my daughter says this a lot. i think she got it from a tv show.

"i have an idea!" what comes next is always interesting.

@leslietownes Thank you!

@leslietownes haha your daughter sounds like a joy :)

just wait until she is coherent enough to get on here and ask interesting math questions.

then you'll see.

I'm experimenting with writing equations that represent the constructive and destructive interference of two same frequency waves at different phases

I'm pretty sure I messed up somewhere because my graph should look like a comb filter and I'm wondering if there is an easier way to do this

desmos.com/calculator/b9caplkvwx

^ is a link to my graph. I want to simulate the effect of having multiple speakers different distances away from eachother

I'm pretty sure q(F) is not correct

I got it by calculating the derivative of p(F,x) (the sum of the two waves) and then solving for X to find the first peak in the wave to get the amplitude

(using wolfram for the calculus)

It seems like the resulting equation is pretty close to what it should be and matches the response of the amplitude of the wave for like 50% of it

Basically I'm looking for a way to calculate the amplitude of a sum of sin waves at the same frequency

and at the same or different phases

does the 'arbitrary phase shift' section of en.wikipedia.org/wiki/… help with this?

@geocalc33 hey mon

yes it's me, shine on your craz diamond.

The absolute coolest thing I've every seen with computers and sound is simulation of stringed / accoustic / percussive instruments.

If you take a 3D model of a membrane of some simulated material and stretch it over an oval say, then trigger a vibration in it, and sample the oscillations coming from one point of it. It will sound like a violin, cello, drum, guitar, anything you want depending on the geometries and material properties.

I don't know where you could find those experiments and the software created, it was 10 years ago when I saw it

Right now I'm working on a sort of "Browser for doing Mathematics Informally" called Abstract Spacecraft. It will take content such as an MSE math post and do more mathy things with in than just storing it as a text string.

Current language is C++ / Qt Framework (for GUI). I will use QWebEngineView to render KaTeX (faster alt. to MathJax). I should perhaps limit the amount of letters in entries stored on the server to maybe 1000 characters. Things get larger only via linking. It's like when coding you can always refactor all your procedures to be < 10 lines of code each. A link will usually mean "implication".

A user can easily scroll through all "equivalent expressions" of something, and also there will be an easy way to pass in variable substitutions to a page (a Propositional Expression)

@leslietownes that looks like it could work, I'll try it and let you know

@AkivaWeinberger I subscribed to your YT channel :)

First subscriber

Aw thanks <3

@leslietownes any idea how I could make it work for an equation that has sin(k*x)+sin(k*x+n)

I have a book "Knots and Primes" (a digital copy), but it seems kind of advanced ANT-wise. Do you think I should learn some ANT first so that I'd be more at ease in that book?

@AkivaWeinberger

I don't know that book

symbolically replace x in the stated formula with kx everywhere. what matters for the identity is that they're the same in each term.

aight, that makes sense

I got it to work!

dotted black was the old model, which is right 50% of the time

cool

now just gotta figure out how to integrate it to simulate a line of speakers

does anyone here have recommendations for online graphing software that has similar functionality to desmos while including logarithmic scales?

offline would work as well, just it would be less convenient

Hello, is there a nice form for an integral of the form $\int_a^b |f'(t)|dt$? Here $f: R \to R^3$

geometrically it's the length of that path in space but even if f(t) has nice formulas in its components, the integral might not. it can simplify in specific cases of course.

kinda similar to arc length of the ellipse in R^2 where even though the formulas are simple a 'special function' is usually introduced to get formulas for the arc length.

ohhh right, forgot about seeing it geometrically, that solves my problem for my particular f, thanks

hmm what about if f is such that f: R to R?

Proof without words of Sperner's lemma

(subdivide a triangle, color the vertices in three colors; the vertices of the big triangle are the three colors, and each edge of the big triangle can only have two colors; there's a small triangle with three differently-colored vertices)

Some words: notice that each edge of the big triangle has an odd number of "flips", which in the picture are "exits"

Focus on one color at a time; you only need blue (or pink or green) to finish the proof