Wednesday, June 20, 2007

Genius

Think you're a genius? Can you solve this?
I took me a while, but there is an answer... I'll give you a clue, think back to high school trig and the ratios that apply to triangles.

I'll post the answer in a few days...

12 comments:

Onyx Stone said...

That's a good one. I got it after a bit of looking - but I won't spoil-the-fun / end-the-suffering by posting my answer ;-)

Anonymous said...

Yeah... right... :)

Onyx Stone said...

You must first check what assumptions you make.

There is actually no problem to solve if you make no false assumptions.

Lord Nazh said...

false assumptions will kill you quick though :)


Got one for you; can you make a triangle with 3 90 degree angles?

Onyx Stone said...

nazh, is that on a flat surface?

Peter said...

The discussion here is sounding distinctly Vulcan, Onyx's comment could have been a quote from any one of the Star Trek movies... :)

I'm impressed you guys find it straight forward, I thought it was scam at first, even now, as Pooh bear would say, "It hurts my thunker..."

Lord Nazh said...

onyx: can't give any more info to the problem (as that is part of the problem you have to figure out)

"Are you stuck?" asked Rabbit. "No," said Pooh, "I'm just resting and thinking and humming to myself." said...

OK, as things are digressing, here's the answer, the red and green triangles look like they're identical but at a different scale, but they're not.

If check the height/base (tan) you'll see they're slightly different.

The hypotenuse of the two composite triangles (meaning the green, red, orange and leafy green areas) are every so slightly different. In fact, they curve and cause the overall triangle to curve differently depending on where they are... and there in lies the extra space.

That's about all I figured out, the rest of the answer comes from the anonymous author of this brain teaser...
__________________
Green triangle....
tan A = opp/adj
tan A = 2/5 = 0.4

Red triangle..
tan A = opp/adj
tan A = 3/8 = 0.375

The entire triangle shape:
tan A = opp/adj
tan A = 5/13 = 0.385

The tangent ratio shows that they are different.
So how does this make the hole appear? It's an illusion.

In the first diagram, the shallower angle of the red triangle dips
inwards and the steeper angle of the green triangle straightens the
line back up to the corner of the full triangle. This leads the whole
triangle to have almost a concave type of effect along the hypotenuse,
losing about 0.5 of a square in area.

In the second diagram, the steeper angle of the green triangle swells
the whole triangle out in a convex shape and the red triangle brings
it back in. This gains an area of 0.5 over the full triangle.

The loss in the first and the gain in the second add up to the missing
space.
__________________

So... how did you do... did you figure it out?

Onyx Stone said...

The puzzle only tricks you if you assume that the overall shape is a triangle.

It's not.

I started by looking at the ratio of the two right angle triangles. One is 3/8 the other is 2/5. They do not slope at the same angle.

Then the long answer is ... what you said. ;-) Good puzzle though, because its so easy to think the two overall shapes should be triangles.

And for Nazh, you can draw a triangle with three right angles on sphere. Or if you curve space time.... arrrggghh.

Lord Nazh said...

correct Oxy; I actually got a A grade on a test I didn't have to take after challenging my Algebra teacher in high school when she stated as FACT that there could only be 1 90 degree angle in ANY triangle :)

I got sent to the office for it also, but the free A was worth it.

(the office trip was for the space-time explanation, not the sphere one)

Anonymous said...

My brain hurts...

Crushed by Ingsoc said...

I must admit, I keep comparing both triangles and am still confused.