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this was so ridiculous it needed its own thread


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Guest SayOne

The two triangles do not have the same proportions. So the first image may appear as a triangle, but is in fact a tetrahedron.

 

When you do a little calculation (let's say the grid-unit is centimeters), the tetrahedron (the real thing) obtain the area of :

 

5 cm * 2 cm * 0,5 + 8 cm * 3 cm * 0,5 + 7 cm2 + 8 cm2 = 32 cm2

 

and below the octahedron obtain exactly the same area; the hole is just a way of explaining the illusion.

 

the dark-green triangle partition (rectangular), has an angle of : arctan (0,40) = 21,801°

the red triangle partition (also rectangular), has an angle of : arctan (0,375) = 20,556°

 

We hereby conclude that the intersection between the dark-green and the red triangle, is not a straight line, but two lines, presented with an outside angle of 181,245° - and this appears as one line.

 

The hole (let's call this A) is obviously 1 cm2.

 

This can and may be presented with a little use of trigonometry:

 

 

http://www.grand-illusions.com/trig.gif'>

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Guest JESTER

Its not that complicated...when you switch the obviously two different sized triangles the negative space(where the green and yellow pieces sit) those dimensions change from a rectangle that is 3 cm high by 5 cm long to a space that is 2 cmhigh by 8 cm long....Therefore you have to organize the green and yellow pieces to sit comfortably allowing that gap to come into play....its simple geometry ...

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Guest imported_El Mamerro

Jester loses, SayOne wins, although by cheating for looking for the solution, and getting overly complex about it.

 

Simplest way to put it: The big diagonal line (hypotenuse) is not really a straight line, which gives the top triangle an area of 32. The other half that would make the rectangle is represented by the bottom figure, which should have an area of 33 cm2, but the offset with the blank space makes it 32 cm2 and therefore constructable (is that a word?) by the same shapes as the ones above.

 

I'm gonna smoke a Hoyo de Monterrey right now.

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