MixedMath - Recent Commentshttps://davidlowryduda.comDavid's personal blog.en-usCopyright David Lowry-Duda (2022) - All Rights Reserved.admin@davidlowryduda.comadmin@davidlowryduda.comWed, 15 Nov 2023 22:01:32 +0000Wed, 15 Nov 2023 22:01:32 +0000mixedmathapp/generate_rss.py v0.1https://cyber.harvard.edu/rss/rss.htmlhttps://davidlowryduda.com/static/images/favicon-32x32.pngMixedMathhttps://davidlowryduda.comDLD on Comments on this sitehttps://davidlowryduda.com/comments-v4<p>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.</p>
<p>I use a couple of different email programs depending on context. See
<a href="https://useplaintext.email/">useplaintext.email</a> for more precise software
recommendations that I also generically support.</p>44d28008f4a5d030b2a8297036c162ccWed, 15 Nov 2023 03:14:15 +0000Sarah on Comments on this sitehttps://davidlowryduda.com/comments-v4<p>What email do you use? Gmail doesn't support plain email? Did this comment
go through?</p>7cc64a4ddfbb2ee336c2a5f6ec36f9dbMon, 13 Nov 2023 03:14:15 +0000DLD on Paper: Congruent number triangles with the same hypotenusehttps://davidlowryduda.com/paper-congruent-triangles-same-hypotenuse<p>Good luck! I'll note that the sparseness means that it is <em>extremely unlikely</em>
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.</p>f10bd640bbb49277eafebbe041a0ddc2Wed, 01 Nov 2023 03:14:15 +0000RB on Paper: Congruent number triangles with the same hypotenusehttps://davidlowryduda.com/paper-congruent-triangles-same-hypotenuse<p>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.</p>4321d77bb11625f59f4191b333be9a8cWed, 01 Nov 2023 03:14:15 +0000DLD on Paper: Congruent number triangles with the same hypotenusehttps://davidlowryduda.com/paper-congruent-triangles-same-hypotenuse<p>Thank you for your comment RB. The conjecture refers to <em>primitive</em> triangles
for exactly this reason. The description above now includes your example in the
description.</p>8493da67b7967e22b20c7aafa5584217Wed, 01 Nov 2023 03:14:15 +0000RB on Paper: Congruent number triangles with the same hypotenusehttps://davidlowryduda.com/paper-congruent-triangles-same-hypotenuse<p>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?</p>d91fb714da097f9986f809cf896e8cc5Wed, 01 Nov 2023 03:14:15 +0000davidlowryduda on Initial thoughts on visualizing number fieldshttps://davidlowryduda.com/pcmi-vis-nf<p>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.</p>
<p>I think this is worth checking out!</p>dd5f5eb696ddc8c8cbc2c038d1250881Thu, 02 Mar 2023 03:14:15 +0000davidlowryduda on Slides from a talk at Concordia Universityhttps://davidlowryduda.com/slides-from-concordia-2023<p>I mean <em>compute an arbitrarily close approximation</em> 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.</p>54f291eaa6e515f8395f4fb98a80bfb0Wed, 01 Mar 2023 03:14:15 +0000AA on Slides from a talk at Concordia Universityhttps://davidlowryduda.com/slides-from-concordia-2023<p>What does it mean to compute something that is uncomputable?</p>2debf2e2c316a5ed24073eda75519023Wed, 01 Mar 2023 03:14:15 +0000DLD on On Mathstodonhttps://davidlowryduda.com/on-mathstodon<p><a href="https://mathstodon.xyz/@davidlowryduda">@davidlowryduda@mathstodon.xyz</a>.</p>8a19677b8293b549c1e68b3f6bdd7029Mon, 02 Jan 2023 03:14:15 +0000PD on Making Plots of Modular Formshttps://davidlowryduda.com/making-plots-of-modular-forms<p>Thanks for the quick reply and your code! I was working already with few libs.</p>3652a9161a1da72b7017f21331085fe6Mon, 02 Jan 2023 03:14:15 +0000DLD on Making Plots of Modular Formshttps://davidlowryduda.com/making-plots-of-modular-formsThis comment is larger than 2500 bytes, which is above the limit for this RSS feed. Please view it directly at the url.76b1770669dd48d2cee6e4661c490f7aMon, 02 Jan 2023 03:14:15 +0000mrita on On Mathstodonhttps://davidlowryduda.com/on-mathstodon<p>What is your name on mastodon?</p>038b45b7433595c2ae0b18e4454e210aSun, 01 Jan 2023 03:14:15 +0000PD on Making Plots of Modular Formshttps://davidlowryduda.com/making-plots-of-modular-forms<p>I see your plots here. Do you have an idea how to plot precisely
