# Explore Minimal, Printing and more!

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Crossing Torus I 3d printed

Paul Nylander has created a beautiful image of Costa’s minimal surface.

Links and knots

Keizo Ushio

'Oushi Zokei', Aarhus, Sculpture by the Sea 2011 by Keizo Ushio via sculpturebythesea via 5000plusnet.au #Keizo_Ushio #Sculpture

Costa's minimal surface | an embedded minimal surface discovered in 1982 by mathematician Celso José da Costa. Also a surface of finite topology, which means that it can be formed by puncturing a compact surface. Topologically, it is a thrice-punctured torus. Costa surface can be described using the Weierstrass zeta and the Weierstrass elliptic functions.

Topology needs to be represented here, specifically knot theory. The following picture is from the Wikipedia page about Seifert Surfaces and was contributed by Accelerometer. Every link (or knot) is the boundary of a smooth orientable surface in 3D-space. This fact is attributed to Herbert Seifert, since he was the first to give an algorithm for constructing them. The surface we are looking at is bounded by Borromean rings.

Trefoil knot minimal surface

bigblueboo: celestial cycles inspired by this image by serescosmicos

Art Meets Mathematics: Dizzying Geometric GIFs by David Whyte