Geometric shape in the context of Orientation (geometry)

In mathematics, a set is a collection of different things; the things are elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.

Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century.

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.

A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form a repeating pattern (an aperiodic set of prototiles). A tessellation of space, also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions.

Futura is a geometric sans-serif typeface designed by Paul Renner and released in 1927. Designed as a contribution on the New Frankfurt-project, it is based on geometric shapes, especially the circle, similar in spirit to the Bauhaus design style of the period. It was developed as a typeface by Bauersche Gießerei, in competition with Ludwig & Mayer's seminal Erbar typeface.

Although Renner was not associated with the Bauhaus, he shared many of its idioms and believed that a modern typeface should express modern models, rather than be a revival of a previous design. Renner's design rejected the approach of most previous sans-serif designs (now often called grotesques), which were based on the models of sign painting, condensed lettering, and nineteenth-century serif typefaces, in favour of simple geometric forms: near-perfect circles, triangles and squares. It is based on strokes of near-even weight, which are low in contrast. The lowercase has tall ascenders, which rise above the cap line, and uses nearly-circular, single-storey forms for the "a" and "g", the former previously more common in handwriting than in printed text. The uppercase characters present proportions similar to those of classical Roman capitals. The original metal type showed extensive adaptation of the design to individual sizes, and several divergent digitisations have been released by different companies.

In mathematics, a group is a set with an operation that combines any two elements of the set to produce a third element within the same set and the following conditions must hold: the operation is associative, it has an identity element, and every element of the set has an inverse element. For example, the integers with the addition operation form a group.

The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics.

In integrated circuit design, integrated circuit (IC) layout, also known IC mask layout or mask design, is the representation of an integrated circuit in terms of planar geometric shapes which correspond to the patterns of metal, oxide, or semiconductor layers that make up the components of the integrated circuit. Originally the overall process was called tapeout, as historically early ICs used graphical black crepe tape on mylar media for photo imaging (erroneously believed to reference magnetic data—the photo process greatly predated magnetic media).

When using a standard process—where the interaction of the many chemical, thermal, and photographic variables is known and carefully controlled—the behaviour of the final integrated circuit depends largely on the positions and interconnections of the geometric shapes. Using a computer-aided layout tool, the layout engineer—or layout technician—places and connects all of the components that make up the chip such that they meet certain criteria—typically: performance, size, density, and manufacturability. This practice is often subdivided between two primary layout disciplines: analog and digital.

An elliptical dome, or an oval dome, is a dome whose bottom cross-section takes the form of an ellipse. Technically, an ellipsoidal dome has a circular cross-section, so is not quite the same.

While the cupola can take different geometries, when the ceiling's cross-section takes the form of an ellipse, and due to the reflecting properties of an ellipse, any two persons standing at a focus of the floor's ellipse can have one whisper, and the other hears; this is a whispering gallery.

In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise". It generalizes the concept of curve orientation, which for a plane simple closed curve is defined based on whether the curve interior is to the left or to the right of the curve. A space is orientable if such a consistent definition exists. In this case, there are two possible definitions, and a choice between them is an orientation of the space. Real vector spaces, Euclidean spaces, and spheres are orientable. A space is non-orientable if "clockwise" is changed into "counterclockwise" after running through some loops in it, and coming back to the starting point. This means that a geometric shape, such as , that moves continuously along such a loop is changed into its own mirror image . A Möbius strip is an example of a non-orientable space.

Various equivalent formulations of orientability can be given, depending on the desired application and level of generality. Formulations applicable to general topological manifolds often employ methods of homology theory, whereas for differentiable manifolds more structure is present, allowing a formulation in terms of differential forms. A generalization of the notion of orientability of a space is that of orientability of a family of spaces parameterized by some other space (a fiber bundle) for which an orientation must be selected in each of the spaces which varies continuously with respect to changes in the parameter values.

In geometry, a lemon is a geometric shape that is constructed as the surface of revolution of a circular arc of angle less than half of a full circle rotated about an axis passing through the endpoints of the lens (or arc). The surface of revolution of the complementary arc of the same circle, through the same axis, is called an apple.

The apple and lemon together make up a spindle torus (or self-crossing torus or self-intersecting torus). The lemon forms the boundary of a convex set, while its surrounding apple is non-convex.

The inverted bell is a metaphorical name for a geometric shape that resembles a bell upside-down.