<a href="https://en.wikipedia.org/wiki/Modular_lambda_function#/media/File:Lambda_function.svg">this curve?</a></p>
<p>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).</p>
<p>No hurry in answering. This is a project I am doing in parallel to my life.</p>4cc69f0a266c153c2ef30d014082ae25Sun, 01 Jan 2023 03:14:15 +0000davidlowryduda on The gamma function, beta function, and duplication formulahttps://davidlowryduda.com/the-gamma-function-beta-function-and-duplication-formula<p>Dear Nishant,</p>
<p>I believe this is called the duplication formula because it's <em>almost</em> a
formula of the form $\Gamma(z)\Gamma(z)$, i.e. this is <em>almost</em> a formula fro
two copies of $\Gamma(z)$. Maybe calling it the "near duplication formula"
wasn't catchy enough.</p>
<p>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
<em>The Gamma Function</em>, which contains far more if you're interested.</p>49ed0a9f58115f4f875bdf7c674763a9Sun, 16 Oct 2022 03:14:15 +0000Nishant on The gamma function, beta function, and duplication formulahttps://davidlowryduda.com/the-gamma-function-beta-function-and-duplication-formula<p>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.</p>e79257fc23bc7fda02819ca9bae1a599Wed, 12 Oct 2022 03:14:15 +0000davidlowryduda on An intuitive introduction to calculushttps://davidlowryduda.com/an-intuitive-introduction-to-calculus<p>Thank you. They should now be fixed.</p>efde99d93ddf70913680b375312f4a9cMon, 06 Jun 2022 03:14:15 +0000MF on An intuitive introduction to calculushttps://davidlowryduda.com/an-intuitive-introduction-to-calculus<p>The graphics aren't loading!</p>70eba4e5a21e513016e99975c319742aMon, 06 Jun 2022 03:14:15 +0000davidlowryduda on Visualizations for Quanta's 'What is the Langlands Program?'https://davidlowryduda.com/quanta-langlands-viz<p>Quanta sent me palettes, and I designed colormaps around these colors.
They adjusted some of the colors afterwards too.</p>7f5ba165d0d033b0e7c4b0a1350428c5Fri, 03 Jun 2022 03:14:15 +0000CA on Visualizations for Quanta's 'What is the Langlands Program?'https://davidlowryduda.com/quanta-langlands-viz<p>What colormap did you use for the video?</p>0b3d422c2e5b166e6e6e172ec943919eFri, 03 Jun 2022 03:14:15 +0000davidlowryduda on colormapplot - like phasematplot, but with colormapshttps://davidlowryduda.com/colormapplot<p>I like that you made a custom colormap and went with it. I think this sort of
experimentation will lead to powerful, informative visualizations.</p>
<p>Congratulations on making a website!</p>4fd4b32003ca4ead78f7be544348e232Wed, 20 Apr 2022 03:14:15 +0000Andrew on colormapplot - like phasematplot, but with colormapshttps://davidlowryduda.com/colormapplot<p>Some plots in SageMath, what do you think:
<a href="https://sheerluck.github.io">https://sheerluck.github.io</a> My first web site
ever in my life :)</p>66b898eac5341e5ff7b7442b209e4fb5Sun, 27 Mar 2022 03:14:15 +0000Markus Nascimento on An intuitive overview of Taylor serieshttps://davidlowryduda.com/an-intuitive-overview-of-taylor-series<p>Very nice note. It really helped me to understand a bit more about Taylor
polynomials’ intuition. Congratulations!</p>53ed03f5caa13e5f14dfd77ed31f9cf7Thu, 17 Mar 2022 03:14:15 +0000Vaskor Basak on Prime rich and prime poorhttps://davidlowryduda.com/prime-rich-and-prime-poor<p>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?</p>3dc95bd2293930cf465b867debd35ebaSat, 25 Dec 2021 03:14:15 +0000davidlowryduda on An intuitive overview of Taylor serieshttps://davidlowryduda.com/an-intuitive-overview-of-taylor-series<p>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.</p>
<p>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.</p>
<p>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.</p>1d16e4fb91641622374a2b5c08866b19Tue, 19 Oct 2021 03:14:15 +0000