brain pickle

[THEINCREDIBLEdork]

Solve this problem. Explain as completely as possible. Any answers that include math must show their work. No more than 500 words. Any number of pictures can be used as long as they are made by yourself. Do not search for the answer. Use reason.

Admissions until tomorrow at 10:00pm EST. Best answer wins internets.

[DDTempest]

Originally Posted by THEINCREDIBLEdork

Solve this problem. Explain as completely as possible. Any answers that include math must show their work. No more than 500 words. Any number of pictures can be used as long as they are made by yourself. Do not search for the answer. Use reason.

Admissions until tomorrow at 10:00pm EST. Best answer wins internets.

You're a dipshit, the two triangles don't have the same dimensions. The top figure only looks like a triangle when it actually has four sides.

It's an optical illusion.

[Ugly Bastard]

Originally Posted by DDTempest

You're a dipshit, the two triangles don't have the same dimensions. The top figure only looks like a triangle when it actually has four sides.

It's an optical illusion.

Does not compute.

[TwoBlackEyes]

Originally Posted by Ugly Bastard

Does not compute.

He's right. You just don't see it because you aren't looking at it right.

[DDTempest]

I am not keen on geometry terms but the two smaller triangles APPEAR to be the same dimensions as the larger triangle. We'll use fractions to check.

Big "triangle" appears to be 5 squares tall by 13 squares long = 5/13
Green triangle is 2/5
Red triangle is 3/8

These triangles are not of equal dimensions, thus can't be a part of a larger triangle.

[Ugly Bastard]

Originally Posted by DDTempest

I am not keen on geometry terms but the two smaller triangles APPEAR to be the same dimensions as the larger triangle. We'll use fractions to check.

Big "triangle" appears to be 5 squares tall by 13 squares long = 5/13
Green triangle is 2/5
Red triangle is 3/8

These triangles are not of equal dimensions, thus can't be a part of a larger triangle.

I mean... I still don't see how you're anything but wrong here.

[DDTempest]

Originally Posted by Ugly Bastard

I mean... I still don't see how you're anything but wrong here.

That's ok, someone who is good at explaining geometry will come along and explain it soon enough.

[Dent]

[Orgazmo]

I laid them on top of each other and then made the top one semi-transparent.

Though close, they're not identical. Their hypotenuses don't match.

[Dent]

Originally Posted by DDTempest

You're a dipshit, the two triangles don't have the same dimensions. The top figure only looks like a triangle when it actually has four sides.

It's an optical illusion.

It kinda has infinate sides, not sure where you got 4 from.
you should get a pair of these glasses, they help with spotting some asshole tricking you.
he doesn't even say its a triangle.
headset optional

^^
thats what I said.

[f3lix]

Nice work, Gaz.

The 4 figures cannot possibly be the same figures in both pictures, as they would require the same amount of space to be taken up and cannot possibly include the addition of the empty box. The slight difference in the diag fulfills all the space left by the lone empty box.

[Ugly Bastard]

Wow... so instead of this being an interesting mathematical problem, it's a dumb sleight of hand. I'd negrep if I didn't know your intentions were pure, ID.

[THEINCREDIBLEdork]

Good call on holding back the negrep, Dent and f3lix are both wrong fyi.

[Dent]

This example fucking sucks, so does the grainy picture with the fat black lines.
much easier to see with graph paper.

[Ugly Bastard]

Originally Posted by Dent

This example fucking sucks, so does the grainy picture with the fat black lines.
much easier to see with graph paper.

This is especially evident when looking at how the hypotenuses relates to the intersection points on the grid.

[Landing Strip]

It can be seen that the hypotenuse of the large triangle is not a straight line, here is how you can calculate that:

Right triangles made within larger right triangles [like the green triangle in the overall triangle] have equal angles. So, the interior angles in all the triangles found in the diagram must be equal to each corresponding interior angle [green triangle's angle at the top of both green and overall triangle must equal the red's top most angle]. With other geometric knowledge, red triangle should be similar to green triangle.

We are not given angle measurements, so trigonometry is needed.

