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Can't figure this out (pic)
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Moderator Emeritus  Join Date: Mar 2001
Location: Austin, MN, USA
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I don't understand this. Using what I know of triangles, the hypotenuse is 13.93 units long. The area is 32.5 square units. But this picture makes it seem like the area can also be 31.5 square units. How is this so?
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Fresh-Faced Recruit
Join Date: Sep 2004
Location: House of music.
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If that was a piece of cheese, I would say a mouse ate it.
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Mac Elite
Join Date: Aug 2002
Location: Kyoto, Japan
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The triangles aren't triangles. Look closely...they are slightly curved. This is especially visible on the top picture.
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Mac Elite
Join Date: Jul 2002
Location: Tronna
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Dang, beaten by Scifience!
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Mac Elite
Join Date: Mar 2001
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Photoshop draws a pretty straight line along the hypotenuse so I don't think it's because of any curve in the lines.
There is something interesting going on.
Areas (arbitrary units):
Red triangle=12
Green triangle=5
Orange = 7
Lt. Green = 8
The area for a triangle is basically an area for a rectangle divided by 2 (because if you inverted the triangle and lined the hypotenuses together you'd have a rectangle who's area you could calculate as lengthXwidth).
So the surface area for the top and bottom SHOULD be 32 if added up by the calculations above.
Well if you figure out the surface are for the top (5x13)/2=32.5 - a 1/2 square unit descrepancy.
The surface area for the bottom is (5x13)-2 [2 missing blocks]/2=31.5 - again a 1/2 square unit descrepancy but in the opposite direction.
The straight line distances from each apex jive if you want to get Pythagorean on me.
Still scratching my head about the surface area...
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Addicted to MacNN
Join Date: Oct 2003
Location: Far above Cayuga's waters.
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here is another one for you-
http://www.funkypages.com/leprechaun/index.php
saw this this past weekend at the local sciencenter with the girlfriend. even with this solution it doesnt make any sense.
really cool to see in person... print it out if you're bored enough.
one arrangement (15 little buggers)-
the other (14  little buggers)-
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Clinically Insane
Join Date: Jun 2001
Location: planning a comeback !
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Originally posted by Scifience:
The triangles aren't triangles. Look closely...they are slightly curved. This is especially visible on the top picture.
Yes, that's it.
I recreated the first shape in in Excel 
Then I copied and moved it to recreate shape 2, and and put a straight line on top of them.
You can clearly see where the difference comes from.
Click for bigger:
http://img.photobucket.com/albums/v4...ial/shapes.png
-t
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Mac Elite
Join Date: Mar 2001
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I stand corrected. The curve would definately be worth .5 square units...
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Moderator Emeritus Join Date: Mar 2001
Location: Austin, MN, USA
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Weird. Well thanks for the answer. I didn't see that at all. I still can't really see it on the ones I posted.
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Clinically Insane
Join Date: Jun 2001
Location: planning a comeback !
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Originally posted by Xeo:
I still can't really see it on the ones I posted.
No wonder.
Your picture has not been created like I did it, with 4 independent shapes and then moving them.
I guess your pictures have been drawn starting with the outlines of the big triangles first, and then subdivided into smaller shapes.
In that case, of course, their surface area doesn't match.
-t
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