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can be defined in several different ways. The "vertex centroid" comes from considering the polygon as being empty but having equal masses at its vertices. The "side centroid" comes from considering the sides to have constant mass per unit length. The usual centre, called just the
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The centre of a hyperbola lies without the curve, since the figurative straight crosses the curve. The tangents from the centre to the hyperbola are called 'asymptotes'. Their contact points are the two points at infinity on the
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The centre of any ellipse is within it, for its polar does not meet the curve, and so there are no tangents from it to the curve. The centre of a parabola is the contact point of the figurative straight.
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in some sense in the middle of the object. According to the specific definition of centre taken into consideration, an object might have no centre. If geometry is regarded as the study of
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358:, these are the same 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.
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or "figurative point" where it crosses all the lines that are parallel to it. The ellipse, parabola, and hyperbola of
Euclidean geometry are called
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is where the diagonals intersect, this is (among other properties) the fixed point of rotational symmetries. Similarly the centre of an
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from a projectivity that is not a perspectivity. A symmetry of the projective plane with a given conic relates every point or
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or circumscribed circle. The centre of the circumcircle, called the circumcentre, can be considered a centre of the polygon.
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or inscribed circle. The centre of the incircle, called the incentre, can be considered a centre of the polygon.
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630:. The concept of centre in projective geometry uses this relation. The following assertions are from
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of a point at infinity with respect to the end points of a finite sect is the 'centre' of that sect.
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The pole of the straight at infinity with respect to a certain conic is the 'centre' of the conic.
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is the point equidistant from the points on the surface, and the centre of a line segment is the
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The polar of any figurative point is on the centre of the conic and is called a 'diameter'.
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Quadrilateral § Remarkable points and lines in a convex quadrilateral
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is the point left unchanged by the symmetric actions. So the centre of a
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This strict definition excludes pairs of bicentric points such as the
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is a function of the lengths of the three sides of the triangle,
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has each of its vertices on a particular circle, called the
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Several special points of a triangle are often described as
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A strict definition of a triangle centre is a point whose
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If a polygon is both tangential and cyclic, it is called
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from the points on the edge. Similarly the centre of a
49:. Unsourced material may be challenged and removed.
684:Fixed points of isometry groups in Euclidean space
618:in projective geometry and may be constructed as
731:"This is PART 20: Centers X(38001) - X(40000)"
537:lists over 39,000 different triangle centres.
493:is symmetric in its last two arguments; i.e.,
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339:, the intersection of the triangle's three
109:Learn how and when to remove this message
708:Algebraic Highways in Triangle Geometry
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541:Tangential polygons and cyclic polygons
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47:adding citations to reliable sources
553:to a particular circle, called the
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736:Encyclopedia of Triangle Centers
689:Instantaneous centre of rotation
535:Encyclopedia of Triangle Centers
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16:Middle of the object in geometry
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224:Circles, spheres, and segments
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754:Synthetic Projective Geometry
284:is where the axes intersect.
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252:For objects with several
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58:"Centre" geometry
626:to a line called its
363:trilinear coordinates
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356:equilateral triangle
132: circumference
127:Circle illustration
43:improve this article
773:Elementary geometry
608:projective geometry
640:harmonic conjugate
547:tangential polygon
436:is homogeneous in
258:centre of symmetry
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778:Geometric centers
727:Kimberling, Clark
612:point at infinity
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602:Projective conics
348:nine-point centre
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41:Please help
36:verification
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674:Centrepoint
429:such that:
337:orthocentre
234:equidistant
767:Categories
695:References
583:See also:
254:symmetries
69:newspapers
573:bicentric
397:) :
381:) :
341:altitudes
288:Triangles
282:hyperbola
266:rectangle
711:Archived
668:See also
596:centroid
555:incircle
448:; i.e.,
413:) where
330:incentre
319:centroid
312:vertices
242:midpoint
169:geometry
752:(1903)
591:polygon
551:tangent
354:For an
278:ellipse
270:rhombus
203:kéntron
196:κέντρον
83:scholar
663:curve.
616:conics
262:square
256:, the
238:sphere
230:circle
210:object
181:center
173:centre
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280:or a
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90:JSTOR
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638:The
624:pole
365:are
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606:In
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321:or
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