# woah...

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#### solrules

##### Well-Known Member
Any ideas?

The only thing that I have is that the area for the big triangle is 32.5 units^2. If you sum the small triangles and the two blocks on the top image, you get 32 units^2. If you do the same to the bottom, you get 33 units^2 (due to the extra block). Average?

It is a visual illusion.

If a finer grid is placed over the objects, even increasing the grid by a factor of 2, it becomes obvious that it is a ganged tolerance problem. Meaning .001+.001+.001=.003. This becomes significant as the level of precision increases. Machinists have to really keep an eye on this stuff or your in a tough spot at assembly time.

To solve your particular problem you will need to increase the resolution of your measuring device.

or

it could be magic!

so essentially you make everyone a little smaller and put the difference in that square?

Take a look at where the green triangle on the bottom figure ends. It is two squares high. Follow that line up to the top figure and you will see that the red triangle at that point is less than 2 squares high.

Same thing with the red triangle on the top figure. Where it ends, it is 3 squares high. Follow the line down to the bottom figure and you will see that it's more than 3 squares at that point.

I have a couple of cheap plastic puzzles like this. Check your local
\$1 store.

I kept one on my desk a few years back as an example of how to
give 110% - Built it with the square full, but an extra piece remained.
Can you add it to the whole?

As leefsmith said, this is a tollerance issue. Non-engineers are still
amazed by it though!

Ahh. I see....the slopes of the triangles are different (leading to the mismatched points). One has a slope of .375 and the other is .4 hard to notice at a quick glance. Not a triangle!

Originally posted by solrules
Ahh. I see....the slopes of the triangles are different (leading to the mismatched points). One has a slope of .375 and the other is .4 hard to notice at a quick glance. Not a triangle!

Yeah, I spotted that, althogh they look like triangles at first glance, particularly on a curved monitor, they are in fact two different quadrilaterals.

if you look closely, you can see that the hypoteneuse of the first "triangle" is concave, and the hypoteneuse of the second "triangle" is convex.

Good trick though ;-)

Originally posted by solrules
Ahh. I see....the slopes of the triangles are different (leading to the mismatched points). One has a slope of .375 and the other is .4 hard to notice at a quick glance. Not a triangle!

Yep, that's the catch. That's were the optical illusion comes in, it *looks* like a straight (fixed) slope so your mind accepts it as such.

Originally posted by leefsmith

it could be magic!

yes,yes its definately magic

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