Paradox?

Ok so i might have had a bit to much beer tonight, but theres something which has been bothering me, and even when I’m 100% with it, i still cant seem to work it out.

Its a paradox which i found on the net the other day, on one of those demotivational posters which i love so much.

Here it is:
http://img511.imageshack.us/img511/1364/paradoxda8.jpg

I cant for the life of me work it out, it is truly a paradox which boggles the mind.
There must be an explanation…

The text says:

Below the four parts are moved around

The partitions are exactly the same as those used above
Yet there is that small block present in the second triangle. They both take up the same space, use the same pieces, yet a single block appears out of nowhere.

:no:

edit Pardon the french in the image, i dont mean to offend people

The “big” triangle has been slightly bent. See http://mathworld.wolfram.com/TriangleDissectionParadox.html for full explanation.

optical illusion - it’s a maths thing

There is a grid in the pictures. Just look at it, at the lower left corner and at the top corner.

check out either link it explains how it works

It’s actually quite hard to see the bend, but apparently it is just enough to create a small empty square. Anything like this is a good brain twister though if you’re willing to try to not look at the solutions.

Hmmm ok interesting links.

I was hoping people would be mesmerized, like i was, for a bit before someone came along with the answer!

Still a bit of a mind bender though, even with the answer…

yeah it is

It warped my brain for 10 mins
then I knew there had to be a reason - so I went looking

so thanks :slight_smile:

(PS I even modeled it in blender with the grid to check)

Heh, did the same thing but with angles. Just to convince myself there wasn’t an 180 degrees angle where the triangle tips touch.

I don’t understand what part of this is hard. I mean, I’m not saying it’s easy, but I just don’t understand why this is a paradox.

There are many types of paradox

this is a geometry paradox - been around since the 1800’s

Trying to explain what makes a paradox so confusing/difficult would be just as hard as explaining the paradox itself…
Making it in blender to test it sounds like a good idea, didnt think of that.

The link to the list of other paradoxes is very interesting, definitely mind melting stuff.

Heh, take a look at their slopes and their left most point, compare.
Not actually exact duplicates are they, hehehe?
woah, woah look how you can create different shapes with the same volume! magic!!
:stuck_out_tongue:

Also, I hate those trying to be clever/funny internet meme images, like the paradox one following a template.

I don’t know… It makes sense to me.
I animated this in Blender and, well, the points aren’t exactly the same, but that’s just because I couldn’t use ctrl-g because it wouldn’t snap directly to the grid.