Fano Plane: The World’s Smallest Projective Geometry

This is short animation of the Fano Plane, which is the smallest projective geometry. We also show how to realize the geometry as the set of linear sub spaces of a three dimensional vector space over the field with two elements.

Thanks!

#mathshorts​ #mathvideo​ #math​ #geometry #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #vectorspaces #projective #projectivegeometry #shorts #fanoplane #fano

To learn more about animating with manim, check out:

[GenericInternetter]

Dude managed to confuse me using only a triangle and a circle.

[MisterSixty]

I am literally the deer staring in the headlights.

[speakingsarcasm]

For those who are criticizing because you did not understand: this is a short so it is expected that the target audience is probably someone who knows about finite fields, basic modular arithmetic, abstract vector spaces and some basics of linear algebra (subspace, basis, dimension etc.)

[drenz]

For those who didn't understand: The three dots on each 'line' each has values. If you add them up, they're all even. That's cool... right?

[leggedsquirrel]

The last one is going to look like a circle and that's because it is

[codatheseus]

This is the shape for the chart of multiplying octonion units.

Each line is really a circle and going against the circle is the opposite result bc anticommutativity

[JakubS]

What's also great is that if you move two of the lines onto a new Fano Plane, then the positions of the rest of the lines are already chosen, because of the symmetries within it.
So you can reorder the Fano plane 6 times because of 6 lines, but also 6 more times because of the reflections of them.

[endersteph]

This is actually related to how the game Dobble is made!

[Leedramor]

I understood about half of it. Quick question, where would be the origin (0, 0, 0)? is any point on any line (0, 0, 0)?

[neitoxotien]

I remember this when I was in school, Fano's Geometry with 5 axioms. That will draw as what is in the video. I hope to see Young's Geometry.

[lolmanthecat]

WHERE DOES IT SHOW UP??? TELL ME WHERE???? I am actually serious, you left out the most important part, I need to know.

[musheeraparveen]

Why does it looks like deathly hallows...😅

[dbamv]

Can't we include the circle that connects the three vertex as we did with the inside circle?

[rk-fbhw]

Wish I had any idea what he's talking about about

[danielfleming]

I could make it smaller. I have really small writing. ✍️

[JavaScripting]

If every three points makes a line wouldn’t there be many more circles? Why only the center one?

[abilalpk]

I liked it. But couldn't understand it 😂

[xiahe]

When do you learn this cause i just started middle school

[nomchomsley]

Why is it a circle and not another triangle?

[Soul-gfvv]

Are there any practical uses for this?