A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre. The distance between any point of the circle and the centre is called the radius; this article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. A circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior. A circle may be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations. A circle is a plane figure bounded by one curved line, such that all straight lines drawn from a certain point within it to the bounding line, are equal; the bounding line is called the point, its centre.
Annulus: a ring-shaped object, the region bounded by two concentric circles. Arc: any connected part of a circle. Specifying two end points of an arc and a center allows for two arcs that together make up a full circle. Centre: the point equidistant from all points on the circle. Chord: a line segment whose endpoints lie on the circle, thus dividing a circle into two segments. Circumference: the length of one circuit along the circle, or the distance around the circle. Diameter: a line segment whose endpoints lie on the circle and that passes through the centre; this is the largest distance between any two points on the circle. It is a special case of a chord, namely the longest chord for a given circle, its length is twice the length of a radius. Disc: the region of the plane bounded by a circle. Lens: the region common to two overlapping discs. Passant: a coplanar straight line that has no point in common with the circle. Radius: a line segment joining the centre of a circle with any single point on the circle itself.
Sector: a region bounded by two radii of equal length with a common center and either of the two possible arcs, determined by this center and the endpoints of the radii. Segment: a region bounded by a chord and one of the arcs connecting the chord's endpoints; the length of the chord imposes a lower boundary on the diameter of possible arcs. Sometimes the term segment is used only for regions not containing the center of the circle to which their arc belongs to. Secant: an extended chord, a coplanar straight line, intersecting a circle in two points. Semicircle: one of the two possible arcs determined by the endpoints of a diameter, taking its midpoint as center. In non-technical common usage it may mean the interior of the two dimensional region bounded by a diameter and one of its arcs, technically called a half-disc. A half-disc is a special case of a segment, namely the largest one. Tangent: a coplanar straight line that has one single point in common with a circle. All of the specified regions may be considered as open, that is, not containing their boundaries, or as closed, including their respective boundaries.
The word circle derives from the Greek κίρκος/κύκλος, itself a metathesis of the Homeric Greek κρίκος, meaning "hoop" or "ring". The origins of the words circus and circuit are related; the circle has been known since before the beginning of recorded history. Natural circles would have been observed, such as the Moon, a short plant stalk blowing in the wind on sand, which forms a circle shape in the sand; the circle is the basis for the wheel, 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 and calculus. Early science geometry and astrology and astronomy, was connected to the divine for most medieval scholars, many believed that there was something intrinsically "divine" or "perfect" that could be found in circles; some highlights in the history of the circle are: 1700 BCE – The Rhind papyrus gives a method to find the area of a circular field. The result corresponds to 256/81 as an approximate value of π. 300 BCE – Book 3 of Euclid's Elements deals with the properties of circles.
In Plato's Seventh Letter there is a detailed explanation of the circle. Plato explains the perfect circle, how it is different from any drawing, definition or explanation. 1880 CE – Lindemann proves that π is transcendental settling the millennia-old problem of squaring the circle. The ratio of a circle's circumference to its diameter is π, an irrational constant equal to 3.141592654. Thus the length of the circumference C is related to the radius r and diameter d by: C = 2 π r = π d; as proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, which comes to π multiplied by the radius squared: A r e a = π r 2. Equivalently, denoting diameter by d, A r
The teeterboard is an acrobatic apparatus that resembles a playground seesaw. The strongest teeterboards are made of oak; the board is divided in the middle by a fulcrum made of welded steel. At each end of the board is a square padded area, where a performer stands on an incline before being catapulted into the air; the well-trained flyer performs various aerial somersaults, landing on padded mats, a human pyramid, a specialized landing chair, stilts, or a Russian bar. The teeterboard is manned by a team of flyers, catchers and pushers; some members of the team perform more than one acrobatic role. In the early 1960s the finest teeterboard acts, trained in the Eastern Bloc countries, performed with Ringling Brothers and Barnum & Bailey Circus. Korean-style teeterboard is a form of teeterboard where two performers jump vertically in place, landing back on the apparatus instead of dismounting onto a landing mat or human pyramid. Korean plank acts are featured in the Cirque du Soleil shows Mystère, Koozå and Amaluna.
