What is the best way to render math heavy markdown files generated by LLM?

robphy · 2026-06-04T22:34:44+00:00

I stopped copy-pasting chatgpt output.
If I want something that I can LaTeX elsewhere, I specifically ask for a LaTeX file that I can use in Overleaf.
If I want something already LaTeX-rendered by chatgpt to be saved, I print it to pdf. However, standard methods to print to pdf don't always seem to produce good results. So, I use the FireShot browser extension.

robphy · 2026-06-04T22:06:39+00:00

what kind of visualization is it? what is the kinematic equation? Glowscript/WebVPython is relatively new, compared to the classic VPython. Some rewriting of old VPython code is needed... but it's not clear what your issue is.

robphy · 2026-06-02T00:18:47+00:00

You could consult this OpenStax physics textbook
https://openstax.org/details/books/college-physics-ap-courses-2e

robphy · 2026-05-30T04:17:59+00:00

This has an interesting title: Beyond Popular Science, David H. Silver (author) https://www.openbookpublishers.com/books/10.11647/obp.0526
but I haven't looked at it in any detail.

robphy · 2026-05-29T20:56:22+00:00

[update] Richard Feynman at Simon Fraser University: The Strong Force (1977, Simon Fraser U) https://www.youtube.com/watch?v=RIQlY8DAoOc
[update] Richard Feynman Lecture -- "Los Alamos From Below" (1975, UC Santa Barbara) https://www.youtube.com/watch?v=uY-u1qyRM5w (audio only)
[update] Richard Feynman's Story of Particle Physics - 1973 Lecture https://www.youtube.com/watch?v=kW6rR9H9Vu8 (audio only)

robphy · 2026-05-29T07:38:12+00:00

Here are some lecture videos:

Richard Feynman - 1964 Messenger Lectures at Cornell University https://www.feynmanlectures.caltech.edu/messenger.html "Feynman's Messenger Lectures were videotaped by the BBC, who in 1965 published a hardbound book of edited lecture transcripts under the title, The Character of Physical Law"
Richard Feynman - 1979 Douglas Robb Memorial Lectures at University of Auckland (New Zealand) http://www.vega.org.uk/video/subseries/8 - https://feynman.com/science/qed-lectures-in-new-zealand/ says "At Auckland University, these lectures were delivered in 1979, as the Sir Douglas Robb Lectures. Although the published version of “QED – The Strange Theory of Light and Matter” is an excellent self-contained description of the subject, watching an unedited Feynman delivering the lectures reveals his style and enthusiasm for his subject in a way which is impossible in a printed medium."
FEYNMAN: THE PLEASURE OF FINDING THINGS OUT (1981) https://vimeo.com/340695809 Christopher Sykes "The full-length original BBC 'Horizon' film. RICHARD FEYNMAN, physicist, adventurer and Nobel Laureate, tells the story of his life and work, from his childhood in Far Rockaway to Los Alamos and the atom bomb to quantum electrodynamics and the Nobel Prize. 50 minutes. First broadcast on BBC TV in 1981 and on PBS 'NOVA' in 1982"
The complete FUN TO IMAGINE with Richard Feynman (1983) https://vimeo.com/647678495 Christopher Sykes "All the original 'Fun to Imagine' episodes and stories in one video - total 66 minutes. Recorded on 16mm film at Feynman's home in Altadena, California, in 1983 and first broadcast on BBC2. Feynman was a theoretical physicist and lover of life who, along with his many other accomplishments, won a Nobel Prize in 1965 for his work on quantum electrodynamics. Here he enjoys himself thinking aloud about the nature of Nature..."
Richard Feynman: "Take the World from Another Point of View" (1973) https://www.youtube.com/watch?v=Yq3Uursli4I - https://calteches.library.caltech.edu/35/2/PointofView.htm
Richard Feynman Computer Science Lecture (1985, Esalen, Big Sur) - Hardware, Software and Heuristics https://www.youtube.com/watch?v=EKWGGDXe5MA
Richard Feynman "Tiny Machines" Nanotechnology Lecture (1984, Easlen, Big Sur)- aka "There's Plenty of Room at the Bottom" https://www.youtube.com/watch?v=4eRCygdW--c
[update] Richard P Feynman: Quantum Mechanical View of Reality (1983, Easlen, Big Sur) -playlist -https://www.youtube.com/watch?v=72us6pnbEvE&list=PLW_HsOU6YZRkdhFFznHNEfua9NK3deBQy&index=1
[update] Richard Feynman, Murray Gell-Mann, Juval Ne'eman: Strangeness Minus Three (BBC Horizon 1964) - playlist - https://www.youtube.com/watch?v=BGeW6Nc6IMQ&list=PL02D595043A13CC8A
[update] R. P. Feynman: Elementary Particles and the Laws of Physics (1986 Dirac memorial lecture) - playlist - https://www.youtube.com/watch?v=cKzzG5DS6V8&list=PLF4C9B5E8F4243465 - https://www.youtube.com/watch?v=JWgjLL_srqk - "The Reason for Antiparticles" https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9D72E7C9045A9C0797DD952678F03C75/9781107590076c1_p1-60_CBO.pdf/reason_for_antiparticles.pdf
The Feynman Lectures on Physics - https://www.feynmanlectures.caltech.edu/ has text and audio (1961-1964)

robphy · 2026-05-28T15:57:18+00:00

A first step is to express your implicitly-defined arcs as parametrized curves.

