Discover and read the best of Twitter Threads about #mathematica

Most recents (8)

@c_drosten Hi, ich habe kurz mal aus Interesse den Welch-Test, bezüglich Figure 2 durchgezogen (ich habe eine solche Rechnung bisher nicht gemacht) und komme für den p-value auf einen Wert von 0.006. Die Unterschrift sagt dies aber für den Mann-Whitney rank test aus, oder?
@c_drosten Ich kann mich da durchaus irren! Kann das jemand validieren?
@c_drosten I implemented the Welch test by hand writing my own function.#Mathematica complains that the data sets are not normally distributed. Hence, I visualized in Mathematica QQ-Plots against the normal distribution. Especially,the healthy data set seems to be off.#CoronaDaten #Drosten
Read 14 tweets
composing circular motion of different frequencies (columns) with harmonic motion of different frequencies (rows). All patterns are centered on zero except the ones on the diagonal.
this is a demonstration that sine waves with integer frequencies are orthogonal (∫ f.g = 0) - a fact that Fourier analysis hinges on
#mathematica code to produce this animation pastebin.com/Jbiwetnh
Read 4 tweets
draw a random polygon, and connect the midpoints of its edges to make a new polygon. Repeat this and it converges to an ellipse
#mathematica code to create this animation pastebin.com/WHKWsMeY
Read 3 tweets
draw a line, and extend it deflected by a fixed angle. Continue, adding the angle again each time. The result is a Euler spiral
with the right angle, it's even possible to create an Euler spiral of Euler spirals Image
#mathematica code

\[Theta]inc = 0.05;
n = 50000;
pts = Accumulate[
Table[With[{\[Theta] = \[Theta]inc i (i - 1)/2}, {Cos[\[Theta]],
Sin[\[Theta]]}], {i, n}]];
Graphics[
{White, Opacity[0.8], Thickness[0.003], Line[pts]},
Background -> Black
]
Read 3 tweets
the centre of a logarithmic spiral traces a straight line as it is rolled. this means a pair can be used as unconventional gears
There is no slipping between the two gears, and the point of contact moves at a constant speed from the centre of one gear to the other (with a discontinuity at each turn).
The slope of the straight line traced by the centre is called the spiral's pitch. A golden spiral is a logarithmic spiral with pitch 17.032°
Read 4 tweets
#mathematica challenge - how many ways can you find to plot a circle?

a few to get started:
Graphics[Circle[]]
PolarPlot[1, {th, 0, 2 Pi}]
ParametricPlot[{Sin[th], Cos[th]}, {th, 0, 2 Pi}]
ContourPlot[x^2 + y^2 == 1, {x, -1, 1}, {y, -1, 1}]
Plot[{-1, 1} Sqrt[1 - x^2], {x, -1, 1}]
RegionPlot[x^2 + y^2 < 1, {x, -1, 1}, {y, -1, 1}, PlotStyle -> None]
Read 3 tweets
there are 627 ways to partition the number 20 into whole-number pieces (such as 15 + 4 + 1). each partition is shown here as a spiral (walk 15, turn xº left, walk 4, turn xº left, walk 1). this animation shows all 627 as paths for varying x.
#math
higher res for 1/8th turns, showing all partitions of 20 Image
Read 3 tweets
fractal built using recursive replacement rules that vary smoothly with their input
Another, based on the Sierpinski carpet
Read 3 tweets

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