Crazy math. Does 64=65?

[clifford_cooley]

Does 64=65? Watch this video and tell me what you think.

Crazy math.

I know why this is not accurate.
I was wondering if anyone else can see why this video is misleading?

 

[catilley1092]

That's the craziest math I've ever seen. BTW, math was not my best subject in school anyway. How did whoever come up with that?

 

[clifford_cooley]

If an angle is cut cross corner across a 2x5 square then another angle is cut cross corner across a 3x8 square. Remembering the angles need to match if they are placed side by side.

Do the angles match or would the second square need to be 3x7.5 to match the angle of the first square?

This mismatch in angles is where they gain an extra square. In other words the pieces do not actually match.

 

[greyCynic]

You are spot on. There are gaps along the internal seams and the total area left uncovered is the missing unit.

Proof:
The first two triangles have an area of 12 squares each.
The second two polygons have an area of 20 squares each.
Total area of the 4 shapes is 2 times 32 squares or 64 squares in total.
65 - 64 = 1 so there have to be gaps that the graphic hides.
Since there is no doubt about the dimensions of the outer edges of the rectangle the only place for these gaps are between the internal boundaries of the shapes.

 

[TrainableMan]

Correct, the angle of the trapezoid is not the same as the angle of the triangle but when he slips them together he makes it appear they are.