To Calculate and Live

Lemma: This is fixable.

Proof: A silly little application of $\neq$ \rotatebox[origin=c]{22}{$\varnothing$}

Remark: There are other options. If you dare.

Corollary:

you guys have no idea how beautiful numbers can get. 256 isnt a secret celebrity! everyone knwos 256! borderline overrated!

65,536 is the sexiest power of two number because its 2^2^2^2. and in theory you could go more twos above that because then the number is just unmanagable huge. too absurd.

i respect your gendering of 256 though. she gets to be a she. forever. now.

i like palindromic numbers. theyre just really hard to get reliably without doing powers of 11. but also, you know, it's a little elementary. hes already famous! everyone knows why 121 is hot. which doesnt make him less hot but its just a lesser developed aestheticism.

ohhhhhhh that flippy thing in the powers is makiny my brain go brrrr. thats hard to do. is that a powers of 2 thing only? 2^3 is not 3^2, so its like... even powers of two? no. no. no. oh. theres a unique little puzzle in that. i had no idea. wonderful taste. thank you. complimentary calculator.

i cant critique these. im glad you are participating and one day i hope you find a number that makes you pull up desmos and make borderline pornographic graphs. but for now 9 and 2 are good. yeah.

44 is the oatmeal raisin cookie of numbers. why is he your favorite. hes not even good. nobody likes him but you. are you old? are you evil? how did you get to this point? bleh.

23 and 29 do that but theyre a lot less sexy. you got flair here. moxiy. PIZZAZ. youre gonna go far. keep this shit up.

i feel like 223 is more interesting than 23 but as you got that and more i cannot fault your taste. you're a little math freak and i appreciate that.

eh.

im taking notes here. im not a homewrecker, im not gonna steal your number husband (nusband?) but like. i get it. exsquisitve taste here. i kind of thought that 144 was amateur hour but the 441-144 thing is like. ooooooo. impressively flexible.

you gotta give me a pitch on the 6561. and 4096 is still amateur hour binary. 2^14 malarky.

honestly surprised it took this long. honestly. i respect it.

okay that is dope. like its not crazy math just sitting there but it takes a special kind of brain to notice that. life is funny of interesting coincidences if you just let your brain run wild looking for them.

you get it you get it. theyre like. atomic. in the greek sense. they are the building block of every other number. when you break something into primes its like hnnng and when those primes are like. 3 or 4 digits long its like HNNNNNNNNNG.

idk then perish 44 is a lame number. lame! i mean. it's an even number for god's sake. yuck.

okay. i. hm. i do like that explanation. 22, twice. that's like three twos in a way. im. im gonna give it a shot. ill try anything once.

you are the only person to include a non-transcendetal number with decimals in it. you're a real freak. i dont get it but im glad youre here. you are like. the furry of the numberphile world. please go draw some 34.6 fanart. sell us on this. dig deep into your mind palace and bring to us its awful treasure.

i hear you. and i get it. i have some love for the 80085 poster. but its 69. theyre 69ing. i dont make the rules.

3*3*3 is like. mm. that makes my brain feel like i just scratched it. i like 729 because it's 27 squared and thats approaching the limits of my mental math. id looooove to be able to do 27 cubed all instantaneous like but 729 times 27 just makes me get all jumped. im like. uh. uh. uh. shit. 729 times 30 is 21000 plus 870, so thats not too bad, thats 21,870, and then i can skip the 729 times 3 part just by going, take 10% of the 21,870, so thats 2,187 #lazymath. but then subtracting that from 21870? too many digits to carry. i cant fucking carry digits in my head. i have to break it into more steps but that point im already out of steps and i need to sit down. smoke pours out my ears. i despair.

(anyway u have succesfully defended your thesis i hereby pronounce you a numblr use. god forth and count with god. )

Field: Combinatorial Number Theory

Journal: Communications in Addition and Subtraction

Title: A Lower Bound on the Largest Natural number

Abbreviated Abstract: We prove a lower bound on the largest number. The proof proceeds in two steps: we begin with 1, and proceed by induction as until we lose count. We then add that number to itself. The main advance in the first step is to get a big number, and the second step notably avoids using multiplication (they don't teach that until 3rd grade).

Field: Topological Geometry

Journal: Advances in Nonlines

Title: The Four-Color Scribbles

Abbreviated Abstract: In this work we show a zoo of examples of nonlines (curves) with the unique property that they are either red, blue, orange, or purple, or some combination therein. The key idea is to use less colors rather than more, creating a clear and easy to follow proof. This provides a clear basis for simplifications to further work, such as scribbling with 5 colors.

Field: Playground Analysis

Journal: Slide Dynamics

Title: Sufficient Conditions to Yell Weeeeeee on Spiral Slides

A ball inscribed in a cube fills 52% of the cube.

A 4-ball inscribed in a hypercube fills 31% of the hypercube.

A 5-ball inscribed in a 5-cube fills 16% of the 5-cube.

⋮

A 9-ball inscribed in a 9-cube fills it up less than 1% of the way, yet there’s no room to fit a second ball of the same size without intersecting the first.

⋮

In dimensions 23 and up, you can fit a little cube in the corner of the diagram, such that the cube has a larger volume than the ball!

if you take a cube with side length 4 and put a unit sphere in each corner and construct a sphere in the center of the cube such that it is tangent to each unit sphere, its radius is √3 - 1 ≈ 0.73

if you take a tesseract with side length 4 and put a unit hypersphere in each corner and construct a hypersphere in the center of the tesseract such that it is tangent to each unit hypersphere, its radius is √4 - 1 = 1, another unit hypersphere

if you take a 5-cube with side length 4 and put a unit 5-sphere in each corner and construct a 5-sphere in the center of the 5-cube such that it is tangent to each unit 5-sphere, its radius is √5 - 1 ≈ 1.24, and indeed from here on out our central n-sphere will be larger than the unit n-spheres it is constrained by

...

if you take a 9-cube with side length 4 and put a unit 9-sphere in each corner and construct a 9-sphere in the center of the 9-cube such that it is tangent to each unit 9-sphere, its radius is √9 - 1 = 2, which means it is now also tangent with the 9-cube that is constraining the unit 9-spheres that are constraining it

if you take a 10-cube with side length 4 and put a unit 10-sphere in each corner and construct a 10-sphere in the center of the 10-cube such that it is tangent to each unit 10-sphere, its radius is √10 - 1 ≈ 2.16, which means it now sticks out of the 10-cube