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

#FloatingPoint #quadratic

Once again I solve a #cubic #equation using the famous method. I explain a little bit how to solve the equation, and then switch to #python to solve the #quadratic equation, and then print all 3 solutions.

https://qr.ae/prmQES

Happy #Monday everyone! What nice day to show teenagers how to solve #quadratic #equations by completing the square!
#mathematics #algebra #PublicEducation

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

Finally the most sophisticated of the three is Simpson’s rule in which pairs of adjacent strips use a #quadratic #parabola to interpolate between the ordinates. This even better at convergence than the trapezium rule. I’ve shown a different function here because for the function shown above the difference between the approximation and the numerical #approximation is not discernible.

#MyWork #Mathematics #Maths #Numerics #SimpsonsRule #FreeSoftware #CCBYSA #Wikipedia #Wikimedia

Got sick of not having a #calculator that can #solve #quadratic #equations, so I made one. In #Rust!

https://gist.github.com/mcb2003/6f6779fce0af8bd9881b63636a280f3f

I was explaining to my wife yesterday how #DifferentialCalculus gives us a way to find the #gradient of a #function at any point and to illustrate it I wrote a short routine in #Maxima to draw the #tangent to any point on a graph of a function. Here we see the example for the #quadratic and #reciprocal functions, x^2 and 1/x i.e. a #parabola and a #hyperbola respectively.

#MyWork #Gif #AnimatedGif #CCBYSA #WxMaxima #Mathematics #Maths #Calculus #Differentiation

I implemented Slow Mating for quadratic polynomials using the equations and hints in Chapter 5 of Wolf Jung's 2017 paper "The Thurston Algorithm for quadratic matings" https://arxiv.org/abs/1706.04177

My code is 145 lines of quite-straightforward C, vs 2249 lines of C++ with various state hidden in mutating objects for the code accompanying the paper (which admittedly does a lot more, working from angles to compute the complex points and (pre)periods that are the input to my code). I'll do a blog post next week once I've tested more cases to make sure I haven't done any big mistakes.

There were a couple of subtleties, 1. needing to use cproj() to normalize infinity's representation and avoid NaNs; and 2. in one place, converting (a - b) / (a - c) to (1 - b/a) / (1 - c/a) so that it still works when a is infinite.

Attached images are the north period 4 island mated with the west period 4 island (blue background), and 2/5 bulb mated with 1/2 bulb (turquoise background).

#Quadratic #JuliaSets #SlowMating #RationalFunction #maths #fractals