Diameter in the context of Line segment

In geometry, the area enclosed by a circle of radius r is πr. Here, the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.

One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = ⁠1/2⁠ × 2πr × r, holds for a circle.

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. It is generally attributed to Thales of Miletus, but it is sometimes attributed to Pythagoras.

A gun barrel is a crucial part of gun-type weapons such as small firearms, artillery pieces, and air guns. It is the straight shooting tube, usually made of rigid high-strength metal, through which a contained rapid expansion of high-pressure gas(es) is used to propel a projectile out of the front end (muzzle) at a high velocity. The hollow interior of the barrel is called the bore, and the diameter of the bore is called its calibre, usually measured in inches or millimetres.

The first firearms were made at a time when metallurgy was not advanced enough to cast tubes capable of withstanding the explosive forces of early cannons, so the pipe (often built from staves of metal) needed to be braced periodically along its length for structural reinforcement, producing an appearance somewhat reminiscent of storage barrels being stacked together, hence the English name.

The Andromeda Galaxy is a barred spiral galaxy and is the nearest major galaxy to the Milky Way. It was originally named the Andromeda Nebula and is cataloged as Messier 31, M31, and NGC 224. Andromeda has a D₂₅ isophotal diameter of about 46.56 kiloparsecs (152,000 light-years) and is approximately 765 kpc (2.5 million light-years) from Earth. The galaxy's name stems from the area of Earth's sky in which it appears, the constellation of Andromeda, which itself is named after the princess who was the wife of Perseus in Greek mythology.

The virial mass of the Andromeda Galaxy is of the same order of magnitude as that of the Milky Way, at 1 trillion solar masses (2.0×10 kilograms). The mass of either galaxy is difficult to estimate with any accuracy, but it was long thought that the Andromeda Galaxy was more massive than the Milky Way by a margin of some 25% to 50%. However, this has been called into question by early-21st-century studies indicating a possibly lower mass for the Andromeda Galaxy and a higher mass for the Milky Way. The Andromeda Galaxy has a diameter of about 46.56 kpc (152,000 ly), making it the largest member of the Local Group of galaxies in terms of extension.

Size in general is the magnitude or dimensions of a thing. More specifically, geometrical size (or spatial size) can refer to three geometrical measures: length, area, or volume. Length can be generalized to other linear dimensions (width, height, diameter, perimeter). Size can also be measured in terms of mass, especially when assuming a density range.

In mathematical terms, "size is a concept abstracted from the process of measuring by comparing a longer to a shorter". Size is determined by the process of comparing or measuring objects, which results in the determination of the magnitude of a quantity, such as length or mass, relative to a unit of measurement. Such a magnitude is usually expressed as a numerical value of units on a previously established spatial scale, such as meters or inches.

The larynx (pl.: larynges or larynxes), commonly called the voice box, is an organ in the top of the neck involved in respiration, producing sound and protecting the trachea against food aspiration. The opening of the larynx into the pharynx known as the laryngeal inlet is about 4–5 centimeters in diameter. The larynx houses the vocal cords, and manipulates pitch and volume, which is essential for phonation. It is situated just below where the tract of the pharynx splits into the trachea and the esophagus.

Yeasts are eukaryotic, single-celled microorganisms classified as members of the fungus kingdom. The first yeast originated hundreds of millions of years ago, and at least 1,500 species are currently recognized. They are estimated to constitute 1% of all described fungal species.

Some yeast species have the ability to develop multicellular characteristics by forming strings of connected budding cells known as pseudohyphae or false hyphae, or quickly evolve into a multicellular cluster with specialised cell organelle functions. Yeast sizes vary greatly, depending on species and environment, typically measuring 3–4 μm in diameter, although some yeasts can grow to 40 μm in size. Most yeasts reproduce asexually by mitosis, and many do so by the asymmetric division process known as budding. With their single-celled growth habit, yeasts can be contrasted with molds, which grow hyphae. Fungal species that can take both forms (depending on temperature or other conditions) are called dimorphic fungi.

The number π (/paɪ/ ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.

