Tangram Paradoxes

I can take the seven pieces of a tangram and arrange them into a shape called the monk, but I can take the same seven pieces and arrange them into a monk with no feet.

Wait, what? Where'd the foot go? How can these be made of the same pieces? Is it magic? No, it's a Tang G Paradox, which is a kind of dissection fallacy.

In my Bonet Tarski video, I showed an example where we fail to notice how the parts have changed, so we're surprised when the whole does. But in this kind, we fail to notice exactly how the whole has changed, so we're surprised to find that the parts haven't.

Illusions like these are caused by the fact that a concentrated area of missing material is much more noticeable than an equal but diffused increase everywhere else that compensates for it.

Both of these figures have the same area. The one with no feet has a slightly larger body, but the area of just the feet spread out amongst an entire arrangement... well, it's kind of hard to see.

Sometimes the things we don't notice can be quite significant.