Arc (geometry) in the context of Subtended

A character arc is the transformation or inner journey of a character over the course of a story. If a story has a character arc, the character begins as one sort of person and gradually transforms into a different sort of person in response to changing developments in the story. Since the change is often substantive and leading from one personality trait to a diametrically opposite trait (for example, from greed to benevolence), the geometric term arc is often used to describe the sweeping change. In most stories, lead characters and protagonists are the characters most likely to experience character arcs, although lesser characters often change as well. A driving element of the plots of many stories is that the main character seems initially unable to overcome opposing forces, possibly because they lack skills or knowledge or resources or friends. To overcome such obstacles, the main character must change, possibly by learning new skills, to arrive at a higher sense of self-awareness or capability. Main characters can achieve such self-awareness by interacting with their environment, by enlisting the help of mentors, by changing their viewpoint, or by some other method.

In astronomy, diurnal motion (from Latin diurnus 'daily', from Latin diēs 'day') is the apparent motion of celestial objects (e.g. the Sun and stars) around Earth, or more precisely around the two celestial poles, over the course of one day. It is caused by Earth's rotation around its axis, so almost every star appears to follow a circular arc path, called the diurnal circle, often depicted in star trail photography.

The time for one complete rotation is 23 hours, 56 minutes, and 4.09 seconds – one sidereal day. The first experimental demonstration of this motion was conducted by Léon Foucault. Because Earth orbits the Sun once a year, the sidereal time at any given place and time will gain about four minutes against local civil time, every 24 hours, until, after a year has passed, one additional sidereal "day" has elapsed compared to the number of solar days that have gone by.

A circular arc is the arc of a circle between a pair of distinct points. If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle greater than π radians. The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that connects the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

In geometry, an angle subtended (from Latin for "stretched under") by a line segment at an arbitrary vertex is formed by the two rays between the vertex and each endpoint of the segment. For example, a side of a triangle subtends the opposite angle.

More generally, an angle subtended by an arc of a curve is the angle subtended by the corresponding chord of the arc.For example, a circular arc subtends the central angle formed by the two radii through the arc endpoints.

In geometry, an angle is formed by two lines that meet at a point. Each line is called a side of the angle, and the point they share is called the vertex of the angle. The term angle is used to denote both geometric figures and their size or magnitude as associated quantity. Angular measure or measure of angle are sometimes used to distinguish between the measure of the quantity and figure itself. The measurement of angles is intrinsically linked with circles and rotation, and this is often visualized or defined using the arc of a circle centered at the vertex and lying between the sides.

In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with a connection. It is a generalization of the notion of a "straight line".

The noun geodesic and the adjective geodetic come from geodesy, the science of measuring the size and shape of Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between two points on the Earth's surface. For a spherical Earth, it is a segment of a great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory, one might consider a geodesic between two vertices/nodes of a graph.

Sun path, sometimes also called day arc, refers to the daily (sunrise to sunset) and seasonal arc-like path that the Sun appears to follow across the sky as the Earth rotates and orbits the Sun. The Sun's path affects the length of daytime experienced and amount of daylight received along a certain latitude during a given season.

The relative position of the Sun is a major factor in the heat gain of buildings and in the performance of solar energy systems. Accurate location-specific knowledge of sun path and climatic conditions is essential for economic decisions about solar collector area, orientation, landscaping, summer shading, and the cost-effective use of solar trackers.

In geodesy and navigation, a meridian arc is the curve between two points near the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length. Both the practical determination of meridian arcs (employing measuring instruments in field campaigns) as well as its theoretical calculation (based on geometry and abstract mathematics) have been pursued for many years.

A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular arc. Rainbows caused by sunlight always appear in the section of sky directly opposite the sun. Rainbows can be caused by many forms of airborne water. These include not only rain, but also mist, spray, and airborne dew.

Rainbows can be full circles. However, the observer typically sees only an arc formed by illuminated droplets above the ground, and centred on a line from the Sun to the observer's eye.

Mathematical sociology is an interdisciplinary field of research concerned with the use of mathematics within sociological research.

A star trail is a type of photograph that uses long exposure times to capture diurnal circles, the apparent motion of stars in the night sky due to Earth's rotation. A star-trail photograph shows individual stars as streaks across the image, with longer exposures yielding longer arcs. The term is used for similar photos captured elsewhere, such as on board the International Space Station and on Mars.

Typical shutter speeds for a star trail range from 15 minutes to several hours, requiring a "Bulb" setting on the camera to open the shutter for a period longer than usual. However, a more practiced technique is to blend a number of frames together to create the final star trail image.

A compass, also commonly known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses can be used for mathematics, drafting, navigation and other purposes.

Prior to computerization, compasses and other tools for manual drafting were often packaged as a set with interchangeable parts. By the mid-twentieth century, circle templates supplemented the use of compasses. Today those facilities are more often provided by computer-aided design programs, so the physical tools serve mainly a didactic purpose in teaching geometry, technical drawing, etc.

A whorl (/wɜːrl/ or /wɔːrl/) is an individual circle, oval, volution or equivalent in a whorled pattern, which consists of a spiral or multiple concentric objects (including circles, ovals and arcs).

In navigation, a rhumb line (also rhumb (/rʌm/) or loxodrome) is an arc crossing all meridians of longitude at the same angle. It is a path of constant azimuth relative to true north, which can be steered by maintaining a course of fixed bearing. When drift is not a factor, accurate tracking of a rhumb line course is independent of speed.

In practical navigation, a distinction is made between this true rhumb line and a magnetic rhumb line, with the latter being a path of constant bearing relative to magnetic north. While a navigator could easily steer a magnetic rhumb line using a magnetic compass, this course would not be true because the magnetic declination—the angle between true and magnetic north—varies across the Earth's surface.

A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle, r the radius of the circle, and L is the arc length of the minor sector.