1.
Centre (geometry)
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In geometry, a centre of an object is a point in some sense in the middle of the object. According to the definition of centre taken into consideration, an object might have no centre. If geometry is regarded as the study of groups then a centre is a fixed point of all the isometries which move the object onto itself. The centre of a circle is the point equidistant from the points on the edge, similarly the centre of a sphere is the point equidistant from the points on the surface, and the centre of a line segment is the midpoint of the two ends. For objects with several symmetries, the centre of symmetry is the point left unchanged by the symmetric actions, so the centre of a square, rectangle, rhombus or parallelogram is where the diagonals intersect, this being the fixed point of rotational symmetries. Similarly the centre of an ellipse or a hyperbola is where the axes intersect. For an equilateral triangle, these are the point, which lies at the intersection of the three axes of symmetry of the triangle, one third of the distance from its base to its apex. e. F=thf for some real power h, thus the position of a centre is independent of scale. F is symmetric in its last two arguments, i. e. f= f, thus position of a centre in a triangle is the mirror-image of its position in the original triangle. This strict definition excludes pairs of points such as the Brocard points. The Encyclopedia of Triangle Centers lists over 9,000 different triangle centres, a tangential polygon has each of its sides tangent to a particular circle, called the incircle or inscribed circle. The centre of the incircle, called the incentre, can be considered a centre of the polygon, a cyclic polygon has each of its vertices on a particular circle, called the circumcircle or circumscribed circle. The centre of the circumcircle, called the circumcentre, can be considered a centre of the polygon, if a polygon is both tangential and cyclic, it is called bicentric. The incentre and circumcentre of a polygon are not in general the same point. The centre of a general polygon can be defined in different ways. The vertex centroid comes from considering the polygon as being empty, the side centroid comes from considering the sides to have constant mass per unit length. The usual centre, called just the centroid comes from considering the surface of the polygon as having constant density and these three points are in general not all the same point. Centrepoint Centre of mass Chebyshev centre Fixed points of isometry groups in Euclidean space

2.
Aerodynamic center
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The aerodynamic center is the point at which the pitching moment coefficient for the airfoil does not vary with lift coefficient, so this choice makes analysis simpler. D C m d C L =0 where C L is the lift coefficient. Forces can be summed up to act through a single point, the center of pressure location however, changes significantly with a change in angle of attack and is thus impractical for analysis. Thus the 25% chord position, or assumed aerodynamic center, is taken about which the forces, at the 25% chord position the moment generated was found and proven to be nearly constant with varying angle of attack. The concept of the center is important in aerodynamics. It is fundamental in the science of stability of aircraft in flight, please note that in highly theoretical/analytical analysis the aerodynamic center does vary slightly and changes location. In most literature however the center is taken at the 25% chord position. This conversely means that if one keeps the assumed AC fixed at 25% chord, a large portion of cambered airfoils have non constant moments about the 25% chord position because the AC does vary slightly. For most analysis the non constant moment about the 25% chord position is not significant enough to warrant consideration, for symmetric airfoils in subsonic flight the aerodynamic center is located approximately 25% of the chord from the leading edge of the airfoil. This point is described as the quarter-chord point and this result also holds true for thin-airfoils. For non-symmetric airfoils the quarter-chord is only an approximation for the aerodynamic center, a similar concept is that of center of pressure. The location of the center of pressure varies with changes of lift coefficient and this makes the center of pressure unsuitable for use in analysis of longitudinal static stability. Read about movement of centre of pressure, Y A C = Y r e f + c d C l d C z + c d C n d C x

3.
Central angle
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Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. The central angle is known as the arcs angular distance. The size of a central angle Θ is 0° < Θ < 360° оr 0 < Θ < 2π. When defining or drawing a central angle, in addition to specifying the points A and B, equivalently, one must specify whether the movement from point A to point B is clockwise or counterclockwise. If the intersection points A and B of the legs of the angle with the form a diameter. Let L be the arc of the circle between points A and B, and let R be the radius of the circle. If the central angle Θ is subtended by L, then 0 ∘ < Θ <180 ∘, Θ = ∘ = L R. If the central angle Θ is not subtended by the minor arc L, if a tangent at A and a tangent at B intersect at the exterior point P, then denoting the center as O, the angles ∠BOA and ∠BPA are supplementary. A regular polygon with n sides has a circle upon which all its vertices lie. The central angle of the polygon is formed at the center by the radii to two adjacent vertices. The measure of this angle is 2 π / n, Inscribed angle Great-circle navigation Central angle. Interactive Inscribed and Central Angles in a Circle

4.
Center of balance (horse)
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In horsemanship, the center of balance of a horse is a position on the horses back which correlates closely to the center of gravity of the horse itself. The term may refer to the horses center of gravity. For the best performance by the horse, as well as for better balance of the rider, the location of the horses center of balance depends on a combination of speed and degree of collection. For a standing or quietly walking horse, it is slightly behind the heart girth, if a horse is moving at a trot or canter, the center of balance shifts slightly forward, and it moves even more forward when the horse is galloping or jumping. If a horse is highly collected, the center of balance will be back, regardless of gait. For example, a close contact style of English saddle, designed for show jumping, places the riders seat farther forward than does a dressage style English saddle

