The two triangles do not have the same slope. The big one rises 3 units over 8 units run, the small one rises two units over 5 units run. Switch the two as shown and you open up the square but appear to have the same endpoints of the figure. I don't think that really explains it, but it has something to do with the triangle pieces not being interchangable.

<strong>The two triangles do not have the same slope. The big one rises 3 units over 8 units run, the small one rises two units over 5 units run. Switch the two as shown and you open up the square but appear to have the same endpoints of the figure. I don't think that really explains it, but it has something to do with the triangle pieces not being interchangable.</strong><hr></blockquote>

did not see that... but I dont think it matters... I dono, I drew it out on a piece of paper... its weird... its like area is coming from nowhere....

BuonRotto nailed it. You have to look closely, but the figure on the top "pinches" slightly in (down) where the two triangles meet. In the bottom figure, it slightly bowes out (up). The difference is small, but comes out to 1 square.

<strong>BuonRotto nailed it. You have to look closely, but the figure on the top "pinches" slightly in (down) where the two triangles meet. In the bottom figure, it slightly bowes out (up). The difference is small, but comes out to 1 square.

-- ShadyG</strong><hr></blockquote>

I still dont get it. In both figures you have a 13X5 triangle... in the bottom one there is an extra square and they ahve the same shapes inside of them... how can this be?

I still dont get it. In both figures you have a 13X5 triangle... in the bottom one there is an extra square and they ahve the same shapes inside of them... how can this be?</strong><hr></blockquote>

Neither of the complete figures is actually a triangle. They're quadrilaterals, although one of their angles is extremely close to 180°.

That still doesn't explain it. I drew out the same shapes in cad and then copied the exact shapes and still get the same results. I just don't get it. I guess I will have to run it by my old college math teacher.

This isn't really needed, but can someone redo that image mathematically? or at least more accurately? The anti-aliasing totally kills it. I redid just the grid and without the anti aliasing making some lines take up 2 lines.. I saved practically an extra square.. It is really messy in its current state.

Look carefully at the picture. Look at the slope of the triangles. Look at the grid. Do they match? NO. The "missing square" is never missing. There is no missing square.

I remember this very same brain teaser from middle school. a10t2 explained it best (except only one is a quadrilateral...the other has 8 edges.) You're looking at two entirely different shapes. Your eyes have fooled you into believe both are the same triangles and that both are actual triangles (on with a missing chunk) at all.

In the top figure, the hypotenuses of the red and green triangles for a very sligh \\/ shape. In the bottom figure, the hypotenuses form a very slight /\\. If you overlaid the two figures on top of each other, you would notice a very, very thin parallelogram between the two sets of hypotenuses. The area from the bottom figure's missing box is relocated to that very thinly sliced parallelogram. Both figures have the exact same area despite the illusion of the missing box in the bottom figure. It's just a lot harder to see that the shifted area is going somewhere else in the figure and not just disappearing.

I took that image into paint (I am at work so pc is all I have) and I drew a line from the the bottom left to top right on both shapes. The top image curves inward, the bottom image curves outward. That would explain it to me. Do it for yourself if you need to see it. I just used the line tool in the application to get a straight edge.

## Comments

6,368member5,278member<strong>The two triangles do not have the same slope. The big one rises 3 units over 8 units run, the small one rises two units over 5 units run. Switch the two as shown and you open up the square but appear to have the same endpoints of the figure. I don't think that really explains it, but it has something to do with the triangle pieces not being interchangable.</strong><hr></blockquote>

did not see that... but I dont think it matters... I dono, I drew it out on a piece of paper... its weird... its like area is coming from nowhere....

Its really pissing me off!!

64member-- ShadyG

5,278member<strong>BuonRotto nailed it. You have to look closely, but the figure on the top "pinches" slightly in (down) where the two triangles meet. In the bottom figure, it slightly bowes out (up). The difference is small, but comes out to 1 square.

-- ShadyG</strong><hr></blockquote>

I still dont get it. In both figures you have a 13X5 triangle... in the bottom one there is an extra square and they ahve the same shapes inside of them... how can this be?

191member<strong>

I still dont get it. In both figures you have a 13X5 triangle... in the bottom one there is an extra square and they ahve the same shapes inside of them... how can this be?</strong><hr></blockquote>

Neither of the complete figures is actually a triangle. They're quadrilaterals, although one of their angles is extremely close to 180°.

50member5,278member<strong>I drew out the same shapes in cad and then copied the exact shapes and still get the same results.</strong><hr></blockquote>

mind posting them?

5,278memberwhere the hell did that box come from?!?!?

151member22,667memberLook carefully at the picture. Look at the slope of the triangles. Look at the grid. Do they match? NO. The "missing square" is never missing. There is no missing square.

22,667memberNote that at the SAME point, the first and second pictures don't meet.

Note that this is not because of a bad drawing or antialiasing or whatever. Any "accurate" version will show this.

[ 01-21-2002: Message edited by: starfleetX ]</p>

8,254memberIn the top figure, the hypotenuses of the red and green triangles for a very sligh \\/ shape. In the bottom figure, the hypotenuses form a very slight /\\. If you overlaid the two figures on top of each other, you would notice a very, very thin parallelogram between the two sets of hypotenuses. The area from the bottom figure's missing box is relocated to that very thinly sliced parallelogram. Both figures have the exact same area despite the illusion of the missing box in the bottom figure. It's just a lot harder to see that the shifted area is going somewhere else in the figure and not just disappearing.

[ 01-21-2002: Message edited by: Eugene ]</p>

4,503member<strong>I cannot explain this:

[snip]

??? <img src="graemlins/bugeye.gif" border="0" alt="[Skeptical]" /> <img src="graemlins/hmmm.gif" border="0" alt="[Hmmm]" /> ???

-Paul</strong><hr></blockquote>

I took that image into paint (I am at work so pc is all I have) and I drew a line from the the bottom left to top right on both shapes. The top image curves inward, the bottom image curves outward. That would explain it to me. Do it for yourself if you need to see it. I just used the line tool in the application to get a straight edge.