mile: you bloody show-off you!

Litany: I think I get what you're saying. That said, I'm gonna lie down now, because my head hurts.

Cheers, Martin :cool:
 
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