Friday, December 19, 2008

Friday's Fun Foptical Filluision (FFFF)

Well, as you know it's a tradition here at AH! that every Friday we have an optical illusion. What's that you say? We have never had an optical illusion on Friday before? Well, we have. Maybe you just didn't realize it when you were reading the seemingly normal posts on Fridays, but I bet if you go back and search you will see that this has been a tradition for some time now. Go ahead and check the last few posts on Fridays, I'll wait.

You checked? Damn. Okay, well maybe it's not a tradition, but it should be.

Anyway, here is one that baffled me for a good portion of the morning. Let's see how you do.
(My answer is below in white so you need to highlight the text with your mouse. Feel free to disagree with me or explain it in your own way in the comments)

After looking at this for longer than I care to share... I figured out that the red and dark green triangles have different slopes. The red has a slope of 3/8 or .375 and the dark green has a slope of 2/5 or .4. So when they combine them to make a "triangle" it's not really a triangle at all. It's really a 4 sided polygon.

In the top drawing, the more gradual triangle is on top, and the steeper triangle at the bottom actually makes a convex shape. Where as in the second figure on the bottom the steeper triangle is on top and the more gradual near the bottom makes the the shape concave. And believe it or not the difference in area between these shapes equals one of the squares.

Visually you can see this by matching up the points along the "triangles" or by printing it out and putting a second piece of paper connecting the two points of the hypotenuse.

Does that make sense? Do you agree or disagree?

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1 comment:

soup said...

I love optical illuision Fridays.