lol is there a less hideous way to implement Taylor polynomials in desmos? www.desmos.com/calculator/u...
Taylor polynomials
www.desmos.com
December 8, 2025 at 4:50 PM
lol is there a less hideous way to implement Taylor polynomials in desmos? www.desmos.com/calculator/u...
I had the reverse of this happen to me. A paper I did in undergrad got cited in a conference paper about AI photo recognition. Unless there's a connection between that and factorization of iterates of integer polynomials that's unknown to me but obvious to AI people, this was a hallucination.
December 9, 2025 at 7:09 PM
I had the reverse of this happen to me. A paper I did in undergrad got cited in a conference paper about AI photo recognition. Unless there's a connection between that and factorization of iterates of integer polynomials that's unknown to me but obvious to AI people, this was a hallucination.
demonstration:
arctan(-x/(y-1)) / arctan(x / (y+1)) = R
(for a portion of the angularbola, due to not using atan2)
let R = n / d
d * arctan(-x/(y-1)) = n * arctan(x / (y+1))
take tan of both sides. now use trig angle sum formulas to get rational polynomials on both sides
arctan(-x/(y-1)) / arctan(x / (y+1)) = R
(for a portion of the angularbola, due to not using atan2)
let R = n / d
d * arctan(-x/(y-1)) = n * arctan(x / (y+1))
take tan of both sides. now use trig angle sum formulas to get rational polynomials on both sides
December 8, 2025 at 2:18 AM
demonstration:
arctan(-x/(y-1)) / arctan(x / (y+1)) = R
(for a portion of the angularbola, due to not using atan2)
let R = n / d
d * arctan(-x/(y-1)) = n * arctan(x / (y+1))
take tan of both sides. now use trig angle sum formulas to get rational polynomials on both sides
arctan(-x/(y-1)) / arctan(x / (y+1)) = R
(for a portion of the angularbola, due to not using atan2)
let R = n / d
d * arctan(-x/(y-1)) = n * arctan(x / (y+1))
take tan of both sides. now use trig angle sum formulas to get rational polynomials on both sides
Cartographers is much more complex in comparison to this.
This one is dry erase and you’re only doing X’s. A little strategy in how you use the polynomials but not nearly as much depth
This one is dry erase and you’re only doing X’s. A little strategy in how you use the polynomials but not nearly as much depth
December 1, 2025 at 10:56 PM
Cartographers is much more complex in comparison to this.
This one is dry erase and you’re only doing X’s. A little strategy in how you use the polynomials but not nearly as much depth
This one is dry erase and you’re only doing X’s. A little strategy in how you use the polynomials but not nearly as much depth
computing Hilbert polynomials and I realized... I fucking love counting
November 26, 2025 at 10:41 PM
computing Hilbert polynomials and I realized... I fucking love counting
I have seen the maw of polynomials and .. . this thing has seen me too
This is a teleological demon; its teeth are peerless and its eyes are manifold
This is a teleological demon; its teeth are peerless and its eyes are manifold
November 27, 2025 at 2:09 AM
I have seen the maw of polynomials and .. . this thing has seen me too
This is a teleological demon; its teeth are peerless and its eyes are manifold
This is a teleological demon; its teeth are peerless and its eyes are manifold
mathematics papers love to describe things and then follow them with statements like '(which we do not do)'. am i undeserving of the polynomials. is that it
November 25, 2025 at 8:58 AM
mathematics papers love to describe things and then follow them with statements like '(which we do not do)'. am i undeserving of the polynomials. is that it
whenever you post about math it always gets me thinking how I would do things if I designed the whole curriculum.
imo determinants could be introduced with characteristic polynomials. you could’ve already done linear algebra. Now you’d be looking at stability or something.
imo determinants could be introduced with characteristic polynomials. you could’ve already done linear algebra. Now you’d be looking at stability or something.
