quote:

Originally posted by zzleeper I ve just returned to town.. so uhm i thought it would be kinda mean to leave you w/out an answer for too much time (at least if u re like me, kinda impatient..).. Oh.. one last thing b4re this thread gets closed :O... Cosmo, do u have more of this type of quizzes\stuff .. ????? Post Them!!!

I've got megatonns of them!
Watch this space!

the hypotinuse of the first triangle is is not a staight line you all are stupid

easy

___________________

Well u re COMPLETELY OUT OF BASE Bondor.. the answer does not relate to that.. in this puzzle the problem lies in the graphic but not in the shape of the hypothenusa, but in the difference of height of the rectangles. The area of the triangles is the same in both graphics (well at least in my solution):

Last edited by zzleeper on Feb-03-2002 at 06:31

u guys are all wrong lol...sumtime back at rmf the same topic came up...i have provided an explanation of the answer there...just read my posts and follow the links i've posted, thou shalt be enlightened in no time...and i know this is the answer, 100% sure of it..

http://www.raremusicfinder.com/foru...&threadid=16026

peace

Hi everybody.. well it seems that there has been some confusion about the answer to this post. Well as I want to set this straight i´m gonna try to answer this in the best possible and easy-to-understand way.

Disclaimer: Even if I believe I´m right I may be.. wrong.. but the chance is very small so...

Well here we go. First of all, I have to sadly say that even AnotherWay83 is wrong. Everybody is

The interrogant in this quiz is the fact that if we rearrange the parts of a triangle that has an area of 32.5 u²(where u is an imaginary unit, it could be inches, centimeters) in a specific way, then there is a space missing. That would mean that the area of the total triangle has been reduced even if the area of the parts have not. Well there is something bad about that, if not then my 11 years of math at school would have been worthless.

The solution is this: (posted before but without good explanation)
Both triangles have the same slope (note: forget about the milesimal error in the graphic, that was a mistake in the drawing) which is 0.3846. The small triangle has a height of 1.92u², NOT 2u². The height of the large triangle has a height of 3.07 u², NOT 3 u². This are the formulas:

LENGHT * SLOPE = HEIGHT
8 * 0.3846 = 3.07
5 * 0.3846 = 1.92

But in BOTH graphics, the red and green triangles are the same, and THE AREA THE TRIANGLES OCUPPY IS THE SAME. The answer lies in the RECTANGLES, that most people forget to analyze:

In the first graph the height of each square is 3.07/3 = 1.02
In the second one the height of the squares under the red triangle is 1.92/2 = 0.96

There are 15 "squares" (well now that we know they arent really squares) in the 1st graph and 16 in the second (counting the blank one)

And the area of the 15 squares of the 1st graph is the same as the area of the 16 squares of the other graph because:

1*1.02*15 = 1*0.96*16 = 15.38

So the FINAL FINAL REASON OF THIS OPTICAL ILUSION LIES IN THE FACT THAT THE YELLOW SORT_OF_RECTANGLE and THE GREENISH SORT_OF_RECTANGLE (SORRY I DONT KNOW THE NAME IN ENGLISH FOR THAT SORT OF FIGURES) DONT HAVE THE SAME AREA IN BOTH GRAPHS!!!!!!!!!!!!!

But, why haven´t we noticed?? Because the difference of height is SO small that we can´t perceive it correctly. The only graphical difference we CAN perceive is the hypothenusa that ironically is only a mistake of the creator.

So, this is the end of my VERY SHORT post. Remember: The area of the first graph equals the area of the second one PLUS the blank space. The green and red triangles have the same area. The slope is the same.

Any hate mail please forward to my math teacher for being such a masochist enslaver.. LOL LOL

i read my solution in math books and even math forums, im pretty sure im rite...ithink u're also rite..we're saying the same thing i think

peace

Well u might be right about that we are both right.

Maybe it can be explained in both ways. But the thing I can´t understand is how exactly the answer u wrote explained the blank space..

I think now i m gonna try to forward the question to my college math teachers and try to fux0r with their minds. Hopefully they´ll go nuts..

Bye..

Ps: If u see around any interesting puzzle like this post it in this forum

becuase as bondor said the hypotenuse is bent outwards...

peace

quote:

Originally posted by AnotherWay83 as bondor said the hypotenuse is bent outwards...

Does that IMPLIES that there should be a blank square?

Piz

quote:

Originally posted by zzleeper Does that IMPLIES that there should be a blank square? Piz

yes it does...the areas of all the individual elements have not been changed...so the sum total of the areas stays the same...

peace

quote:

Originally posted by Bondor the hypotinuse of the first triangle is is not a staight line you all are stupid easy

1.If ANY side of the triangle is not a straight line its not a triangle! (Well, unless it's drawn on a ball, or any other not_flat surfuce)
2.Hypotinuse is a side of the triangle, it's cannot be "not straight"!
So, what u said about "stupid"?

quote:

Oroginally posted by zzleeper in this puzzle the problem lies in the graphic but not in the shape of the hypothenusa

Wrong! But...hmmm...probably, this is becouse our basic assumptions are different. Me, and others (sorry, I don't say who exactly ) consider all measurements of all small parts and all squares to be integer, thus the reason of difference in two figures is it's "hipotinuse" - it's not straight, becouse tans (or slope, how u call it) of smaller angles in triangles are different. While u consider it to be straight, and measurements are not integer.

So, becouse the pic has no exact description, we have to depend only on our sight.
And here comes analysis of the pic!
If you won't see it here it's wether you are blind or it's just sometning about me :
1.Here's the analysis of the slope:

(small grey lines at the ends of "hipotinuse" are equil, Iv'e just copied and pasted them)
2.Here's the analysis of the figures' height - it's completely equil:


So, let me continue on my solution.
Lets see... The area of the figure (not triangle! In reality it's [u]quadrangle[u] ) that consists of:
Red tri.+dark green tri.+yellow/light green rectangle= 0.5*3*8+0.5*2*5+3*5=32
If this figure would be triangle it's area would be? Correct! : 0.5*13*5=32.5
On upper figure we have -0.5 from area of the triangle
On lower figure we have +0.5 from area of the triangle
But becouse both figures consist of the same parts we have (0.5+0.5)=extra square.