can anyone figure this logic puzzle out?

[spanky]

puzzle


i think Slappy00 got the answer. thanx bro :beer:
and kudos to Iron Woode for the lengthy logical explanation :beer:

 

[t3hmuffinman]

that's unpossible! (sorry had to say that before i looked at it more)

 

[Slappy00]

its not a perfect right triangle

 

[Malak]

I don't understand how you are supposed to answer it. Clearly it's possible and clearly you can see how to do it, so what are you supposed to say?

 

[Ikonomi]

What do they want you to say? I don't see how it's not possible. What form should an answer take?

 

[spanky]

i dunno how to explain the extra square. what i go so far is that the area on the rectangles are different, but the area of the triangle is the same. i dunno how to make sense of that, being that the other two triangle have the same area. hmmm....

 

[Slappy00]

the hypothenuse is not a streight line in the top triangle it curves down ever so slightly, you make the assumption that all the lines are streight but they are not. The second one has the lines perfectly streight and you lose the area you gain a bit of open space.

 

[t3hmuffinman]

Originally posted by: Slappy00
the hypothenuse is not a streight line in the top triangle it curves down ever so slightly, you make the assumption that all the lines are streight but they are not. The second one has the lines perfectly streight and you lose the area you gain a bit of open space.

you are clever

 

[Iron Woode]

Simple, really. All they did was shove the triangles out a little more. All the space they push out actually is enought room for a cubic square

 

[Crusty]

.

 

[WhiteWonder]

Originally posted by: Iron Woode
Simple, really. All they did was shove the triangles out a little more. All the space they push out actually is enought room for a cubic square

yeah, the triangles do look a little bigger if you look close enough.

 

[jagec]

Originally posted by: Slappy00
the hypothenuse is not a streight line in the top triangle it curves down ever so slightly, you make the assumption that all the lines are streight but they are not. The second one has the lines perfectly streight and you lose the area you gain a bit of open space.

exactly. Count the squares on both triangles; you'll see they are not similar.

 

[spanky]

hmm... they said the shapes are exactly the same dimensions tho.

 

[dethman]

Originally posted by: Slappy00
the hypothenuse is not a streight line in the top triangle it curves down ever so slightly, you make the assumption that all the lines are streight but they are not. The second one has the lines perfectly streight and you lose the area you gain a bit of open space.

winnar.

 

[Iron Woode]

Originally posted by: spanky
hmm... they said the shapes are exactly the same dimensions tho.

The real true answer is:

The second triangle is not a true triangle. That is why it is tricky.

Here is a lengthy explaination:

The curse on Plato's triangle basically comes down to this from what I have figured out:

It's an optical illusion.

If you calculate the area of "Plato's triangle", it gives you [(13 x 5) / 2] = 32.5

Now take a good look at the hypothenus of Plato's triangle. The hypothenus should be a straight line (obviously). The blue and red triangles both have a right angle, and a base angle, and a top angle. The base angles of the red and blue triangles should be the same if the hypothenus is to be a straight line.

Let's calculate the hypothenus of the red and blue triangle:

Hyp(Blue)= SQR[(2x2)+(5x5)] = 5.38
Hyp(Red) = SQR[(8x8)+(3x3)] = 8.54

Now let's calculate the cosines of the base angles of the red and blue triangles:

cos(Blue) = adjacent side / Hypothenus = 5 / 5.38 = 0.928476 => equivalent to: 21.66 degrees.

cos(Red) = adjacent side / Hypothenus = 8 / 8.54 => equivalent to 20.48 degrees.

So although they seem similar, they are different angles. Therefore the hypothenus is not a straight line and Plato's triangle is not a real triangle. Therefore again, the formula used in the beginning to calculate it's area is false mathematically.

Before the magic the hypothenus of Plato's cursed triangle is in fact 2 segments pointing to the inside of the triangle. After the magic the hypothenus is in fact the same 2 segments pointing to the outside. Simply said, before the magic trick, the 2 segments are eating in Plato's triangle an area of 0.5. After the trick they are sticking out an extra 0.5 of area from Plato's triangle. The total difference is 1. Hence the mysterious appearance of a square of area 1 out of nowhere.

 

[spanky]

Originally posted by: Slappy00
the hypothenuse is not a streight line in the top triangle it curves down ever so slightly, you make the assumption that all the lines are streight but they are not. The second one has the lines perfectly streight and you lose the area you gain a bit of open space.

yeah, i think u r right, but i am just slow in interpreting this. i dunno why, but i am thinking about the slopes of the triangles... in the top diagram, the triangle on top has a bigger slope, so if u draw a straight line from the top to the lower left corner, u will end up with some area outside the "triangle". on the bottom diagram, the slope of the top triangle is smaller, so if u draw a line from the top to the lower left corner, the "triangle" is not really complete... it still has a bit of blank space. err... am i getting this right?

 

[jagec]

Originally posted by: spanky
hmm... they said the shapes are exactly the same dimensions tho.

The shapes are the same from one scenario to another. However, since the two triangles have different slopes (the lines actually DON'T have to curve at all for the puzzle to work), you can gain or lose area by rearranging them.

 

[spanky]

Originally posted by: jagec

Originally posted by: spanky
hmm... they said the shapes are exactly the same dimensions tho.

The shapes are the same from one scenario to another. However, since the two triangles have different slopes (the lines actually DON'T have to curve at all for the puzzle to work), you can gain or lose area by rearranging them.

yeah, i think i got the grasp of this now. the individual shapes have the same dimensions, but the overall shape of the bigger "triangle" is altered due the rearrangement.

 

[OulOat]

Originally posted by: spanky

Originally posted by: Slappy00
the hypothenuse is not a streight line in the top triangle it curves down ever so slightly, you make the assumption that all the lines are streight but they are not. The second one has the lines perfectly streight and you lose the area you gain a bit of open space.

yeah, i think u r right, but i am just slow in interpreting this. i dunno why, but i am thinking about the slopes of the triangles... in the top diagram, the triangle on top has a bigger slope, so if u draw a straight line from the top to the lower left corner, u will end up with some area outside the "triangle". on the bottom diagram, the slope of the top triangle is smaller, so if u draw a line from the top to the lower left corner, the "triangle" is not really complete... it still has a bit of blank space. err... am i getting this right?

In the bottom picture, the triangle is convex, so the "blank" space is present to keep the area the same at the top large triangle, which is concave.

 

[Slappy00]

Originally posted by: OulOat

Originally posted by: spanky

Originally posted by: Slappy00
the hypothenuse is not a streight line in the top triangle it curves down ever so slightly, you make the assumption that all the lines are streight but they are not. The second one has the lines perfectly streight and you lose the area you gain a bit of open space.

yeah, i think u r right, but i am just slow in interpreting this. i dunno why, but i am thinking about the slopes of the triangles... in the top diagram, the triangle on top has a bigger slope, so if u draw a straight line from the top to the lower left corner, u will end up with some area outside the "triangle". on the bottom diagram, the slope of the top triangle is smaller, so if u draw a line from the top to the lower left corner, the "triangle" is not really complete... it still has a bit of blank space. err... am i getting this right?

In the bottom picture, the triangle is convex, so the "blank" space is present to keep the area the same at the top large triangle, which is concave.

yah i just looked at the top one primarily, 1280 x 1024 dont help either, but i can see how both can be "off" a bit.

 

[TTM77]

Print it out, cut and try it yourself. I have done it long time ago. It's very awsome. Magic infront of your eyes.

This is one of those thing Physically seem imposible but mathamatically possible.