November 24, 2025 at 10:21 PM
whenever you post about math it always gets me thinking how I would do things if I designed the whole curriculum.
imo determinants could be introduced with characteristic polynomials. you could’ve already done linear algebra. Now you’d be looking at stability or something.
imo determinants could be introduced with characteristic polynomials. you could’ve already done linear algebra. Now you’d be looking at stability or something.
sometimes babygirl is a 19th century french mathematician who developed a core theory for the solvability of general polynomials before dying young in a mysterious duel, & that's okay
November 18, 2025 at 7:11 PM
sometimes babygirl is a 19th century french mathematician who developed a core theory for the solvability of general polynomials before dying young in a mysterious duel, & that's okay
Mathematician Ruth Aaronson Bari was born 108 years ago today. After surrendering her grad school position to make room for returning WW2 soldiers, she did not resume her career until the age of 47, after which she was widely recognized for her work on chromatic polynomials.
#WomenInSTEM #MathSky 🧮
#WomenInSTEM #MathSky 🧮
November 17, 2025 at 2:56 PM
Mathematician Ruth Aaronson Bari was born 108 years ago today. After surrendering her grad school position to make room for returning WW2 soldiers, she did not resume her career until the age of 47, after which she was widely recognized for her work on chromatic polynomials.
#WomenInSTEM #MathSky 🧮
#WomenInSTEM #MathSky 🧮
Part of the focus of the combinatorics class is polynomials at the moment and it’s like a switch flipped, now I have so much buy in. Love those guys
November 16, 2025 at 7:19 PM
Part of the focus of the combinatorics class is polynomials at the moment and it’s like a switch flipped, now I have so much buy in. Love those guys
I think this is entirely reasonable, esp. when you realize that it’s really not different from ordinary long division because the numbers we write are polynomials in disguise
November 14, 2025 at 7:00 PM
I think this is entirely reasonable, esp. when you realize that it’s really not different from ordinary long division because the numbers we write are polynomials in disguise
Confusing stats language:
The "linear" is linear regression means "linear in the parameters".
It does not mean "can only fit straight lines", and things like polynomials and splines can be included in linear models.
online.stat.psu.edu/stat501/less...
1/2
The "linear" is linear regression means "linear in the parameters".
It does not mean "can only fit straight lines", and things like polynomials and splines can be included in linear models.
online.stat.psu.edu/stat501/less...
1/2
November 14, 2025 at 9:08 AM
Confusing stats language:
The "linear" is linear regression means "linear in the parameters".
It does not mean "can only fit straight lines", and things like polynomials and splines can be included in linear models.
online.stat.psu.edu/stat501/less...
1/2
The "linear" is linear regression means "linear in the parameters".
It does not mean "can only fit straight lines", and things like polynomials and splines can be included in linear models.
online.stat.psu.edu/stat501/less...
1/2
Most relatable sentence in all of fanfic idc idc (I hate polynomials so bad)
November 10, 2025 at 5:56 PM
Most relatable sentence in all of fanfic idc idc (I hate polynomials so bad)
I read it like a gift label...
From: Univariate Polynomials
To: Probabilistically Checkable and Error-Tolerant Proofs
Merry Christmas to you both! x
From: Univariate Polynomials
To: Probabilistically Checkable and Error-Tolerant Proofs
Merry Christmas to you both! x
November 1, 2025 at 11:06 PM
I read it like a gift label...
From: Univariate Polynomials
To: Probabilistically Checkable and Error-Tolerant Proofs
Merry Christmas to you both! x
From: Univariate Polynomials
To: Probabilistically Checkable and Error-Tolerant Proofs
Merry Christmas to you both! x
how many iterated degree-n complex polynomials have julia sets with self-similarity?
October 30, 2025 at 6:57 PM
how many iterated degree-n complex polynomials have julia sets with self-similarity?
Pain.
Do I hate polynomials or do I hate f32? Yes.
Do I hate polynomials or do I hate f32? Yes.
October 30, 2025 at 9:56 AM
Pain.
Do I hate polynomials or do I hate f32? Yes.
Do I hate polynomials or do I hate f32? Yes.
