yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Tangram Paradoxes


less than 1m read
·Nov 10, 2024

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.

More Articles

View All
How Wildlife Overcame South Georgia's Haunting Past — Ep. 5 | Wildlife: Resurrection Island
When this place was in full swing, a cloud of smoke covered the skies. 300 men toiled as thousands of whales lost their lives in Salieri. But who started this, and how did we get to the point of nearly exterminating the wildlife from this island? How is i…
Multiplying complex numbers graphically example: -1-i | Precalculus | Khan Academy
We are told suppose we multiply a complex number z by negative one minus i. So, this is z right over here. Which point represents the product of z and negative one minus i? Pause this video and see if you can figure that out. All right, now let’s work th…
How to take AI from vision to practice. Part 2
Uh, my name is Danielle Sullivan. I am currently the senior regional manager of Northeast District Partnerships at KH Academy, and I have been in education for a really long time. Lifelong learner. I was a former special education teacher and have been wi…
Worked example: finding relative extrema | AP Calculus AB | Khan Academy
So we have G of X being equal to X to the fourth minus X to the fifth. What we want to do, without having to graph G, is figure out what X values G has a relative maximum. Just to remind us what’s going on in a relative maximum, let me draw a hypothetica…
UChicago's Jim Nondorf on authentic applications to get accepted into college | Homeroom with Sal
Hi everyone! Welcome to our daily homeroom live stream. This is our way at Khan Academy of keeping everyone in touch during school closures. Obviously, as an organization with a mission of providing a free world-class education for anyone, anywhere, we pu…
The Most Dangerous Stuff in the Universe - Strange Stars Explained
Neutron stars are the densest things that are not black holes. In their cores, we might find the most dangerous substance in existence: Strange matter. A bizarre thing so extreme, that it bends the rules of the universe and could infect and destroy everyt…