Math.

[shonk]

Stereographic cube

[picturesquephysics]

A Canadian Mathematical Olympiad training question. 

[curiosamathematica]

A curious limit

Consider the following sequence of fractions.

As it turns out, these fractions converge to 0.70710678118…, or to be precise, to sqrt(2)/2. The sequence is related to the Thue–Morse sequence.

[hyrodium]

There exists locally isometric transformation between helicoid and catenoid. This is because they have same Gaussian curvature on each points.

[curiosamathematica]

Today I learned about a rather remarkable open problem in mathematics, which looks tantalizingly easy. The question was posed by Ron Graham.

Consider the following recursively defined sequence:

Innocent question: is this sequence unbounded? Surprisingly, the answer to this is unknown—at least according to the source article dating from 2000, Unbounded orbits and binary digits by M. Chamberland and M. Martelli.

(Source: http://www.math.grinnell.edu/~chamberl/papers/mario_digits.pdf)

[aufenthaltsraumspizza]

I’ll let you be my mutually alien copy <3

[quasibee-deactivated20220523]

you

me

[hyrodium]

Chaotic behaviour in 30-link pendulum.

[garadinervi]

[alexyar]

(Spivak “Calculus on manifolds”)

[data-and-vision]

“Illustration of the belt trick, showing a homotopy between two one-parameter subgroups of the rotation group, one through an angle of 2π and one through an angle of −2π.” By Slawekb - Created in Mathematica 9.0 , CC BY-SA 3.0

[hyrodium]

The curvature of curves.

x²

x³

sin(x)

exp(x)

Normal distribution (y=exp(-x²/2))

Ellipse

r=5/2+cos(3τθ)

x=(t-1)(t+1), y=t(t-1)(t+1)

Archimedes’ Spiral

Logarithmic spiral

If you want to try your own curve, try on Desmos graphing calculator!

https://www.desmos.com/calculator/lpm3igzbhy

[mathleticism]

…smh

[matthen]

Rolling a circle in a circle to draw a cosine wave [code]

[twocubes]

well this is a good sign

[maxwellsequations]

Re[arctan(x+iy)], x,y∈[0,2π]. This was my first one with colored cardstock. (Also the back of my business cards.)

[just-shower-thoughts]

Today’s date is 2²/3²/4².

[graveltotempomp3]

YOU CAN ONLY REBLOG THIS TODAY

[patrickat]

Be there and be square.

[dailyminimal]

#AU16-679

A new geometric design every day

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