Aś

∆ = b² - 4 a c http://as-gotuje.tumblr.com/ http://slodka-kuchnia.tumblr.com/ http://instagram.com/as_asia

[as-mathematical]

π

dzień aproksymacji π (22 lipca) (europejski sposób zapisu daty 22/7 ≈ 3,1428).

[as-mathematical]

Miło że nawet Tumblr pamięta!!  Najlepszego π!

[as-mathematical]

I ate some pie... And it was delicious!

Kawałek ciasta w święto pi na pewno się przyda ;)

[as-mathematical]

Happy birthday π!

[ipiphi-blog]

[dailycube]

Cube#163

Title: Two rotating pyramids in a cube

Material: Animation / gif / drawing (graphite, pen and quad-ruled paper)

Year: 2013

[1ucasvb]

Villarceau circles on a torus

Next time you have a donut or bagel at hand, give this a try. Slice it diagonally in a way that the cutting plane is tangent to the donut both below and above its inner hole. If you do it just right, what you get is two perfectly symmetric pieces whose boundaries are the union of two perfect circles (for a sufficiently round donut).

Mathematically speaking, if you have a torus (what mathematicians call that donut shape) and cut it diagonally at the correct angle, you will reveal a pair of perfect circles on the surface of the torus, known as Villarceau circles.

For every point on the surface of a torus, you can trace exactly 4 distinct perfect circles, on the surface of the torus, that pass through that point: one is around the hole of the torus, and the other around its circumference. The other two are Villarceau circles, but not really the pair shown in the animation.

Villarceau circles play an important role in Hopf fibrations. Roughly speaking, you can fill the entire 3D space with an infinite number of such circles. Apparently, this sort of thing even shows up in quantum physics, but I can’t offer any information on that.

I was first introduced to the concept of Villarceau circles through this great POV-Ray render by Tor Olav Kristensen.

This was one of the first animations I did for Wikipedia, and I’m still rather proud of it.

On a side note, I’ve been very busy with college lately, that’s why I haven’t been posting much. But I’m working on a series of animations on vector calculus and electromagnetism, and I think they’ll turn out great. Stay tuned!

[as-mathematical]

Matematyka, everywhere

[as-mathematical]

Na matematykę wszędzie znajdzie się miejsce :)

[as-mathematical]

Każdemu spacer się przydaje ; )

[homonymforhappiness-blog-blog]

boxwood tree shop, www.etsy.com/shop/boxwoodtree

This shop sells beautiful pieces for any terrarium project you’ve wanted to do, or even just use it as something to hold other things in your home.  The shapes of the terrariums is what sets these apart from others, they are geometric, making them a statement wherever you have them.  Take a peek at these wonderful pieces.

[visualizingmath]

I want to have a fish and have it live in a dodecahedron fish bowl. (The dodecahedron is the top terrarium.) Wouldn’t that be kinda cool?

[escape30]

Poincaré Hyperbolic Disk

[as-mathematical]

I tu matematyka się przydaje ;)

[as-mathematical]

Najbardziej matematyczny dom, Delta wszędzie (:

[visualizingmath]

Submitted by Ambitious-drawings: Recursive Tree in Sine Motion by Gerhard Funk. Code.

[ryshke]

[as-mathematical]

7ryshke:

In my school… MATHS. O.o

Wymarzony zegar

[matthen]

Given n identical circles, the problem is to find the smallest circle they can all fit into. For n up to 10, the exact answers are known- and this animation shows the best known solutions up to 50 circles. [circle packing] [code & more]