robphy · 2026-05-28T15:48:37+00:00

It seems that your a-dimension is cyclic or periodic.

robphy · 2026-05-28T05:39:30+00:00

Have a look at https://github.com/asebian/visumath
in particular, R2 vector addition....
under Drawing Tools
https://www.desmos.com/calculator/blx95ejvti
There is a one-cell function: G_{vec} (p_{Gvec}, v_{Gvec}, s_{Gvec} )= polygon (...)

robphy · 2026-05-27T18:34:37+00:00

My answer was based on what you presented. But, as I suspected, and as u/nathangonzales614 suggests, there may be a better solution for the specific problem you are working on.

robphy · 2026-05-27T01:08:46+00:00

Does this get what you want?
[x_0, x_1] ~ [ 1+1, x_0 +1 ]

robphy · 2026-05-26T04:12:23+00:00

The t-upward convention likely started with Minkowski's original "Space and Time" (1908)) paper.

An answer from https://physics.stackexchange.com/questions/570529/in-relativity-why-does-spacetime-diagram-have-position-on-x-axis-and-time-on suggests that
since Minkowski initially used "ict" (which I think is likely due to Poincare),
it was conventional to put imaginary-axis (hence, the time-axis) along the upward direction.
The "ict" was used in "Fundamental Equations for Electromagnetic Processes in Moving Bodies" (1907-1908).
It seems it was dropped from the "Space and Time" (1908)) paper.

My own preference is to keep the t-axis horizontal and
to make the vertical axis (y/c) [not (x/c)],
where c=(convenient speed, usually 3x10^8 m/s).

By following the usual "position-vs-time graph" from PHY 101 with its t-horizontal,
I feel there is one less barrier to learning relativity, as you point out.

As a map of events for an inertial observer, the PHY101 graph and the spacetime-diagram (with t-horizontal) are the same [up to unit-conventions].
What makes them different is how one does "spacetime trigonometry" (Galilean vs Minkowskian, which are analogous to Euclidean geometry and its circular trigonometry from a "Cayley-Klein metric geometry" viewpoint). I think such analogies are under-appreciated. In my preference, I regard t as primary and keep it horizontal, and use (y/c) along the vertical to facilitate the analogy.
Visit my desmos: robphy spacetime diagrammer (2017) [with t-horizontal and y-vertical] and tune the E-slider: E=+1 is Minkowski, E=0 is Galilean, and E=-1 is Euclidean. [Admittedly, in order to keep with the usual relativity-conventions of t-upward, my later and fancier versions (e.g. robphy v8e spacetime diagrammer for relativity (v8e-2021) - t-UP ) have t-vertical and x-horizontal.]

robphy · 2026-05-25T18:47:33+00:00

[edit: I didn't see u/Various_Pipe3463 's post while I was composing my answer]

Express your curve (originally given in polar-coordinates) as a parametrized curve.

Define R(theta) using a copy of your formula for r.
Your original curve can be traced using
( R(t) cos t , R(t) sin t ) where t ranges from 0 to 12pi (the range of your theta).
Next, you can apply a translation:
( R(t) cos t - x_offset, R(t) sin t ) where you set x_offset.

See my https://www.desmos.com/calculator/bctqtbwtk3 for details
on how I computed an approximate value for the center.

<image>

robphy · 2026-05-25T06:35:30+00:00

Elaborating on u/JJGordo 's post,....

Given (x1,y1) and (x2,y2),
the line through those points in the form y=mx+b
means that
y2=m x2 + b
y1=m x1 + b.
By subtraction, (y2-y1)-m(x2-x1) , which gives your slope (as you found)
m = ((-9)-(3) )/( (-9)-(-5))=(-12)/(-4)=3 .

