Zeta
Freya Holméryou've heard of sine and cosine
now get ready for uh squine and cosquare
source code. source math? idk
Dana@acegikmo Oh no I do NOT like that asymmetrical curve one bit
jazz mickle@danana_dread @acegikmo its rotationally symmetric!
Tumby@danana_dread @acegikmo Just like sine and cosine, one has rotational symmetry and the other has mirror symmetry.
Eibriel@acegikmo I see 🤷♂
ml@acegikmo I hope you brought some food while descending down that rabbit hole ;-)
PypeBros@acegikmo you mean we could approach sin(t) and cos(t) by considering the infinite limit of a converging series of squine and cosquine for increasing size of polygonial sides ? (but preferrably with even polygons)
@acegikmo I love how restoring the x=cos(t) in the square example gives you a barrel tracer :P
Packbats, HTML fangirls ΘΔ&@acegikmo what happens if you use star polygons? 🤔
David Cantrell 🏏@acegikmo is this the path followed by a point on a pentagon as you roll it along a line? And it varies depending on what point you choose? I now regret you exposing me to them too!
Vicente ⁂@acegikmo what about n-gonal?
Antoine Webanck@acegikmo let's generalize all the way through the regular polygons on the way to the limit of the circle?
laurent@acegikmo there must be a whole series of curves, one for each platonic solid. I'm sure they have cool properties. Wonder what they sound like.
j_bertolotti@acegikmo AKA as "sine and cosine in the taxicab metric" 😃
TobyBartels@j_bertolotti @acegikmo : The circle in the taxicab metric (l¹) is a diagonal square with half this size. This is the circle in the l^∞ metric (which doesn't have a cute name as far as I can remember).
Andrew@TobyBartels @j_bertolotti @acegikmo i think it's sometimes called the chessboard metric, as it's kind of "distance in king's moves"?
@TobyBartels @andrewt @j_bertolotti I've usually hear it called Chebyshev distance, but idk how commonly used it is!
or max-norm or something of the kind
there's also rectilinear distance but I always forget if that's taxicab or chebyshev
@acegikmo @TobyBartels @j_bertolotti I think I did use it in my PhD but only really to speed up a calculation, it wasn't actually *better* for anything
space slut 
@acegikmo @TobyBartels @andrewt @j_bertolotti when i studied maths (in german) it was called supremum norm, but i've also heard it be called chebyshev distance
@spacekatia @acegikmo @andrewt @j_bertolotti : Both ‘max’ and ‘supremum’ strike me as straightforward descriptions, not fun names like ‘Manhattan’ and ‘chessboard’, while ‘Chebyshev’ lies in between. (But it makes a counterpart to ‘Euclidian’, so now I want to know who to name the l¹ metric after.)
@TobyBartels @acegikmo @andrewt @j_bertolotti doctor manhattan of course (minkowsky already has too many metrices named after him)
jokes aside, you could probably name it after frigyes riesz, who first considered it as a distance metric at the same time as minkowsky
@TobyBartels @acegikmo @andrewt @j_bertolotti also i always found manhattan metric a nice illustratine example of why you'd consider metrics besides euclidean even in day to day life tbh
@spacekatia @TobyBartels @acegikmo @j_bertolotti oh yeah, dr manhattan, the guy who invented the bomb, i think they named a street after him or something
PlasmaGryphon@j_bertolotti @acegikmo for a square with sides parallel to axes it would be Chebyshev or L_inf metric. Taxicab/Manhattan/L_1 metric gives a square 45 degrees from axes (a diamond) for points equidistant from origin.
[66178] Mistress Sparkles in Twilight@acegikmo I wonder what they sound like
- posted by Sparkles-Sericea
- posted by Sparkles-Sericea
Bob Nystrom
Oblomov@acegikmo very peculiar (though it took me a while to catch it because the color choice for the plots isn't too colorblind-friendly).
I'm trying to think if they satisfy an equation similar to that of sin/cos, but abs(s) + abs(c) = 1 doesn't work. Is it something like abs(s+c) + abs(s-c) = 1 maybe?
James King
0xC01DC0FFEE@acegikmo how about hexagons? 
Joshua A.C. Newman (he/they)
greeeen :nb_verified::verifiedbi::verifiedlesbian:@acegikmo does a Fourier transform with those
Les capsules du prof Lutz@acegikmo what about phase? Higher order Lissajous figures?
@lutzray @acegikmo
Man, I’m just gonna go down these responses and recommend https://plugdata.org , aren’t I?
Man, I’m just gonna go down these responses and recommend https://plugdata.org , aren’t I?
thejikz@acegikmo seems like this leads to colipses ans silipses? Could it perchance? Sindiamonds? ... :O
My wordplay/math/concepts wires are a little all over today.
My wordplay/math/concepts wires are a little all over today.
rosalyn 
Methylzero@acegikmo when the cheap solar inverters kick in
SE2Dev@acegikmo I like how if you add a third line that fills in the gap and use them as RGB channels you get a pretty nice color gradient over time!
Morten Hilker-Skaaning
Riley S. Faelan@acegikmo What if it was the angle, not the travel time, on your x-axis?
enoch_exe_inc@acegikmo Already did something like this, except generalised to all polygons: https://www.desmos.com/calculator/ya2ph4frsf
I have a lot—and I mean a *LOT*—of random Desmos graphs full of weird maths, physics, and computer science-related experiments.
Alba 🌸 
@acegikmo this is the pseudo-polar coordinate system used in this paper
John Kaniarz@acegikmo I used a function like this for pixel art interpolation. Where you want it mostly blocky with just a little blending at the edges. I never would have guessed how powerful it was as a sin/cos replacement.
AN/CRM-114@acegikmo deadpan: sin cos tan
hyperbole: sinh cosh tanh
boxy: sins coss tans
secs cosecs cots
¡arccosecs!
Marcus Müller@acegikmo in communications engineering, we call that "O-QPSK with a square pulse shape", and I think that's beautiful.
Melroy van den Berg@acegikmo And Tangent?
jsiehler@acegikmo There's a nice Math Magazine article about the analogous functions for \(x^4+y^4=1\).
https://www.tandfonline.com/doi/abs/10.4169/math.mag.84.4.257
Serge from Babka
Jerobeam Fenderson - Planets
The Right Irreverend@acegikmo Instead of π, you use SheetCake?
Benjohn@acegikmo Cool :-) I implemented a Mandelbrot that used complex numbers that rotate in squares like this. It was crap and i wouldn’t bother.