This Defies Everything!!!!!!!!!

[ROD]

Yeah, but gradients or degrees don't matter here. Just the freaking side lengths. It could be curved for all we care. If they are all curved in the same manner, it is the same thing as if they were straight.

 

[ROD]

Tru dat Chris_D!

 

[Orcist]

The forumla for working out the area of any triangle is ONLY true when your sides are straight. In this case the hypotenuse is NOT straight (one is concave and one is convex). As mentioned by various people, this is extremely evident as when looking at where it intersects with the graph lines. If you can not still see it, I've pasted the outline from the bottom onto the top.

 

[Reaper978]

xtasy hit it right on the nail, if you look at the middle of both hypotinuses (the longest line) you can see that they are different because of the grid.

 

[ValVed RaY]

yes

now it's noticable

 

[Kamakiri]

OMG. They ARE different

 

[krogoth]

if they are not similar triangles proven above then they do not share the same area

 

[ROD]

Ok, ok, PRETEND they were straight, not curved. Draw it out, and you will see that the missing square is still there.

 

[MIWojo11]

I just noticed that the slope is off on one of them compared to the othere one.

 

[ValVed RaY]

yeah you're right rod

hmm this isnt as simple at it seems

 

[krogoth]

it's a straight hypot

 

[krogoth]

guys use the numbers u can prove they are not similar triangles and therefore does not share same area heh

 

[Xtasy0]

Originally posted by ROD
Ok, ok, PRETEND they were straight, not curved. Draw it out, and you will see that the missing square is still there.

but they aren't straight, and if they were straight then the situation wouldn't be the same.

 

[Reaper978]

Drawing it out is not perfect like on a comp which this picture was obviously made on. If you add the space up that the hypos miss it equals out to the damn missing square.

 

[MIWojo11]

the top one is bent a little and the bottom one looks strait. the 2 hypotenuses arent congruent.

 

[ROD]

We know they don't have the same area because there was a transformation. The question is, WHEN DID THE TRANSFORMATION OCCUR?

 

[Gojin]

Rod is saying, draw it out on a program where you can snap to grid, then draw the same shapes. See if it still happens.

 

[Chris D]

Let's say those squares are 1cm... How can a little discrepancy between the hypotenuse create a whole new square from nowhere?

 

[krogoth]

the left most angle is different that is where the difference comes in that is why the area is less 1 :S the green tirangle has a larger angle

 

[Gojin]

Those spaces add up.

 

[krogoth]

IT DIDN"TMAKE A SQUARE THE larger angle mde the triangle smaller making it loose a unit square

 

[krogoth]

heh the spaces seem to add up it's just a bad drwaing Edit: so as to make it seem like they are the same triangle :S

i been reading this forum for a week now and i am waiting for the video, it is hot and late so i wanted to join in the arguement .

 

[Reaper978]

I think you know what he means krog. Angles are decieving, the smallest change can create massive changes down the line.

 

[Reaper978]

Btw I love this topic. Got to get my mind working for a change.

 

[MIWojo11]

im hosting a pic of how to do it 1 sec

 

[ValVed RaY]

photoshop doesnt deceive me :O

 

[Reaper978]

I meant that the very small discrepencies between the two hypotenuses created the missing square. Thats all there is to it.

 

[MIWojo11]

precisely i drew a pic of that
http://img.villagephotos.com/p/2003-4/159723/trigrid.gif

 

[krogoth]

u guys all know how to do trig right? lol this was in a math contest from grade 10

 

[Reaper978]

btw photoshop cant select the exact point of which the lines start.

 

[MIWojo11]

reaper has it right

 

[Reaper978]

I just graduated grade 8

 

[Gojin]

I just passed Grade 11 (June somethin, so I guess it's just) GO ME!

 

[krogoth]

I think some one already at the begining found the solution u guys just dunt read hardenough

edit:
gmaniac posted that
"i.e. You are assuming that both triangles have the same angle. They don't. The extra area comes from that obtuse angle created by the first arrangement. The larger triangle has a 20.5560 degree angle. The smaller has a 21.8014 degree angle.
"

 

[mannyfresh027]

why are you all so dumb?

one of them isnt even a triangle, it has an extra angle, and the area of this triangle is different, meaning thats where the extra space came from.

 

[Reaper978]

I know xtasy solved it already just nobody believed.

 

[ValVed RaY]

ok problem solved, now trick your friends and pretend to be smart or something..

 

[Gojin]

Sorry guys but Orcist solved it. Give credit where credit is due.

He was like 4th post.

 

[Reaper978]

I am glad to know there are some intelligent people here who didnt just shrug off the thread going "man, what a geek question"

 

[Chris D]

How is it solved?

I drew the shapes out to scale and set them up and coloured them like the top picture.

I make a copy of the top picture and rearrange it like the bottom. No fancy convex, concave...

and....