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Radial Tessellation derived from a square.

More Ghee Beom Kim magic!

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math

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Why do mathematicians love pi so much? It's related to some shape, but they like that shape because it explains why pi shows up? Sounds like circular reasoning to me

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I love when a textbook has a theorem that is just the most obviously true shit, like girl I sure hope so, if that weren't true I think math would fall apart!

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“2 is the only even prime” well 17 is the only prime that’s divisible by 17 so 2 being divisible by 2 is not that big of a deal

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There's this thing called a cyclic ordering, where things are ordered in a cycle instead of a line, like mods instead of natural numbers. Unlike standard orderings, where it requires two arguments, like a<b, cyclic orderings need three, because saying a comes before b, is the same as saying b comes before a, so you have you say after a, b is reached before c, which is not the same as after c, b is reached before a. It has this property called cyclicity, which is the same one that was described in last ask.

Ooh, interesting!

So, for example, in mod 6, after 2, 5 is reached before 1, but after 1, 5 is not reached before 2. That kind of deal?

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"ohh my god you can't just-"

Am I yours to command? Does the collar 'round my neck have your name on it? I kneel to no king nor god, and I see no crown on you.

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Can I ask a question?

So Commutativity is when the order of inputs in an operator can be swapped: a°b=b°a

And Associativity is when the order of which operator is taken first can be swapped: (a°b)°c=a°(b°c)

Is there a name for when order of inputs of an operator can be shifted? Like a°b°c=b°c°a=c°a°b≠c°b°a

1. Yes you can

2. There could be, but I haven't heard of it... if I got to name it I'd call it something like cyclability.

Now I'm wondering what an example of that might be... and what would result from it...

If this is a thing and you know what it's called, please do chime in!

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Godelian jokes

A mathematician and a contrarian walk into a bar

Bartender: "So what'll you girls be having?" Mathematician: "The contrarian won't order anything." Contrarian: "I'll have a drink." Mathematician: "It's now obvious that she's having a drink."

The mathematician has contradicted herself. She is inconsistent.

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A mathematician and a contrarian walk into a bar

Bartender: "So what'll you girls be having?" Mathematician: "The contrarian will have a drink." Contrarian: *leaves* Mathematician: "She'll be back."

The contrarian never comes back. The mathematician is consistent, but unsound.

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A mathematician and a contrarian walk into a bar

Bartender: "So what'll you girls be having?" Contrarian: "I'll have the opposite of whatever the mathematician thinks I'll have". Bartender: "So... uh..." Mathematician: "If I'm consistent, then I won't speak for her and she won't order anything." Bartender: "Are you? Consistent, I mean?" Mathematician: "Let me have a drink while I think about it."

The mathematician never decides. She is consistent and sound, but doesn't know it. The contrarian doesn't have a drink.

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Several hours later...

Bartender: "I'm pretty sure she's consistent. My shift is over, I'm going home."

The bartender has a higher consistency strength than the mathematician.

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An infinite amount of time passes. An oracle walks into the bar.

Oracle: "The mathematician never decided, the contrarian never had a drink, and the Bartender was consistent too."

She speaks in an ancient and impossible tongue which nobody can understand. Everyone else is dead. The oracle is uncomputable.

A contrarian oracle walks into the bar....

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Meme that my math teacher put on our lessons:

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I know I've seen this number because of the 60,000 bees meme

Do you ever wonder what's the smallest whole number (in terms of absolute value) that you've never encountered before?

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I know I've definitely interacted with every whole number below 100. I've probably at least seen every whole number below 1000. Beyond that who can say? Maybe the smallest number I've never seen is in the billions. Maybe it's only 4 digits long. I don't think there's any way to find out.

Do you ever wonder what's the smallest whole number (in terms of absolute value) that you've never encountered before?

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Do you ever wonder what's the smallest whole number (in terms of absolute value) that you've never encountered before?

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A simple group isn’t simple. A free group isn’t free. Modern Algebra is just false advertising.

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For reference, here's all of the primes between 1900 and 2025:

1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017