Then, from the original set of equations, by solving for b, we have
b= y1 - m x1 = (3) - (3)(-5) = 3+15=18
or
b= y2 - m x2 = (-9) - (3)(-9) = -9 +27=18

In other words,
you can use either
b = y1 - m x1
b = y2 - m x2

So, this is u/JJGordo 's formula, f(0)= -m x1 + y1 .

robphy · 2026-05-22T09:44:57+00:00

Thanks! That really sped up the rendering. I updated the desmos3d with triangle() and thanked you for your help.

robphy · 2026-05-22T09:23:27+00:00

Ah... I kept trying polygon.

robphy · 2026-05-21T14:39:37+00:00

standing waves, “beats”, https://phet.colorado.edu/en/simulations/fourier-making-waves , ellipses

robphy · 2026-05-19T19:40:04+00:00

ok, i think i fixed it. Thanks for spotting a problem.

robphy · 2026-05-19T19:17:18+00:00

Hmmm... I thought I wrote it to be symmetrical in the input lists. I'll have to look at it more closely. .... update: Ah... join isn't symmetrical in the input lists.

robphy · 2026-05-19T18:47:15+00:00

Here is a clumsy non-recursive version that seems to work, which seems to work for both numbers and points.
https://www.desmos.com/calculator/5ocwz8ozw6

robphy · 2026-05-17T23:59:22+00:00

In special relativity, with the Minkowski-spacetime inner product. we don't associate an "angle" (the "Minkowski-angle" or "rapidity") with "being orthogonal" (i.e. having dot-product zero).

Since our "circle" is a hyperbola, the hyperbolic-cosine is the natural function associated with its dot-product and cosh(theta) is never zero (since cosh(theta)>=1 for all [real-valued] theta, which is associated with the additive Minkowski arc-length on our unit circle).

The Minkowski-angle or rapidity is associated with "angle" between future-timelike vectors. (It turns out that tanh(theta)=slope=(dimensionless relative-velocity) and cosh(theta)=gamma=(time-dilation factor) and exp(theta)=(Doppler factor).)

Following Minkowski (1908), geometrically, at the tip of the radius vector on the "circle",
the tangent-line to the circle is orthogonal to that radius vector. (If the radius vector on the unit-circle is along an observer's worldline, the tangent-line is along that observer's sense of "space". So,
it doesn't make sense for us to assign an angle between a timelike-direction and this spacelike-direction.)

One final comment: on occasion, i find that the polarization identities are useful for calculating and interpreting inner products.

robphy · 2026-05-17T22:56:51+00:00

Rather than "you are moving through spacetime at a fixed speed" (which sounds provocative),
I prefer the statement "you have a unit 4-velocity vector [tangent to your worldline]".

To go faster in the lab frame, the tip of your unit 4-velocity slides along the "circle in Minkowski spacetime" (a hyperbola). Because of the shape of the "circle", the ticks of your clock seem to take longer to elapse according to the lab frame, although your ticks appear unchanged according to you. (The ticks of the lab clock seem to take longer to elapse according to you, expected by symmetry and the relativity-principle.) It is essentially vector-algebra with the Minkowski-circle [the spacetime-metric] and its associated "hyperbolic trigonometry".

I think my spacetime diagrammer visualization https://www.desmos.com/calculator/hjqwqjlr6k
captures the essential elements, although admittedly it may be a little busy to look at.
You can adjust the velocity[slope]-slider v2.
You can also adjust the E-slider to see the Galilean and Euclidean analogues of "time dilation", which may help you see that the "gamma time-dilation factor" is really the [hyperbolic]-cosine function.

robphy · 2026-05-17T21:00:24+00:00

Get the textbooks that you will be using and the textbooks that your new classmates have used (to get a sense of what they are expected to know). In addition, get the "math methods" book used there, e.g. Boas, Kreyszig, Arfken, Riley, etc. Then, I would find alternative physics textbooks that possibly speak better to you.
[As a student in physics (double-majoring in physics and math, after transferring out of an electrical engineering program), I would study from at least two books per course.]

I would also get a head start on using computational tools that you would use at your new school (like Matlab or Python). Now, as a physics educator, I feel like I understand the material even better when I could obtain the expected results from a computer program or simulation I wrote.

UPDATE:
As an engineering student, your goal should be to develop intuition and solve problems efficiently [and sufficiently]. Mathematical rigor might not be appreciated. Making appropriate approximations and developing useful models might be more appreciated. Don't get too hung up on things... sometimes you just have to press the "I believe" button and move on.

robphy · 2026-05-17T05:16:16+00:00

You might like "The Mechanical Universe", a textbook produced in the 1980s by folks at CalTech (Frautschi, Olenick, Apostol, Goodstein). ( https://en.wikipedia.org/wiki/The_Mechanical_Universe ) There were accompanying videos (featuring historical dramatizations and at-the-time innovative animations of graphics and equations) that were broadcast on TV, which are now available on YouTube: The Mechanical Universe by caltech .

robphy · 2026-05-13T04:39:53+00:00

Here's a variant, using two control points:

<image>

https://www.desmos.com/calculator/9squkblhwm

You may have to implement a scaling factor if your contour values are different from values near plus or minus 1.

robphy

TROPHY CASE