One day, one decomposition
A198773: Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A198773.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A198773.html

One day, one decomposition
A198772: Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= y

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A198772.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A198772.html

I Cooked a reliable winding number filler for quadratic bezier curves. But now which tools edit vector graphics with quadratic bezier paths? SVG supports it, but @inkscape and the like seem to degree-elevate to cubic per se. #demoscene #svg #quadratic #bezier #distance #windingnumber #filler #vector #vectorgraphics #graphics #illustration

One day, one decomposition
A094619: Fundamental discriminants of real quadratic number fields with class number 2

3D graph, threejs - webGL https://decompwlj.com/3Dgraph/A094619.html
2D graph, first 500 terms https://decompwlj.com/2Dgraph500terms/A094619.html

Flattening Bézier Curves and Arcs
https://minus-ze.ro/posts/flattening-bezier-curves-and-arcs/
#ycombinator #graphics #vector_graphics #flattening #approximation #Bézier #quadratic #cubic #elliptical #arcs #blossom #De_Casteljau #subdivision #arc_length #path_length

Rect + Pegs Infused

#mathart #mathober #mathober2023 #mathober11 #mathober8 #counting #quadratic

Video https://youtu.be/4JyAFd7VmkQ

Blogpost: https://blog.illestpreacha.com/mathober2023countingquadratic

AudioVisuals coded in #livecodelab
Tweaked for Visuals

For this combinational prompt, I will be taking my submission for Quadratic: Rect ^ 2 and merging it with a new coded entry for Counting. The counting occurs through different iterations of assessing the time variable

Overlaid sketches that were coded in LiveCodeLab

Poem

Rectangles roaming
Rotating & rolling
Running & rimming along
Reciting the rhymes that belong
Twirling and twisting
Avoiding the mistakes that were tripping
As the angles of the others are tilting
Tiling and tipping
Tipping to the ways as the rectangles are roaming

#creativecoding #coding
#newmedia #scifi #animation
#math #geometricart #geometry #3danimation

#codeart #programming #programmer #newmediaart #creativecodeart
#dailyart #generativeart #artoftheday #instaartist #digitalart #sqaures
#scifiart #worldbuilding

I have some thoughts I'm attempting to write up WRT that quadratic paper (1) shared by @fatlimey. But anyway since probably most peeps seeing this are interested in single precision results....handling that case (if you can promote to doubles) is almost no work (2) at all. (Of course it's all moot if spurious over/underflows aren't a concern)

1) https://mastodon.gamedev.place/@fatlimey/110584284601341773

2) https://gist.github.com/Marc-B-Reynolds/7dee8803d22532e12d2a973c16a33897

For me, this is the best method to solve #quadratic #equations (better than completing squares, general quadratics formula, factorization, ...)

https://twitter.com/l_d_hodge/status/546712133732696064

(Credits from "l hodge" - @l_d_hodge on twitter)

It's easy to understand, it works with $a \neq 1$ and it has meaning.

It's based on change of variables and #symmetry