MYSTERIOUS TRIANGLE AREA

The yellow triangle is now to the left of the green one instead of above it..........

Monger

Great puzzle. I've printed it and will look it over some more.

No solution yet.

LOL, this one I spent 10 minutes on. It is kind of hard, but here's the logic:

Use pythagorean's theorem and you find out that the third side has to be:

c = sqrt(a^2+b^2) = sqrt(13^2+5^2) = 13.928

The side drawn ISN'T actually 13.928. Why? It's an illusion. If you would zoom in on the picture, it would actually look like this:


When your rearrange the pieces, it now looks something like this:

The piece that was put out (see below) is now removed by the one empty square, so that the area will still remain equal.

= empty square

I admit this problem was pretty tricky

The lines are thickened, or otherwise you could notice the illusion. That is why this cannot be solved by vision alone...

technoguy,

Those images are hosted on a private MSN group. I can't see them.

There is a sophomoric remark about the mysterious triangle area with a hole in it in here somewhere, but I'll let it ride, so to speak.

oops. sorry craven...um...where should i post them then?

On any publically accesible site that allows hotlinking.

You can use my old MSN group if you'd like:

http://groups.msn.com/TheRavensRealm

For those who can't see the images, I will try to draw the pictures myself (triangle is other way around in these pictures)

Picture 1:

.
....
........
...........
...............< this angle is not 180 degrees (smaller than 180)
...............|.......
...............|...................
...............|...............................

Picture 2:
.
.....
...........
.....................
............................. < angle not 180 degres (bigger than 180)
...................................
......................................
..........................................
...............................................
.................................................

Picture 3:
_'s represent spaces

.
...
.....
.......
_.....
__...
___.

I hope you can see how this mystery triangle works!

o ok thanks craven!

Here's the site:
http://groups.msn.com/ROBERTschool/mysterytriangle.msnw

The pictures are on:
http://groups.msn.com/ROBERTschool/mysterytriangle.msnw

The documents folder of MSN groups requires one to be signed in to access files. I still can't see the pics unless I sign in to MSN (something I avoid).

I've gone to the linked sites and I cannot see any pictures. I do not understand the explanation you gave, Tech.

I still do not understand how this works -- and I sure want to.

uh...the pictures are in .bmp so it might take a minute if your PC is slow; try waiting for like a minute or 2, or press "show picture" or something like that when you right click your mouse. Craven, you should be able to view the site without any login. If it doesn't work, uh....try the local library PC

Okay, I've been to the site four times now and it is obvious I am not going to get those pictures.

This last time I waited almost five minutes and finally came to the conclusion that Tech was just bustin' my chops with that suggestion because of something I said to him in another thread.

I guess I'll go to the library -- although I don't know what the hell I'm looking for.

My plans at the moment involve handing a copy of the puzzle to the reseach librarian and ask what book I should read to solve the goddam thing -- so obviously I am not going to do this sober.


Monger -- where the hell are you. Tell me you didn't post this puzzle without a solution in your hand? I gotta get some sleep!

lol ok i'll try again

here's the explanation:
When you put the pieces that form the hypothenuse, you do not get the real value what it's supposed to be (square root of 13^2 plus 5^2). This is because the angle of the blue piece is smaller than the angle of the red piece (with angle i mean the left lower corner of each piece). When we rearrange them, the red and blue switch places and now the angle of the red is bigger than the angle of the blue. The first time the triangle bent in a bit if you would zoom in. Now the triangle bends out. You cannot see this because the line is thick. The area added when the triangle changed from bent in to bent out (really thin parallelogram) is now subtracted by the empty square. That way matter is conserved. Otherwise (it may seem weird) matter would be lost!!!

Hope you understand it.

P.S. Anyone who still doesn't get it e-mail me at [email protected]

TGR,
It's not a matter of download time connection speed or individual computers.

It's that MSN groups do not allow access to files in the file folders unless you are logged in to MSN. If you upload it to the photo album they will be publically viewable.