The number π is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as ${\displaystyle {\tfrac {22}{7}}}$ are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be randomly distributed, but no proof of this conjecture has been found.

In geography, the antipode (/ˈæntɪˌpoʊd, ænˈtɪpədi/) of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points antipodal (/ænˈtɪpədəl/) to each other are situated such that a straight line connecting the two would pass through Earth's center. Antipodal points are as far away from each other as possible. The North and South Poles are antipodes of each other.

In the Northern Hemisphere, "the Antipodes" may refer to Australia and New Zealand, and Antipodeans to their inhabitants. Geographically, the antipodes of the British Isles are in the Pacific Ocean, south of New Zealand. This gave rise to the name of the Antipodes Islands of New Zealand, which are close to the antipode of London. The antipodes of Australia are in the North Atlantic Ocean, while parts of Spain, Portugal, France and Morocco are antipodal to New Zealand.

In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center.

Given any point on a sphere, its antipodal point is the unique point at greatest distance, whether measured intrinsically (great-circle distance on the surface of the sphere) or extrinsically (chordal distance through the sphere's interior). Every great circle on a sphere passing through a point also passes through its antipodal point, and there are infinitely many great circles passing through a pair of antipodal points (unlike the situation for any non-antipodal pair of points, which have a unique great circle passing through both). Many results in spherical geometry depend on choosing non-antipodal points, and degenerate if antipodal points are allowed; for example, a spherical triangle degenerates to an underspecified lune if two of the vertices are antipodal.

An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.

In planetary geology, a ray system comprises radial streaks of fine ejecta thrown out during the formation of an impact crater, looking somewhat like many thin spokes coming from the hub of a wheel. The rays may extend for lengths up to several times the diameter of their originating crater, and are often accompanied by small secondary craters formed by larger chunks of ejecta. Ray systems have been identified on the Moon, Earth (Kamil Crater), Mercury, and some moons of the outer planets. Originally it was thought that they existed only on planets or moons lacking an atmosphere, but more recently they have been identified on Mars in infrared images taken from orbit by 2001 Mars Odyssey's thermal imager.

Rays appear at visible, and in some cases infrared wavelengths, when ejecta are made of material with different reflectivity (i.e., albedo) or thermal properties from the surface on which they are deposited. Typically, visible rays have a higher albedo than the surrounding surface. More rarely an impact will excavate low albedo material, for example basaltic-lava deposits on the lunar maria. Thermal rays, as seen on Mars, are especially apparent at night when slopes and shadows do not influence the infrared energy emitted by the Martian surface.

In classical geometry, a radius (pl.: radii or radiuses) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is the line segment or distance from its center to any of its vertices. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel. The typical abbreviation and mathematical symbol for radius is R or r. By extension, the diameter D is defined as twice the radius:

If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter, which is usually defined as the maximum distance between any two points of the figure. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity.

The Tusi couple (also known as Tusi's mechanism) is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle. The Tusi couple is a two-cusped hypocycloid.

The couple was first proposed by the 13th-century Persian astronomer and mathematician Nasir al-Din al-Tusi in his 1247 Tahrir al-Majisti (Commentary on the Almagest) as a solution for the latitudinal motion of the inferior planets and later used extensively as a substitute for the equant introduced over a thousand years earlier in Ptolemy's Almagest.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc.

The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus.

Grain size (or particle size) is the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. This is different from the crystallite size, which refers to the size of a single crystal inside a particle or grain. A single grain can be composed of several crystals. Granular material can range from very small colloidal particles, through clay, silt, sand, gravel, and cobbles, to boulders.

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longest semidiameter or one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. The semi-minor axis (minor semiaxis) of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. For the special case of a circle, the lengths of the semi-axes are both equal to the radius of the circle.

The length of the semi-major axis a of an ellipse is related to the semi-minor axis's length b through the eccentricity e and the semi-latus rectum ${\displaystyle \ell }$, as follows:

A chord (from the Latin chorda, meaning "catgut or string") of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow").

More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse. A chord that passes through a circle's center point is the circle's diameter.