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Trivia (merged)

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vowels.

Too many letter puzzles in a row makes it easy to notice things like that. :)

Another oldie. I doesn't work so well when written out.

What's long, round, hard, and full of semen?
 
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The second triangle is formed by rearranging pieces used to create the first. Yet there is a strange gap in the second triangle. Has area vanished? Is the conservation of matter bogus? Explain this madness.
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triangle_area.gif
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The blue and red pieces are not proportioned such that conservation of matter applies. Put simply, the first collection of shapes does not form a triangle, but a quadrilateral. The area of both figures is the same, but neither is a triangle.
 
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vrbryant said:
The blue and red pieces are not proportioned such that conservation of matter applies. Put simply, the first collection of shapes does not form a triangle, but a quadrilateral. The area of both figures is the same, but neither is a triangle.
Click to expand...

In my eyes, the area of each shape is not the same. The top "triangle" is a quadrilateral with a concave "hypotenuse". The bottom "triangle" has a "hypotenuse" that is convex, meaning that the bottom shape has a larger area.

I don't have the official answer, but that's my understanding of it.
 
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Bucky Katt said:
In my eyes, the area of each shape is not the same. The top "triangle" is a quadrilateral with a concave "hypotenuse". The bottom "triangle" has a "hypotenuse" that is convex, meaning that the bottom shape has a larger area.

I don't have the official answer, but that's my understanding of it.
Click to expand...

I'm pretty certain the area is the same. The bottom shape's convex "hypotenuse" is what compensates for the 1x1 unit of area missing from the base.

Area of red shape = 5 units
Area of blue shape = 12 units
Area of yellow shape = 7 units
Area of green shape = 8 units

Sum of the areas is 32, area should be 32 for both, since the shapes don't change.
 
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vrbryant said:
I'm pretty certain the area is the same. The bottom shape's convex "hypotenuse" is what compensates for the 1x1 unit of area missing from the base.

Area of red shape = 5 units
Area of blue shape = 12 units
Area of yellow shape = 7 units
Area of green shape = 8 units

Sum of the areas is 32, area should be 32 for both, since the shapes don't change.
Click to expand...

Right, but the area of the top shape is 32 units and the area of the bottom shape is 33 units.

I suspect we are, more or less, saying the same thing. The fact that the hypotenuses of the two small triangles do not have the same slope means that the two larger shapes are not, in fact, identical.
 
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Bucky Katt said:
Right, but the area of the top shape is 32 units and the area of the bottom shape is 33 units.

I suspect we are, more or less, saying the same thing. The fact that the hypotenuses of the two small triangles do not have the same slope means that the two larger shapes are not, in fact, identical.
Click to expand...

Stupid meeting... I'm missing out on puzzles here!

The area of the bottom shape is not 33. It would be 33 only if there were not a 1-unit square gap. Because they are not triangles, you cannot use b*h/2 to calculate area, which, in you could calculate it, would equal 32.5.

Edit - what I just typed doesn't really make sense. Never mind. You're both right, however you want to explain it.
 
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