5.
Cardinal point (optics)
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In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the points, the principal points, and the nodal points. The only ideal system that has achieved in practice is the plane mirror. Cardinal points provide a way to simplify a system with many components. The cardinal points lie on the axis of the optical system. Each point is defined by the effect the optical system has on rays that pass through that point, the paraxial approximation assumes that rays travel at shallow angles with respect to the optical axis, so that sin θ ≈ θ and cos θ ≈1. Aperture effects are ignored, rays that do not pass through the stop of the system are not considered in the discussion below. The front focal point of a system, by definition, has the property that any ray that passes through it will emerge from the system parallel to the optical axis. The rear focal point of the system has the reverse property, the front and rear focal planes are defined as the planes, perpendicular to the optic axis, which pass through the front and rear focal points. An object infinitely far from the optical system forms an image at the focal plane. For objects a finite distance away, the image is formed at a different location, but rays that leave the object parallel to one another cross at the rear focal plane. A diaphragm or stop at the focal plane can be used to filter rays by angle, since. No matter where on the object the ray comes from, the ray will pass through the aperture as long as the angle at which it is emitted from the object is small enough. Note that the aperture must be centered on the axis for this to work as indicated. Using a sufficiently small aperture in the plane will make the lens telecentric. Similarly, the range of angles on the output side of the lens can be filtered by putting an aperture at the front focal plane of the lens. This is important for DSLR cameras having CCD sensors, the pixels in these sensors are more sensitive to rays that hit them straight on than to those that strike at an angle. A lens that does not control the angle of incidence at the detector will produce pixel vignetting in the images and this means that the lens can be treated as if all of the refraction happened at the principal planes

6.
Centroid
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In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape. The definition extends to any object in space, its centroid is the mean position of all the points in all of the coordinate directions. Informally, it is the point at which a cutout of the shape could be balanced on the tip of a pin. While in geometry the term barycenter is a synonym for centroid, in astrophysics and astronomy, in physics, the center of mass is the arithmetic mean of all points weighted by the local density or specific weight. If a physical object has uniform density, then its center of mass is the same as the centroid of its shape, in geography, the centroid of a radial projection of a region of the Earths surface to sea level is known as the regions geographical center. The geometric centroid of an object always lies in the object. A non-convex object might have a centroid that is outside the figure itself, the centroid of a ring or a bowl, for example, lies in the objects central void. If the centroid is defined, it is a point of all isometries in its symmetry group. In particular, the centroid of an object lies in the intersection of all its hyperplanes of symmetry. The centroid of many figures can be determined by this principle alone, in particular, the centroid of a parallelogram is the meeting point of its two diagonals. This is not true for other quadrilaterals, for the same reason, the centroid of an object with translational symmetry is undefined, because a translation has no fixed point. The centroid of a triangle is the intersection of the three medians of the triangle and it lies on the triangles Euler line, which also goes through various other key points including the orthocenter and the circumcenter. Any of the three medians through the centroid divides the area in half. Let P be any point in the plane of a triangle with vertices A, B, and C and centroid G. The sum of the squares of the sides equals three times the sum of the squared distances of the centroid from the vertices, A B2 + B C2 + C A2 =3. A triangles centroid is the point that maximizes the product of the distances of a point from the triangles sidelines. For other properties of a centroid, see below. The body is held by the pin inserted at a point near the perimeter, in such a way that it can freely rotate around the pin

7.
Concentric objects
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In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another, in the Euclidean plane, two circles that are concentric necessarily have different radii from each other. However, circles in three-dimensional space may be concentric, and have the radius as each other. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth, more generally, every two great circles on a sphere are concentric with each other and with the sphere. The circumcircle and the incircle of a regular n-gon, and the regular n-gon itself, are concentric, for the circumradius-to-inradius ratio for various n, see Bicentric polygon#Regular polygons. The region of the plane between two circles is an annulus, and analogously the region of space between two concentric spheres is a spherical shell. For a given point c in the plane, the set of all circles having c as their forms a pencil of circles. Each two circles in the pencil are concentric, and have different radii, every point in the plane, except for the shared center, belongs to exactly one of the circles in the pencil. Every two disjoint circles, and every hyperbolic pencil of circles, may be transformed into a set of circles by a Möbius transformation. The ripples formed by dropping an object into still water naturally form an expanding system of concentric circles. Evenly spaced circles on the used in target archery or similar sports provide another familiar example of concentric circles. Coaxial cable is a type of cable in which the combined neutral. Johannes Keplers Mysterium Cosmographicum envisioned a system formed by concentric regular polyhedra. Concentric circles are found in diopter sights, a type of mechanic sights commonly found on target rifles. They usually feature a disk with a small-diametre hole near the shooters eye. When these sights are aligned, the point of impact will be in the middle of the front sight circle. Centered cube number Homoeoid Focaloid Circular symmetry Magic circle Geometry, Concentric circles demonstration With interactive animation

8.
Center of curvature
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In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the curvature is zero, the osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the point of two infinitely close normal lines to the curve. The locus of centers of curvature for each point on the curve comprise the evolute of the curve, curvature Differential geometry of curves Hilbert, David, Cohn-Vossen, Stephan, Geometry and the Imagination, New York, Chelsea, ISBN 978-0-8284-0087-9