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Posts tagged math

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mathmajik:

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

http://flavorwire.com

How many of these have you been to?

(Personally, I’ve only seen the Gaudí Sagrada Família church, which isn’t a cathedral btw.)

Filed under math architecture

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curiosamathematica:

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!). 

curiosamathematica:

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!). 

(via beautyandthemaths)

Filed under pi math integrals

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A properly, conformally embedded once-punctured torus in R^3, parametrized by 

1/(1-sin(u)sin(v))*(cos(u)cos(v),cos(u)sin(v),sin(u)sin(v))

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.)

Filed under math torus

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twocubes:

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.

Filed under math Menger sponge 4d geometry