Arc (geometry) in the context of "Central angle"

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.