No it´s more basic than that. You have to differnt triangles one large and one small. The ratios between them is matching so that you can count the area of both of them by only knowing the measurements of one... No angles involved.

I just confirmed the theory by printing it out and cutting it in half and laying the drawings over top one another. There is an almost imperceptable slope change on the hypotenuse that creates a very thin convex sliver about 8 squares long - making up the missing square. Quite cool. Any teachers on this board? - show it to math students.

Yeah, the term is "similar." Your theory doesn't work mathematically though because one of the shapes is not in fact a triangle - it has a chunk cut out, and a non-linear "hyptenuse." ;)

<font color="#00ccff">You have entirely too much free time at work mister! ;) </font>

I thought you were our curmudgeon! :D [img]tongue.gif[/img]

However, people are learning. I know I did. I have been staring at that puzzle for close to nearly 5 years already at the transit stations. It feels good to know and understand the answer now. :D

Was it that simple? Oh dear lol :D ! Thanks for the info. [img]smile.gif[/img]

[ 11-07-2002, 12:37 PM: Message edited by: WillowIX ]

Actually the triangle bit is a red herring. All three triangles are similar (angles equal, sides proportional), and the total area of the reconfigured large triangle is the same in each case.

The "hole" is created by the differeces in area of the two rectangles that make the difference in the large triangle when the two small triangles are lined up.

With the small triangle on top, the resulting rectangle is 3x5, which has an area of 15.

With the med triangle on top, the resulting rectangle is 2x8, which has an area of 16.

So, when using discreate parts as shown in the picture, there is not enough material to complete the triange in the second configuration, even though the total area is the same for each large triangle.

I thought you were our curmudgeon! :D [img]tongue.gif[/img] </font>[/QUOTE]A challenging DUAL ROLE to be sure. :D

As for me having free time at work, we all obviously do. But, I've gotten several projects off my desk today, including pleadings in 2 cases, and I intend to finish up a bunch of discovery to pound the other side into the dirt by the time the day is finished. For young lawyers, a lot of the day is spent awaiting feedback on projects - I take work home at night most days.

'SNAP' *breaks arm patting self on back*

I count two triangles. The red on and the green one. The other two triangle-like forms are *not* true triangles. The first is an irregular quadrilateral - the 4th vertice is at the point where the red and green trianlges meet. The second is an irregular octagon. Your only looking at one part of the puzzle. You need to explain why the 4 pieces are the same area and in the same space, but leave a gap There are no large triangles.

Red triange is 3*8, green is 2*5. They are not similar, the gradient of the hypotenuse is different, rearranging them therefore allows for this gap to be created.

This can bee seen, if you look at the point where the triablges meet in the first picture. IF your eyesight is super human, you can see a slight angle there.

For the rest of us, look at the same point in the second diagram. The hypotenuse of the red triangle passes close to this point, not through it.