In mathematics, a Möbius strip, Möbius band, or Möbius loop, also spelled Mobius or Moebius, is a surface with only one side and only one boundary curve. The Möbius strip is the simplest non-orientable surface. It can be realized as a ruled surface. Its discovery is attributed independently to the German mathematicians Johann Benedict Listing and August Ferdinand Möbius in 1858, though similar structures can be seen in Roman mosaics c. 200–250 AD. Möbius published his results in his articles "Theorie der elementaren Verwandtschaft" (1863) and "Ueber die Bestimmung des Inhaltes eines Polyëders" (1865).
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.
In mathematics, the graph of a function is the set of ordered pairs , where In the common case where and are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.
A catenoid is a type of surface, arising by rotating a catenary curve about an axis. It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally described in 1744 by the mathematician Leonhard Euler.
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature.
Wetting is the ability of a liquid to maintain contact with a solid surface, resulting from intermolecular interactions when the two are brought together. This happens in presence of a gaseous phase or another liquid phase not miscible with the first one. The degree of wetting (wettability) is determined by a force balance between adhesive and cohesive forces.
A gyroid is an infinitely connected triply periodic minimal surface discovered by Alan Schoen in 1970.
In differential geometry and algebraic geometry, the Enneper surface is a self-intersecting surface that can be described parametrically by:
In mathematics, a Scherk surface is an example of a minimal surface. Scherk described two complete embedded minimal surfaces in 1834; his first surface is a doubly periodic surface, his second surface is singly periodic. They were the third non-trivial examples of minimal surfaces. The two surfaces are conjugates of each other.
In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in ℝ3 that is invariant under a rank-3 lattice of translations.
In differential geometry, the Schwarz minimal surfaces are periodic minimal surfaces originally described by Hermann Schwarz.
In differential geometry, the associate family of a minimal surface is a one-parameter family of minimal surfaces which share the same Weierstrass data. That is, if the surface has the representation
In differential geometry, the lidinoid is a triply periodic minimal surface. The name comes from its Swedish discoverer Sven Lidin.
In differential geometry, Catalan's minimal surface is a minimal surface originally studied by Eugène Charles Catalan in 1855.
In differential geometry, the Henneberg surface is a non-orientable minimal surface named after Lebrecht Henneberg.
In mathematics, Bour's minimal surface is a two-dimensional minimal surface, embedded with self-crossings into three-dimensional Euclidean space. It is named after Edmond Bour, whose work on minimal surfaces won him the 1861 mathematics prize of the French Academy of Sciences.
Alan Lindsay Mackay FRS is a British crystallographer, born in Wolverhampton.
A frequency-selective surface (FSS) is any thin, repetitive surface designed to reflect, transmit or absorb electromagnetic fields based on the frequency of the field. In this sense, an FSS is a type of optical filter or metal-mesh optical filters in which the filtering is accomplished by virtue of the regular, periodic pattern on the surface of the FSS. Though not explicitly mentioned in the name, FSS's also have properties which vary with incidence angle and polarization as well - these are unavoidable consequences of the way in which FSS's are constructed. Frequency-selective surfaces have been most commonly used in the radio frequency region of the electromagnetic spectrum and find use in applications as diverse as the aforementioned microwave oven, antenna radomes and modern metamaterials. Sometimes frequency selective surfaces are referred to simply as periodic surfaces and are a 2-dimensional analog of the new periodic volumes known as photonic crystals.
Alan Hugh Schoen is an American physicist and computer scientist best known for his discovery of the gyroid, an infinitely connected triply periodic minimal surface.
