Area / Optical Illusion... how can this be?

Question

I found this optical illusion...

http://www.eyetricks.com/1406.htm

This is really bugging me! Help!

Thank you! I cut out the squares and examined the shapes. Now I can see how the gap makes up the area of the extra square.

Answer 1

They don't really fit together. Look at the yellow piece. The slope of it's hypotenuse is 3/8. In five steps to the side it goes (3 * 5)/8 or 15/8, just a bit less than 2.

Look at the pink piece. It's slope is 5/2, or when turned sideways, 2/5. In five spaces, it's going to go 2, not "a bit less than 2."

The two slopes are not identical. The pieces don't fit.

If you cut out the pieces in the square on the left and tried to arrange them into the shape at the right, there would be gaps.

Answer 2

The left-hand figure is a perfect fit. The right-hand figure is not a perfect fit, and the tiny little imperfections add up to exactly 1 square unit.

Proof: The slope of the trapezoid is (2/5) = .4
But the slope of the triangle is (3/8) = .375
So when the trapezoid is next to the triangle, the lines are NOT congruent, in spite of appearances.

Answer 3

Well two shapes are exactly equal to each other even if they are cut to pieces and arranged another way. That is one basic rule of geometry. Look at the shapes and you will realize they are not equal.

Good luck.

Answer 4

the asnwer is that the slopes of the lines do not match. there is a thin parallelogram between the upper and lower shapes, whose are is 1 square,

Answer 5

we did this in math a week or two ago. There is nothing to it. If the site did it corectlyy you would notice a small hole thats visible. You can try it at home and you can see the hole yourself. =)