Maths Stuff

Who came up with these shapes?

Gyroid Minimal Surface Area

Discovered Alan Schoen in 1970. It is an example of minimal surface area it also extends to infinity in all directions. It is defined by the equation:

cos(x) * sin(y) + cos(y) * sin(z) + cos(z) * sin(x) = 0

Further Resources

Wikipedia: http://en.wikipedia.org/wiki/Gyroid

YouTube: http://www.youtube.com/watch?v=hgHZNGs8duY

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Costa's Minimal Surface Area

Discovered by Brazilian mathematician Celso José da Costa in 1982. It is an example of a minimal surface area.

Further Resources

Wikipedia: http://en.wikipedia.org/wiki/Costa%27s_minimal_surface

YouTube: http://www.youtube.com/watch?v=6pD5UxfwbKQ

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Seifert Surface

A Seifert surface is named after German mathematician Herbert Seifert. It is defined as a surface created within the boundaries of a knot. There is a whole branch of mathematics dedicated to knots. http://en.wikipedia.org/wiki/Knot_(mathematics)

Further Resources

Wikipedia: http://en.wikipedia.org/wiki/Seifert_surface

YouTube: http://www.youtube.com/watch?v=px3Gq_gvvac

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Scherk's Second Surface

Defined by the formula:

sin(z)- sinh(x) * sinh(y) = 0

Further Resources

Wikipedia: http://en.wikipedia.org/wiki/Saddle_tower, http://en.wikipedia.org/wiki/Scherk_surface

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Henneberg's Surface

Defined by the formula:

x = 2 * cos(v)* sinh(u) - (2/3) * cos(3*v) * sinh(3*u)
y = 2 * sin(v)* sinh(u)  + (2/3) * sin(3*v) * sinh(3*u)
z = 2 * cos(2 * v) * cosh(2 * u)
			

Further Resources

Wikipedia: http://en.wikipedia.org/wiki/Henneberg_surface

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Minimal Surface Areas

In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having a mean curvature of zero.

Further Resources

Wikipedia: http://en.wikipedia.org/wiki/Minimal_surface

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