Orthogonality in the context of "The Arnolfini Portrait"

In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or ⁠${\displaystyle \pi }$/2⁠ radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line.

Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry.

The Chile Ridge, also known as the Chile Rise, is a submarine oceanic ridge formed by the divergent plate boundary between the Nazca plate and the Antarctic plate. It extends from the triple junction of the Nazca, Pacific, and Antarctic plates to the Southern coast of Chile. The Chile Ridge is easy to recognize on the map, as the ridge is divided into several segmented fracture zones which are perpendicular to the ridge segments, showing an orthogonal shape toward the spreading direction. The total length of the ridge segments is about 550–600 km (340–370 mi; 300–320 nmi).

The continuously spreading Chile Ridge collides with the southern South American plate to the east, and the ridge has been subducting underneath the Taitao Peninsula since 14 million years (Ma). The ridge-collision has generated a slab window beneath the overlying South America plate, with smaller volume of upper mantle magma melt, proven by an abrupt low velocity of magma flow rate below the separating Chile ridge. The subduction generates a special type of igneous rocks, represented by the Taitao ophiolites, which is an ultramafic rock composed of olivine and pyroxene, usually found in oceanic plates. In addition, the subduction of the Chile Ridge also creates Taitao granite in Taitao Peninsula which appeared as plutons.

The Arnolfini Portrait (or The Arnolfini Wedding, The Arnolfini Marriage, the Portrait of Giovanni Arnolfini and his Wife, or other titles) is an oil painting on oak panel by the Early Netherlandish painter Jan van Eyck, dated 1434 and now in the National Gallery, London. It is a full-length double portrait, believed to depict the Italian merchant Giovanni di Nicolao Arnolfini and his wife, presumably in their residence at the Flemish city of Bruges.

It is considered one of the most original and complex paintings in Western art, because of its beauty, complex iconography, geometric orthogonal perspective, and expansion of the picture space with the use of a mirror. According to Ernst Gombrich "in its own way it was as new and revolutionary as Donatello's or Masaccio's work in Italy. A simple corner of the real world had suddenly been fixed on to a panel as if by magic... For the first time in history the artist became the perfect eye-witness in the truest sense of the term". The portrait has been considered by Erwin Panofsky and some other art historians as a unique form of marriage contract, recorded as a painting. Signed and dated by van Eyck in 1434, it is, with the Ghent Altarpiece by the same artist and his brother Hubert, the oldest very famous panel painting to have been executed in oils rather than in tempera. The painting was bought by the National Gallery in London in 1842.

Centripetal force (from Latin centrum 'center' and petere 'to seek') is the force that makes a body follow a curved path. The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton coined the term, describing it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In Newtonian mechanics, gravity provides the centripetal force causing astronomical orbits.

One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path. The centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path. The mathematical description was derived in 1659 by the Dutch physicist Christiaan Huygens.

Go is an abstract strategy board game for two players in which the aim is to fence off more territory than the opponent. The game was invented in China more than 2,500 years ago and is believed to be the oldest board game continuously played to the present day. A 2016 survey by the International Go Federation's 75 member nations found that there are over 46 million people worldwide who know how to play Go, and over 20 million current players, the majority of whom live in East Asia.

The playing pieces are called stones. One player uses the white stones and the other black stones. The players take turns placing their stones on the vacant intersections (points) on the board. Once placed, stones may not be moved, but captured stones are immediately removed from the board. A single stone (or connected group of stones) is captured when surrounded by the opponent's stones on all orthogonally adjacent points. The game proceeds until neither player wishes to make another move.

In mathematics, an inner product space is a real or complex vector space endowed with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in ${\displaystyle \langle a,b\rangle }$. Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or scalar product of Cartesian coordinates. Inner product spaces of infinite dimensions are widely used in functional analysis. Inner product spaces over the field of complex numbers are sometimes referred to as unitary spaces. The first usage of the concept of a vector space with an inner product is due to Giuseppe Peano, in 1898.

An inner product naturally induces an associated norm, (denoted ${\displaystyle |x|}$ and ${\displaystyle |y|}$ in the picture); so, every inner product space is a normed vector space. If this normed space is also complete (that is, a Banach space) then the inner product space is a Hilbert space. If an inner product space H is not a Hilbert space, it can be extended by completion to a Hilbert space ${\displaystyle {\overline {H}}.}$ This means that ${\displaystyle H}$ is a linear subspace of ${\displaystyle {\overline {H}},}$ the inner product of ${\displaystyle H}$ is the restriction of that of ${\displaystyle {\overline {H}},}$ and ${\displaystyle H}$ is dense in ${\displaystyle {\overline {H}}}$ for the topology defined by the norm.