The Hungarian board has a higher fulcrum, the pushers jump from a height
The New Zealand sand flounder is a righteye flounder of the genus Rhombosolea, found around New Zealand in shallow waters down to depths of 100 m. New Zealand dab, diamond, square flounder. Like other flatfish, the larval sand flounder begins its life with an eye on each side of its head and a round body shape, swimming upright through the midwater; as it grows out of this larval stage entering the juvenile stage one eye moves to the right side leaving the other blind and it takes on a flat diamond shape swimming flat/parallel to the ground. On the right side, the fish is a greenish brown dark colour or grey with faint mottling and on the left side it is white; the average length of an adult sand flounder is 25–35 cm with the maximum being 45 cm. In the day time, they lie on the seabed camouflaged perfectly in sand or mud, they swim in a flowing style with an undulating movement of the side fins and when threatened by predators their tail is used for propulsion. Technically the adult swims on its side with the continuous dorsal fin fringing one edge of its diamond shaped body and its extended anal fin on the other.
It only leaves the seabed for courtship and spawning activities. Sand flounder are native to New Zealand so they are not found anywhere else in the world but they are found all over New Zealand. New Zealand sand flounder is found in a majority of coastal waters around New Zealand, its largest population is found on the East Coast of the South Island. Around New Zealand they can be found in harbours, inlets and open water, they prefer coastal areas and are found in waters up to 50m deep but deeper. They can be found in harbours, inlets and open water, they are common on mudflats but seem to have no preference of bottom substrate as they are found on sand, clay and gravel bottoms. They can be found in estuaries; when they are juveniles they are found in sheltered inshore areas such as estuaries and sand flats where they will stay for around two years. They prefer a temperate climate; the geographic location of the New Zealand sand flounder determines its spawning period. In the north, it has a long spawning period from March to December.
In the south, spawning occurs in the spring. A study in the Hauraki Gulf found sand flounder lay between 500,000 eggs when spawning; the variation in the number of eggs laid was attributed to the difference in size of the female laying the eggs. After a period of time dependent on the temperature of the water, the larval sand flounder hatches. Larval sand flounders have a large yolk sac attached to their underside, providing nutrients to the fish until it is large enough to feed itself. At this stage, they are less than a half a centimetre in length, they have an eye on each side of their swim upright, as most fish do. As sand flounders grow they begin utilising external food sources such as seaweed spores and algae, as they grow further, small shrimp and plankton; the extra nutrients they receive from these new food sources enables them to grow to around one and a half centimetres by the time they are three weeks old. Above each eye of the sand flounder is a bar of cartilage, at this stage of its development the cartilage above the left eye is absorbed and the eye begins to move from the side of the head, until it is next to the right eye.
The unusual, twisted shape of the mouth of the sand flounder is due to the movement of the skull and bones as the left eye migrates to the right side of the body. While this slow process is occurring, the sand flounder begins to grow out to the side and flatten, losing its rounded shape; this metamorphism makes exhausting. The now juvenile sand flounders sink to the bottom and begin swimming as adult flatfish do, by undulating their side fins and for rapid acceleration, use their tail; the juvenile R. plebeia migrate to the shallow water of the estuaries and mudflats where they remain until they mature at two years old. Once R. plebeia reach a mature age and size, they migrate to deeper water of around 30 to 50 metres deep to spawn. After this first migration, they continue to migrate from shallow waters in spring and summer to deeper waters in autumn and winter. Male R. plebeia are smaller than female R. plebeia, maturing at a length of 10 cm, but can grow to 15–17 cm. The females grow faster, with mature size being 16 -- 20 cm long.
By age of three, female sand flounders grow to an average size of 30 cm. The average life span of flounder is three to four years; this equates to being able to have two years of spawning. The sand flounder feeds off a yolk-sac attached to its under surface until they are capable of fending for themselves; as an adult it is adapted to feed best at night on mud. They are ambush predators, going unnoticed by camouflage and attacking their prey when it comes near, they eat a variety of bottom-dwelling invertebrates such as crabs, shrimps, whitebait and tiny fishes located by touch and vision. They ingest mud detritus and seaweed while feeding. Sand flounder are a important commercial fish in New Zealand which means that humans are a predominant predator for them. Flat fishes including the sand flounder are good at camouflage which allows them to hide well from any predators, they are good at it because when they settle they wiggle their marginal fins throwing up a shower of sand or mud which lands on them and makes them un