Posts tagged math
Posts tagged math
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having a mean curvature of zero. The term “minimal surface” is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of area-minimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However the term is used for more general surfaces that may self-intersect or do not have constraints.
Art by Paul Nylander.
What dynamical system is this? Is it known? Has it been studied?
If someone offers you $1 today, $2 tomorrow, $3 the next day, and so on in perpetuity, watch out! They are trying to steal 1⁄12 of a dollar from you…
This is amazing.
The Lord of the Rings :D
(Source: Adam Plouff)
This is good, because I can never remember how the construction of a regular pentagon works.
Mathematics and Architecture
The link between math and architecture goes back to ancient times, when the two disciplines were virtually indistinguishable. Pyramids and temples were some of the earliest examples of mathematical principles at work. Today, math continues to feature prominently in building design. We’re not just talking about mere measurements — though elements like that are integral to architecture. Thanks to modern technology, architects can explore a variety of exciting design options based on complex mathematical languages, allowing them to build groundbreaking forms. Take a look at several structures past the break that were modelled after mathematics.
1. Mobius Strip Temple, China
2. Tetrahedral-Shaped Church, Colorado
3. Pentagonal, Phyllotactic Greenhouse and Education Center. The Eden Project, Cornwall
4. A Mathematically-Inclined Cucumber in the Sky, London
5. Experimental Math-Music Pavilion, 1958 World’s Fair
6. Modern Music-Math Home, Toronto
7. Solar Algorithm Wizardry, Barcelona
8. Cube Village, Holland
9. Magic Square Cathedral, Gaudi Cathederal, Barcelona
10. Fractal Gas Station Makeover, Los Angeles
How many of these have you been to?
(Personally, I’ve only seen the Gaudí Sagrada Família church, which isn’t a cathedral btw.)
The closer to the end the more satisfying it gets…
OH MY GOD
find out YOUR NAME if you were SOME KIND OF MATHEMATICAL OBJECT for SOME REASON
The Coxeter rigidity law.
I’m good with that.
Poster for Math Awareness Month 2014, celebrating the centennial of Martin Gardner’s birth.
Pi in its full glory, popping up in all kinds of formulas.
Which one do you find the most beautiful or intriguing?
I like its appearance in the values of various integral-defined functions: Gamma(1/2), the integral of exp(-x^2) over R (which is related to the error function), and the integral of sin(x)/x over R (which is the limit of the sine integral Si(x), and I didn’t know before today!).
A properly, conformally embedded once-punctured torus in R^3, parametrized by
with 1≤u≤2π, 1≤v≤2π, obvs.
(A surface in R^3 is properly embedded if its intersection with any compact set is compact. Thus, the puncture in this surface is placed “at infinity”. A surface is conformally embedded if angles in the intrinsic metric match angles in the ambient metric. Here, you can see that latitude and longitude lines on the torus meet orthogonally.)
The Julia set of 2*cos(z) on the complex plane. I was inspired to make this by this post.
chaotic-renan replied to your post: If you’re still looking for stuff to do, I think a 4D Sierpinski sponge would be pretty neat to render.How the heck does that work?
Well, first you think of one of these, but one dimensions up. Then, you conceive of a way to spin it around. Then, you intersect it with an appropriate hyperplane. Finally, you express this thought to a machine capable of generating an image from it. With your help, it should be able to produce something like this.
I would pay money to see slices of a 4d Menger sponge.