#### smryan

##### Perspective.
Spoiler alert - text in white below
Its an optical illusion - the slope of the red triangle and the slop of the green triangle are not the same. In the top configuration they go slightly "concave", in the bottom they go slightly "convex" - the difference between the two is 1 square's worth.

K

#### keego

Spoiler alert - text in white below
Its an optical illusion - the slope of the red triangle and the slop of the green triangle are not the same. In the top configuration they go slightly "concave", in the bottom they go slightly "convex" - the difference between the two is 1 square's worth.
I never did buy that explanation. You can cut these shapes out of graph paper, with the 2 triangles having the same slope, and duplicate this re-arrangement and get the hole. Something else is going on.

#### smryan

##### Perspective.
OK. The excel sheet has the math behind my above statement.

#### Attachments

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#### keego

Can't open the file smryan. Can you save down to v2003 SP3 and repost?

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Spelling it out without Excel

The slope of the red triangle is 3 over 8 = 0.375
The slope for the dark green triangle is 2 over 5 = 0.4

So, in neither picture is the Big triangle really a Triangle! One convexes out just slightly, and the other convexes in slightly, and the difference over the lenght of the apparent hypotenuse is an entire square.

#### smryan

##### Perspective.
Sorry - didn't even think about version issues

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#### keego

Thanks all, it's mathematically sound. But that still doesn't explain why I can cut these shapes out of graph paper (and using a straight edge to draw the hypotenuse) and duplicate the 'hole'.

#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
Thanks all, it's mathematically sound. But that still doesn't explain why I can cut these shapes out of graph paper (and using a straight edge to draw the hypotenuse) and duplicate the 'hole'.
Because it is NOT a hypotenuse. Neither big shape is a triangle. The top shape (which is 4 sided) is not the same shape as the lower shape (which is 4 sided).

K

#### keego

I believe you Steve, and the math. But I suggest you perform this exercise with graph paper, a steel rule, and scissors. Then you'll see what I'm talking about.