Hypnotizing you to solve polynomials! 🌀😵💫
October 28, 2025 at 1:11 AM
Hypnotizing you to solve polynomials! 🌀😵💫
I've added an appendix to my "Enough Polynomials and Linear Algebra to Implement Kyber" article with the little extra needed to implement Dilithium/ML-DSA.
Maybe I'll stream an ML-DSA implementation tomorrow at www.twitch.tv/filosottile.
Maybe I'll stream an ML-DSA implementation tomorrow at www.twitch.tv/filosottile.
Enough Polynomials and Linear Algebra to Implement Kyber
How much linear algebra and polynomials do you need to know to implement Kyber? Turns out, very little!
words.filippo.io
October 26, 2025 at 12:55 AM
I've added an appendix to my "Enough Polynomials and Linear Algebra to Implement Kyber" article with the little extra needed to implement Dilithium/ML-DSA.
Maybe I'll stream an ML-DSA implementation tomorrow at www.twitch.tv/filosottile.
Maybe I'll stream an ML-DSA implementation tomorrow at www.twitch.tv/filosottile.
The whole subject of "classical orthogonal polynomials" appears repeatedly in physics, but usually isn't studied in its own right. We end up having to look up whether a certain polynomial is Hermite, or Legendre, or Chebyshev, or whatever. (At least I do.)
en.wikipedia.org/wiki/Classic...
en.wikipedia.org/wiki/Classic...
Classical orthogonal polynomials - Wikipedia
en.wikipedia.org
October 24, 2025 at 3:13 PM
The whole subject of "classical orthogonal polynomials" appears repeatedly in physics, but usually isn't studied in its own right. We end up having to look up whether a certain polynomial is Hermite, or Legendre, or Chebyshev, or whatever. (At least I do.)
en.wikipedia.org/wiki/Classic...
en.wikipedia.org/wiki/Classic...
I'll be at the FiO LS 2025 conference in Denver, CO this weekend through mid-week next week to show off my latest paper on tricks to computing Zernike Polynomials; happy to chat about improving process flow management in your wafer fab / device lab using panmo.cloud #Conference #Optica #DOE 🧪
October 24, 2025 at 8:36 PM
I'll be at the FiO LS 2025 conference in Denver, CO this weekend through mid-week next week to show off my latest paper on tricks to computing Zernike Polynomials; happy to chat about improving process flow management in your wafer fab / device lab using panmo.cloud #Conference #Optica #DOE 🧪
TorchCurves - differentiable parametric curves in PyTorch
PyTorch parametric curves spanned by B-Splines or Legendre polynomials for KANs, Embeddings, or PDE solvers.
https://github.com/alexshtf/torchcurves
PyTorch parametric curves spanned by B-Splines or Legendre polynomials for KANs, Embeddings, or PDE solvers.
https://github.com/alexshtf/torchcurves
October 21, 2025 at 9:15 PM
TorchCurves - differentiable parametric curves in PyTorch
PyTorch parametric curves spanned by B-Splines or Legendre polynomials for KANs, Embeddings, or PDE solvers.
https://github.com/alexshtf/torchcurves
PyTorch parametric curves spanned by B-Splines or Legendre polynomials for KANs, Embeddings, or PDE solvers.
https://github.com/alexshtf/torchcurves
what if instead of dividing polynomials I actually exploded instead
October 14, 2025 at 7:36 PM
what if instead of dividing polynomials I actually exploded instead
In #MathsToday (actually last year, first year teaching), we trained with Y10 on quadratic substitution with the challenge to be the first to find a non prime number generated by special polynomials (mathworld.wolfram.com/Prime-Genera...). Drawback is not using negative integer values to substitute.
Prime-Generating Polynomial -- from Wolfram MathWorld
Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime for all integer values (N...
mathworld.wolfram.com
October 14, 2025 at 10:40 PM
In #MathsToday (actually last year, first year teaching), we trained with Y10 on quadratic substitution with the challenge to be the first to find a non prime number generated by special polynomials (mathworld.wolfram.com/Prime-Genera...). Drawback is not using negative integer values to substitute.