We do know the lengths of the legs of each triangle. So the basic trigonometric function of tan A = a/b, where both a and b represent the triangle's legs. We don't know the value of A (the angle) so we will need to use tangent's inverse, arctan [sometimes expressed as 1/tan x or tan x ^-1]

For shorthand, I will use the symbol "#" for an angle.
# = arctan (a/b)

For red triangle and green triangle to be similar, using # = arctan (a/b) must equal each other when used on both triangles.

For green triangle I will use # = arctan (a/b)
For red triangle I will use # = arctan (a'/b')

arctan (a/b) must equal arctan (a'/b') for these triangles to be similar, thus making the overall triangle really a triangle and not a quadrilateral.

Is this equation valid?
Does arctan (a/b) = arctan (a'/b')

arctan (2/5) = arctan (3/8)
after some calculations..
arctan (2/5) does not equal arctan (3/8)

This is means the angles are not equal to each other, meaning the triangles are not similar, meaning the whole triangle is quadrilateral. Because this picture is a quadrilateral and not a triangle, smaller triangles cannot be cut and pasted anywhere to form a solid triangle.

After all this, I feel as if I've used trigonometry wrong and that I am wrong. I haven't taken trig or done math in a while.

[Ugly Bastard]

Wow... nice fucking work on the solution, LS. Posrepped. Tits now? Haha... just kidding kidding, f3lix.

No but seriously, show us your tits please.

[f3lix]

She's a keeper.

[Mr. Blonde]

Originally Posted by Landing Strip

It can be seen that the hypotenuse of the large triangle is not a straight line, here is how you can calculate that:

Right triangles made within larger right triangles [like the green triangle in the overall triangle] have equal angles. So, the interior angles in all the triangles found in the diagram must be equal to each corresponding interior angle [green triangle's angle at the top of both green and overall triangle must equal the red's top most angle]. With other geometric knowledge, red triangle should be similar to green triangle.

We are not given angle measurements, so trigonometry is needed.

We do know the lengths of the legs of each triangle. So the basic trigonometric function of tan A = a/b, where both a and b represent the triangle's legs. We don't know the value of A (the angle) so we will need to use tangent's inverse, arctan [sometimes expressed as 1/tan x or tan x ^-1]

For shorthand, I will use the symbol "#" for an angle.
# = arctan (a/b)

For red triangle and green triangle to be similar, using # = arctan (a/b) must equal each other when used on both triangles.

For green triangle I will use # = arctan (a/b)
For red triangle I will use # = arctan (a'/b')

arctan (a/b) must equal arctan (a'/b') for these triangles to be similar, thus making the overall triangle really a triangle and not a quadrilateral.

Is this equation valid?
Does arctan (a/b) = arctan (a'/b')

arctan (2/5) = arctan (3/8)
after some calculations..
arctan (2/5) does not equal arctan (3/8)

This is means the angles are not equal to each other, meaning the triangles are not similar, meaning the whole triangle is quadrilateral. Because this picture is a quadrilateral and not a triangle, smaller triangles cannot be cut and pasted anywhere to form a solid triangle.

After all this, I feel as if I've used trigonometry wrong and that I am wrong. I haven't taken trig or done math in a while.

[Orgazmo]

Guys, did you see where I put them on top of one another to show that they're different?

[DDTempest]

Or how I explained that they were different before you put them on top of each other =P

[Orgazmo]

=P

[f3lix]

or that I put words to the difference.

[Dent]

I have 4 pictures, thats 4000 words if we're talking science.
Preparing for me +nets now,

[Ugly Bastard]

A variation on this may have already been said somewhere in this thread, but this is what my friend Lisa's dad had to say about this (he got his PhD in mathematics from Yale and was an actuary for AIG for 20+ years before retiring well before all the shit hit the fan... like the guy has somewhat limited social skills because his mind is so preoccupied with thinking about math... ala Beautiful Mind just w/o the craziness):

As I was saying on the phone, you can tell, for instance, that the upper large triangle is not really a triangle, if it were the upper right acute angles on each of the green and red little triangles would be the same. But the upper acute angle of the green triangle has a tangent (ratio of opposite to adjacent sides) of 5/2=2.5. The red is 8/3=2.666.

But yea, pretty sure others have said something to that effect already.