MixedMath - Recent Comments

DLD on Comments on this site

Wed, 15 Nov 2023 03:14:15 +0000

Yes, your message came through just fine. For a typical message, it's easy to extract plain messages from email. If someone were to try to send formatted content inside an HTML email, that might be a problem.

I use a couple of different email programs depending on context. See useplaintext.email for more precise software recommendations that I also generically support.

Sarah on Comments on this site

Mon, 13 Nov 2023 03:14:15 +0000

What email do you use? Gmail doesn't support plain email? Did this comment go through?

DLD on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

Good luck! I'll note that the sparseness means that it is extremely unlikely that a naive search, even very efficiently coded, would beat the approach guided by elliptic curves I describe in the paper. But I would be very interested to know a counterexample (if it exists) or a proof (if it exists) to my conjecture.

RB on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

Ah, I missed "primitive" so I will go back to my GP-Pari routines, since I have an efficient way of finding square pairs summing to a third square.

DLD on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

Thank you for your comment RB. The conjecture refers to primitive triangles for exactly this reason. The description above now includes your example in the description.

RB on Paper: Congruent number triangles with the same hypotenuse

Wed, 01 Nov 2023 03:14:15 +0000

David, the triangles $(740, 777, 1073)$ and $(348, 1015, 1073)$ both have the same hypotenuse. They both have the same non-square area $210$. In your paper you say these triangles do not exist? Did I miss something?

davidlowryduda on Initial thoughts on visualizing number fields

Thu, 02 Mar 2023 03:14:15 +0000

At CIRM in Luminy, a great alternative idea was proposed. The idea is to replicate parts of Mumford's famous picture on $\mathrm{Spec}(\mathbb{Z}[x])$, but presumably focus on only a single horizontal line (which corresponds to a fixed number field). This would display splitting behavior of various primes with some sort of line plot.

I think this is worth checking out!

davidlowryduda on Slides from a talk at Concordia University

Wed, 01 Mar 2023 03:14:15 +0000

I mean compute an arbitrarily close approximation here. And I should note that there are a fixed set of Maass forms with eigenvalues in some range $\frac{1}{4} < \lambda < \lambda_2$, so there are a precise list of forms that I am trying to find close approximations to.

AA on Slides from a talk at Concordia University

Wed, 01 Mar 2023 03:14:15 +0000

What does it mean to compute something that is uncomputable?

DLD on On Mathstodon

Mon, 02 Jan 2023 03:14:15 +0000

@davidlowryduda@mathstodon.xyz.

PD on Making Plots of Modular Forms

Mon, 02 Jan 2023 03:14:15 +0000

Thanks for the quick reply and your code! I was working already with few libs.

DLD on Making Plots of Modular Forms

Mon, 02 Jan 2023 03:14:15 +0000

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mrita on On Mathstodon

Sun, 01 Jan 2023 03:14:15 +0000

What is your name on mastodon?

PD on Making Plots of Modular Forms

Sun, 01 Jan 2023 03:14:15 +0000

I see your plots here. Do you have an idea how to plot precisely this curve?

I am simulating few mathematical things (I am not a mathematician, only engineer) and would like to identify the coordinates of the points of the curve for making a comparison with tetraetion curves. I know how to start python scripts and was using sometime matplotlib (No clue of Sage).

No hurry in answering. This is a project I am doing in parallel to my life.

davidlowryduda on The gamma function, beta function, and duplication formula

Sun, 16 Oct 2022 03:14:15 +0000

Dear Nishant,

I believe this is called the duplication formula because it's almost a formula of the form $\Gamma(z)\Gamma(z)$, i.e. this is almost a formula fro two copies of $\Gamma(z)$. Maybe calling it the "near duplication formula" wasn't catchy enough.

It was first proved by Adrien-Marie Legendre, hence the name. Legendre also gave the notation $\Gamma$ for the gamma function. I read this in Artin's book The Gamma Function, which contains far more if you're interested.

Nishant on The gamma function, beta function, and duplication formula

Wed, 12 Oct 2022 03:14:15 +0000

I just had a query that why is this form called duplication formula, and above all why Legendre duplication formula. Any information shared will find me highly motivated.

davidlowryduda on An intuitive introduction to calculus

Mon, 06 Jun 2022 03:14:15 +0000

Thank you. They should now be fixed.

MF on An intuitive introduction to calculus

Mon, 06 Jun 2022 03:14:15 +0000

The graphics aren't loading!

davidlowryduda on Visualizations for Quanta's 'What is the Langlands Program?'

Fri, 03 Jun 2022 03:14:15 +0000

Quanta sent me palettes, and I designed colormaps around these colors. They adjusted some of the colors afterwards too.

CA on Visualizations for Quanta's 'What is the Langlands Program?'

Fri, 03 Jun 2022 03:14:15 +0000

What colormap did you use for the video?

davidlowryduda on colormapplot - like phasematplot, but with colormaps

Wed, 20 Apr 2022 03:14:15 +0000

I like that you made a custom colormap and went with it. I think this sort of experimentation will lead to powerful, informative visualizations.

Congratulations on making a website!

Andrew on colormapplot - like phasematplot, but with colormaps

Sun, 27 Mar 2022 03:14:15 +0000

Some plots in SageMath, what do you think: https://sheerluck.github.io My first web site ever in my life :)

Markus Nascimento on An intuitive overview of Taylor series

Thu, 17 Mar 2022 03:14:15 +0000

Very nice note. It really helped me to understand a bit more about Taylor polynomials’ intuition. Congratulations!

Vaskor Basak on Prime rich and prime poor

Sat, 25 Dec 2021 03:14:15 +0000

What polynomials are allowable for prime-poor polynomials? Could I claim that I have found a better example of a prime-poor polynomial than $x^{12}+488669$ by presenting the example $(x+3)^{12}-488601$, for example?

davidlowryduda on An intuitive overview of Taylor series

Tue, 19 Oct 2021 03:14:15 +0000

Hi Bob! The behavior of $c$ is actually quite subtle. It's not true that $c$ is actually a constant. For "nice" functions, what is true is that the mean value $c$ varies continuously over intervals (except at finitely many points). Combined with a form of Darboux's theorem (stating that every function that is the derivative of another function has the intermediate value property, even if it's not continuous) is enough.

I published a paper with Miles Wheeler (preprint available at https://arxiv.org/abs/1906.02026) in the American Mathematical Monthly that showed that the mean values generically can be chosen to vary locally continuously on the right endpoint, the key analytic ingredient.

Making this rigorous is substantially more complicated than other proofs. As a heuristic, I like that it suggests the right shape of Taylor's formula (which is often nonobvious to a beginner), but I don't think it's the right way to actually go about proving it.