Circumference in the context of Unit circle

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 mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of both distances to the two focal points is a constant. It generalizes a circle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by its eccentricity ${\displaystyle e}$, a number ranging from ${\displaystyle e=0}$ (the limiting case of a circle) to ${\displaystyle e=1}$ (the limiting case of infinite elongation, no longer an ellipse but a parabola).

An ellipse has a simple algebraic solution for its area, but for its perimeter (also known as circumference), integration is required to obtain an exact solution.

In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not.

For a radius ${\displaystyle r}$, an open disk is usually denoted as ${\displaystyle D_{r}}$, and a closed disk is ${\displaystyle {\overline {D_{r}}}}$. However in the field of topology the closed disk is usually denoted as ${\displaystyle D^{2}}$, while the open disk is ${\displaystyle \operatorname {int} D^{2}}$.

Earth's circumference is the distance around Earth. Measured around the equator, it is 40,075.017 km (24,901.461 mi). Measured passing through the poles, the circumference is 40,007.863 km (24,859.734 mi).

Treating the Earth as a sphere, its circumference would be its single most important measurement. The first known scientific measurement and calculation was done by Eratosthenes, by comparing altitudes of the mid-day sun at two places a known north–south distance apart. He achieved a great degree of precision in his computation. The Earth's shape deviates from spherical by flattening, but by only about 0.3%.

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.

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.

A pulley is a wheel on an axle or shaft enabling a taut cable or belt passing over the wheel to move and change direction, or transfer power between itself and a shaft.

A pulley may have a groove or grooves between flanges around its circumference to locate the cable or belt. The drive element of a pulley system can be a rope, cable, belt, or chain.

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.

In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere.

A perimeter is the length of a closed boundary that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional line. The perimeter of a circle or an ellipse is called its circumference.

Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden. The perimeter of a wheel/circle (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter; if the length of the string was exact, it would equal the perimeter.

A basketball is a spherical ball used in basketball games. Basketballs usually range in size from very small promotional items that are only a few inches (some centimeters) in diameter to extra large balls nearly 2 feet (60 cm) in diameter used in training exercises. For example, a youth basketball could be 27 inches (69 cm) in circumference, while a National Collegiate Athletic Association (NCAA) men's ball would be a maximum of 30 inches (76 cm) and an NCAA women's ball would be a maximum of 29 inches (74 cm). The standard for a basketball in the National Basketball Association (NBA) is 29.5 inches (75 cm) in circumference and for the Women's National Basketball Association (WNBA), a maximum circumference of 28.5 inches (72 cm). High school and junior leagues normally use NCAA, NBA or WNBA sized balls.

Aside from the court and the baskets, the basketball is the only piece of equipment necessary to play the game of basketball. During the game, the ball must be bounced continuously (dribbling), thrown through the air to other players (passing) or thrown towards the basket (shooting). Therefore, the ball must be very durable and easy to hold on to. The ball is also used to perform tricks (sometimes called freestyling), the most common of which are spinning the ball on the tip of one's index finger, dribbling in complex patterns, rolling the ball over one's shoulder, or performing aerobatic maneuvers with the ball while executing a slam dunk, most notably in the context of a slam dunk contest.

A pyrotechnic fastener (also called an explosive bolt, or pyro, within context) is a fastener, usually a nut or bolt, that incorporates a pyrotechnic charge that can be initiated remotely. One or more explosive charges embedded within the bolt are typically activated by an electric current, and the charge breaks the bolt into two or more pieces. The bolt is typically scored around its circumference at the point(s) where the severance should occur. Such bolts are often used in space applications to ensure separation between rocket stages, because they are lighter and much more reliable than mechanical latches.

In applications that require safety, precision and reliability, such as the aerospace industry, pyrotechnic fasteners are triggered using exploding bridgewire detonators, which were themselves later succeeded by slapper detonators. Classical blasting caps are generally avoided for such usage.

In physics, circular motion is movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves the circular motion of its parts. The equations of motion describe the movement of the center of mass of a body, which remains at a constant distance from the axis of rotation. In circular motion, the distance between the body and a fixed point on its surface remains the same, i.e., the body is assumed rigid.

Examples of circular motion include: special satellite orbits around the Earth (circular orbits), a ceiling fan's blades rotating around a hub, a stone that is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism.

Arc measurement, sometimes called degree measurement (German: Gradmessung), is the astrogeodetic technique of determining the radius of Earth and, by extension, its circumference. More specifically, it seeks to determine the local Earth radius of curvature of the figure of the Earth, by relating the latitude difference (sometimes also the longitude difference) and the geographic distance (arc length) surveyed between two locations on Earth's surface. The most common variant involves only astronomical latitudes and the meridian arc length and is called meridian arc measurement; other variants may involve only astronomical longitude (parallel arc measurement) or both geographic coordinates (oblique arc measurement).Arc measurement campaigns in Europe were the precursors to the International Association of Geodesy (IAG).Nowadays, the method is replaced by worldwide geodetic networks and by satellite geodesy.

Enewetak Atoll (/ɛˈniːwəˌtɔːk, ˌɛnɪˈwiːtɔːk/; also spelled Eniwetok Atoll or sometimes Eniewetok; Marshallese: Ānewetak, [ænʲeːwɛːdˠɑk], or Āne-wātak, [ænʲeːwæːdˠɑk]; known to the Japanese as Brown Atoll or Brown Island; Japanese: ブラウン環礁) is a large coral atoll of 40 islands in the Pacific Ocean and with its 296 people (as of 2021) forms a legislative district of the Ralik Chain of the Marshall Islands. With a land area total less than 5.85 square kilometers (2.26 sq mi), it is no higher than 5 meters (16.4 ft) and surrounds a deep central lagoon, 80 kilometers (50 mi) in circumference. It is the second-westernmost atoll of the Ralik Chain and is 305 kilometers (190 mi) west from Bikini Atoll.

It was held by the Japanese from 1914 until its capture by the United States in February 1944 during World War II, then became Naval Base Eniwetok. Nuclear testing by the US, totaling the equivalent of over 30 megatons of TNT, took place during the Cold War; in 1977–1980, a concrete dome (the Runit Dome) was built on Runit Island to deposit radioactive soil and debris.

In manufacturing or mechanical engineering a groove is a long and narrow indentation built into a material, generally for the purpose of allowing another material or part to move within the groove and be guided by it. Examples include:

1. A canal cut in a hard material, usually metal. This canal can be round, oval or an arc in order to receive another component such as a boss, a tongue or a gasket. It can also be on the circumference of a dowel, a bolt, an axle or on the outside or inside of a tube or pipe etc. This canal may receive a circlip, an o-ring, or a gasket.
2. A depression on the entire circumference of a cast or machined wheel, a pulley or sheave. This depression may receive a cable, a rope or a belt.
3. A longitudinal channel formed in a hot rolled rail profile such as a grooved rail. This groove is for the flange on a train wheel.

Grooves were used by ancient Roman engineers to survey land.