From where comes this 'hole'?
eric
::28 apr 2005 :: 09:53pm
The pieces are the same size! They should take up the same space. The universe is playing tricks on me - and I hate that.
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The pieces are the same size! They should take up the same space. The universe is playing tricks on me - and I hate that.
It's a crappy drawing, meant to trick you. Note that, in the top drawing, the green triangle comes to a point on a grid intersection point. Follow the vertical line down, the red triangle doesn't pass through that point: the shapes are NOT exactly the same. The extra area comes from the fact that the new triangle is slightly larger.
Thank you, Nobody. I had seen that a while ago and was confused how this could have been missed.
The crappiness of the drawing can't help but when drawn perfectly to scale, in a CAD program for example, this "illusion" still holds true. With the base dimension of a simple 1 unit the larger triangle has a slope of (3 units)/(8 units)=.375 while the smaller has a slope of (2 units)/(5 units)=.400 which is just over 1° of difference. This produces a slight "sag" to the overall diagonal when the larger triangle is on the left and a slight bow when it is on the right. The area of this sliver of difference in fact equals the missing 1 square unit.
The hypotenuses of both the triangle have different slopes. So the overall big structure can't be considered a triangle. If considered, the hypotenuse of the overall structure is bent inside in the first figure and bent outside in the second figure covering up larger area which came from the "hole" !!!
it `s too difficult
These aren't triangles so end of discussion.