How do ya solve this?

[Synista]

http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/jigsaw-paradox.html

[DsRsF]

Everyone *thinks* that everything can be divided nicely into units and things work out ok. The unfortunate problem is that SOMETIMES it doesn't work that way.

Our number system (1,2,3,4) is very lacking when we try to explain numbers of gigantic importance to the universe and mathematics itself. Take Pi for example: 3.141592653.... etc. into infinity. Also undefined is e. These "paradoxes" are just shortfalls showing the fragility of the current number system.

Or at least, that's my take on it.

[Synista]

I think someone solved it at another forum, but I am not 100% sure. It's supposedly an optical illusion of some sort, and the triangles don't fit perfectly. I'll have to wait for the results to come in. I've also showed it to my math teacher and I'll see what he says

[Heikki]

Rather simple, actually. The small triangles are shaped slightly differently (2/5 != 3/8), therefore the entire figure is not exactly a triangle, which you may notice if you try to draw the figure yourself with a sharp enough pen. Basically an optical illusion, yes.

[Synista]

Yeah. 2/5 and 3/8. If you calculate the slopes on the triangles and those other two shapes, they're a bit different.


Now how do you solve the one with the big triangle?

[Kate]

Since the green triangle and the red triangle are not similar, meaning that their hypotenuses do not meat at 180*. In the first case they form as angle greater then 180*, in the second case, less then 180*, which gives the area difference of one unit squared.

[Silenced Sonix]

This is to DsRsF - you constantly b*tch and moan about our current systems, yet you never suggest anything better... There is an old saying that goes as such:
"Do not critize that which you cannot better"

I suggest you keep that in mind next time you're busy pointing out the flaws in others and their work.

I don't know why, but you posts are always offensive.. just keep that in mind next time you post!

[Synista]

Originally posted by katbeidar
Since the green triangle and the red triangle are not similar, meaning that their hypotenuses do not meat at 180*. In the first case they form as angle greater then 180*, in the second case, less then 180*, which gives the area difference of one unit squared. Could you explain that with a formula, because I don't understand what you're trying to say. The hypothenuse on the big triangle (The composed one) *seems* to be a straight line.

[Kate]

The hypothenuse on the big triangle (The composed one) *seems* to be a straight line.

It is a streight line. But combined with the streight line of the small triangle, it forms an angle smallet then 180*. There is no formula to explain this, not every mathematical or geometrical problem is explained with a formula.

[Synista]

I don't think you get what I'm saying. But whatever.






So anyone else can solve that second one?

[Kate]

Synista, what are you saying? Try to explain? I love to solve maths, you know, lol. :heh:

[tmp]

I guess you can explain it with a formula, but you will need to denote angles and blah-blah, which would require some drawing... so in this case it's easier to explain in words and you've done it already :) The upper "triangle" has its "hypothenuse" bent in, the lower one - bent out creating a void in the shape.

[Eminem]

You gotta think for dat one? I ain't solvin' it den.

[PS4FA]

Calculate the sum of the areas of the 4 pieces, then calculate the area of the total triangle. They're different, the dissection shown is simply impossible. It just looks as though it works because they use thick lines around each piece. The area of these lines, or if you do it with real pieces of paper or card, the slight positional inaccuracies that most people will not notice, are enough to make the pieces apparently fit in the first arrangement, and then create the hole in the second one.

(I dunno, I join a Tatu forum and my first post is about math)

[tmp]

Originally posted by PS4FA
... the slight positional inaccuracies that most people will not notice, are enough to make the pieces apparently fit in the first arrangement, and then create the hole in the second one.

(I dunno, I join a Tatu forum and my first post is about math)

They not only appear, they do fit together, but not in a triangle.

for me math is a lot more interesting than tatu :)

[QueenBee]

Originally posted by Eminem
You gotta think for dat one? I ain't solvin' it den.

hahahah! :D

[shizzo]

I'm noticing two things about this problem:

1) The congruency among the two smaller triangles and the larger one don't factor in as components to solving this problem, since the fact that it's simply an optical illusion denote irregularity by definition.

2) The aforementioned text is not readily evident because this problem is fixed on a two-dimensional base.

Rearranging the pieces both allows and disallows a given amount of displacement. Because the two triangles aren't of equal mass, changing their position also changes the amount of "lenience area" where the pieces could fall. [This implies that the because the red triangle reached three blocks farther into the entire figure than the green one, as well as being one unit larger in heighth than the latter, the four figures together share a total given amount of space in which to adjust edges and so forth.] Calculating the angles of degrees will eventually lead to finding the exact amount of displacement room available, but I'm just working with this problem from the view that displacement exists, though it's momentarily not calculated. Just acknowledging its existence is enough to surmise that it's a two-dimensional optical illusion. [Had it been on the three-dimensional scale, the limit of displacement would have been severalfold easier to manipulate, but when only length and heighth are factored, that aforementioned limit is more difficult both to recognize and to evaluate.

I'm hoping that makes sense. ^_^

// Loki

[Veritas]

does anyone in here speak english???