∞ [ℵμ∰β⨊ℝ] □ [+ℏ∈∅⪆γ] ∞

I promise, I do not think I am too cool to follow back. I am too distracted.

Mathematics is community. <3

Crop your cat’s face. Parametrize it. 

Do it! You are free now.

Cycles of circles. 

It’s interactive. Go play! 

https://www.desmos.com/calculator/dzwz7e02i3

Remarkable.

Edit: Here is a brief, rough (bad) explanation of how I like to “visualize” this. Find yourself ANY continuous function with the graphical property that it regularly repeats along the x-axis over pi length intervals. Draw one, if you like--you’re free! This is your f(x). 

Now multiply your f(x) by that gnarly sinc-squared(?) function in the LHS integrand, and graph that monstrosity. Call it g(x), where the g is short for “gnarly.”

What is the area between g(x) and the ENTIRE x-axis (i.e. from negative to positive ∞)? A note to those without a calc background: “negative area,” underneath the x-axis, is a thing. It additively “cancels” with positive area above the x-axis.

Okay, almost there. Take your drawing of f(x) and slice it vertically, so that only extends from zero to pi, with respect to the x-axis. (Cuts are along the lines x = 0 and x = pi). Shade the region between the x-axis and the curve (accounting for negative area, if any).

The fact above says that the shaded area in your truncated f(x) drawing will be EXACTLY the same as the area under the ENTIRETY of the gnarly g(x) curve. 

Mathematics is beautiful. <3

That’s it. Move along folks, we’re done here. 

Cool lemme get uhhh (a)&(b) combo?

yeah imma need like, 1/2 uhh... that derivative, uhh 3-piece of that Cantor 3-adic McFractalFood meal

You have attempted a

Please, do not disturb the Platonic Heavens any further.

A little something I made on desmos.com. I currently lack the time to put together a passable “explainer”, but I will add a how-to and source materials when I can. Seeing as I’ve been awful about posting recently, I’m going to just go for it now and amend later.

The quotation, “Mathematics is inexhaustible,” is a succinct expression of Kurt Gödel’s ontological outlook on mathematics vis-a-vis logic and his Incompleteness results.

∞ [⫙4τℏξmατ!ℂ5 1∫ ⅈℵ∑×ℏ∆∪∮τiβ⌊ε] ∞ 

Well, he is.

But have you seen those wide-legged jeans!?

Have you seen them hyperbolically?

Do it here:

Life has been complicated as of late--demanding much of the energy and focus that would have otherwise gone towards social media. That said, I am alive and well. 

Better yet, I return with many new mathematical wonders to share. All in good time, of course. :)

Weierstrass functions.

Quoting Wikipedia, “In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for Karl Weierstrass. The relation between the sigma, zeta, and p-functions is analogous to that between the sine, cotangent, and squared cosecant functions: the logarithmic derivative of the sine is the cotangent, whose derivative is negative the squared cosecant.”

The stunning colors come from domain coloring.

Strange attractors.