Which fundamental axioms of mathematics can be illustrated pictorially, without using any symbolic notation? We could show pic related to an extraterrestrial civilisation and they would immediately realise that we understand Pythagoras' Theorem (or whatever it's called on their planet). Are there any other axioms that can be shown the same way?
Are there any fundamental ideas in physics that could be communicated in this way?
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I have an autistic fantasy where I am abducted by aliens, but they're nice and don't anally probe me or anything like that. They just want to gauge my intelligence.
Among some other bric-a-brac, a collection of exactly fifty metal cubes are available for me to play with. Upon one early sit-down examination, I arrange the cubes into this pattern. They seem to be impressed, mildly amused even.
A human to an intelligent being capable of space travel is like a chimp to us.
show them deez nuts n they will immediately understand how big they r
That is really autistic, honestly.
If they are indeed AXIOMS, they cannot be proved.
Category theory is probably the closest you can get to pictorially DEFINING your AXIOMS.
A better question woulds be what proofs are there for algebra that only exist geometrically?
Top kek.
The Pythagorean theorem is not an axiom, that's why there is proofs of it.
The Steiner inellipse always intrigued me.
Take a cubic polynomial whose roots are not co-linear (they form a triangle in C).
There is a unique ellipse that can be inscribed in the triangle that touches the midpoints of the sides of the triangle.
The foci of this ellipse are located at the roots of the derivative of the cubic.
OP Are you retarded? Pythagorean Theorem has a proof, it's not an axiom
Lol I read that book.
I used to call my dog Bulger (STL Rams had a horrible QB by the same name)
Also try reading Steiner.
wew why are elliptical functions so weird?
Everything went better than expected.
Anything is weird to the unacquainted.
(pic: every 2 points defines a line, every 2 lines defines a point)
Look how to partition a number using a Ferrers/Young diagram. If you flip across the diagonal, you get another valid diagram.
Instantly you get the theorem: The number of partitions of n having largest part k is equal to the number of partitions of n into exactly k parts.
Thales' Theorem. I'd post the gif but I'm away from my computer. Pretty much every old school theorem has a plain, geometric proof.
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Really? Nobody?
>world.mathigon.org
This website provides illustrations of the ZF axioms
wait, thats autistic? I thought everyone had those
they were right about geometers, I gotta get outa here.
Wow, I hope OP actually reads this. Thanks.