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Geek Culture / Odd geometric behaviour

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C0wbox
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Posted: 30th Nov 2009 01:21 Edited at: 30th Nov 2009 01:24
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Well, it doesn't need much of an explanation, just rearrange the shapes that make up the top triangle, and bam, there it is. (A gaping hole)


Anyone understand why this happens?

As someone who enjoys his mental-geometric manipulation and understanding, this phenomenon induces primal fear to my brain.

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David R
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Posted: 30th Nov 2009 01:29 Edited at: 30th Nov 2009 01:31
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Because the green and purple parts have two surfaces on which they can connect (vertically for the first image and 'one notch down' causing the green to jut out sideways like the second image). The latter form gives enough width for the yellow and red to swap places whilst also creating a gap. There's nothing more to it I don't think..

09-f9-11-02-9d-74-e3-5b-d8-41-56-c5-63-56-88-c0
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Sigh
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Posted: 30th Nov 2009 01:29
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The key lies in comparing the red & yellow triangles.

I'll leave it here Don't wanna give the complete answer myself.

Keep your Hope & Change to yourself, I choose Liberty! Stop by for a chat! [IXE]Nateholio on irc.maxgaming.net:6667 #GarageGames
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C0wbox
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Posted: 30th Nov 2009 02:01 Edited at: 30th Nov 2009 02:04
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Lol, I can see how it happens, but how is the area changing?

The top triangle has an area of 32.5 squares and the bottom triangle has an area of 31.5 squares yet the pieces all have the same area.
Yellow triangle has an area of 5, green thing has an area of 7, blue thing has an area of 8, red triangle has an area of 12. (5+7+8+12=32)

So in other words, the overall triangle should be somewhere between 32.5 and 31.5?

EDIT:
I just understood what you meant about the red and yellow triangles.

They aren't congruent. The whole shape isn't actually a triangle.

Still, surely the areas should be the same regardless of this change? (I don't see why there would randomly be a missing square)



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AndrewT
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Posted: 30th Nov 2009 02:23 Edited at: 30th Nov 2009 02:27
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Sigh is right.

Here's an image I made to make it clearer:



Compare the corresponding circled areas on the two triangles. They aren't actually triangles. If they were, the area of the top one would be (13*5)/2 or 32.5, and the area of the bottom one would be 31.5. however, since the hypotenuses of the red and yellow triangles have different slopes, you can't calculate the area that way. The actual area is the area of each shape added together, or 32.

It's still a very neat trick, though.

i like orange
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C0wbox
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Posted: 30th Nov 2009 02:48
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Yeh, that all makes sense, but I still don't see where this square at the bottom has gone? xD

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demons breath
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Posted: 30th Nov 2009 02:51
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It's gone to make up the space for the rest.
In the same way that if I had something going
::
:::
and then it became
:::
: :
There are the same amount of colons there, they've just moved.
The area is still identical, the shape is just different.

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AndrewT
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Posted: 30th Nov 2009 02:54 Edited at: 30th Nov 2009 02:54
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Yes, demos breath is right. If you look at a point on the hypotenuse on the first "triangle", it will be lower than the corresponding point on the hypotenuse of the second "triangle".

i like orange
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demons breath
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Posted: 30th Nov 2009 02:55 Edited at: 30th Nov 2009 02:59
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To emphasise this, you could copy one picture over the other. You will see if you put the top one over the bottom then they will not line up.

EDIT: In fact, here it is. The top triangle is the purple one, the other is the pink. The line of pink is where they do not match up



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C0wbox
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Posted: 30th Nov 2009 03:10
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Ah I see, I was under the impression the point on the hypotenuse was just shifting up and down the length of it, not up and down vertically. xD

Thanx everyone

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dark coder
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Posted: 30th Nov 2009 07:00 Edited at: 30th Nov 2009 07:00
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Reminds me of this:



How many people do you see?

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Lemonade
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Posted: 30th Nov 2009 07:26
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Quote: "
How many people do you see?"


I've seen that before, and I still don't get it.
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