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62 relations: Altitude (triangle), American Mathematical Monthly, Area, Barnes & Noble, Barycentric coordinate system, Bisection, Cartesian coordinate system, Circle, Circumconic and inconic, Circumgon, Circumscribed circle, Concyclic points, Convex hull, Cut-the-Knot, Equilateral triangle, Euler's theorem in geometry, Ex-tangential quadrilateral, Extended side, Extouch triangle, Feuerbach point, Forum Geometricorum, Geometry, Group (mathematics), Harcourt's theorem, Heron's formula, Holt McDougal, Identity element, Incenter, Incircle and excircles of a triangle, Inscribed sphere, Internal and external angles, Isotomic conjugate, Law of cosines, Law of sines, Line segment, Medial triangle, Midpoint, Nagel point, Nine-point circle, Orthocentric system, Orthocentroidal circle, Perpendicular, Pitot theorem, Point (geometry), Power of a point, Problem of Apollonius, Quadrilateral, Semiperimeter, Splitter (geometry), Steiner inellipse, ..., Symmedian, Tangent, Tangent circles, Tangent lines to circles, Tangential polygon, Tangential quadrilateral, The Mathematical Gazette, Triangle, Triangle center, Trilinear coordinates, Trillium theorem, Vertex (geometry). Expand index (12 more) »
Altitude (triangle)
In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).
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American Mathematical Monthly
The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.
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Area
Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.
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Barnes & Noble
Barnes & Noble, Inc., a Fortune 500 company, is the bookseller with the largest number of retail outlets in the United States, and a retailer of content, digital media, and educational products.
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Barycentric coordinate system
In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices.
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Bisection
In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Circle
A circle is a simple closed shape.
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Circumconic and inconic
In triangle geometry, a circumconic is a conic section that passes through the three vertices of a triangle, and an inconic is a conic section inscribed in the sides, possibly extended, of a triangle.
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Circumgon
In mathematics and particularly in elementary geometry, a circumgon is a geometric figure which circumscribes some circle, in the sense that it is the union of the outer edges of non-overlapping triangles each of which has a vertex at the center of the circle and opposite side on a line that is tangent to the circle.
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Circumscribed circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.
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Concyclic points
In geometry, a set of points are said to be concyclic (or cocyclic) if they lie on a common circle.
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Convex hull
In mathematics, the convex hull or convex envelope or convex closure of a set X of points in the Euclidean plane or in a Euclidean space (or, more generally, in an affine space over the reals) is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X., p. 3.
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Cut-the-Knot
Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.
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Equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides are equal.
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Euler's theorem in geometry
In geometry, Euler's theorem states that the distance d between the circumcentre and incentre of a triangle is given by.
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Ex-tangential quadrilateral
In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral.
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Extended side
In plane geometry, an extended side or sideline of a polygon is the line that contains one side of the polygon.
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Extouch triangle
In geometry, the extouch triangle of a triangle is formed by joining the points at which the three excircles touch the triangle.
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Feuerbach point
In the geometry of triangles, the incircle and nine-point circle of a triangle are internally tangent to each other at the Feuerbach point of the triangle.
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Forum Geometricorum
Forum Geometricorum: A Journal on Classical Euclidean Geometry (often abbreviated Forum Geom.) is a peer-reviewed open-access academic journal that specializes in mathematical research papers on Euclidean geometry.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Harcourt's theorem
Harcourt's theorem is a formula in geometry for the area of a triangle, as a function of its side lengths and the perpendicular distances of its vertices from an arbitrary line tangent to its incircle.
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Heron's formula
In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulae for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.
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Holt McDougal
Holt McDougal is an American publishing company, a division of Houghton Mifflin Harcourt, that specializes in textbooks for use in secondary schools.
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Identity element
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
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Incenter
In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale.
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Incircle and excircles of a triangle
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.
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Inscribed sphere
In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.
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Internal and external angles
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.
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Isotomic conjugate
In geometry, the isotomic conjugate of a point P with respect to a triangle ABC is another point, defined in a specific way from P and ABC: If the base points of the lines PA, PB, and PC on the sides opposite A, B, and C are reflected about the midpoints of their respective sides, the resulting lines intersect at the isotomic congugate of P.
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Law of cosines
In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
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Law of sines
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles.
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Line segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
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Medial triangle
The medial triangle or midpoint triangle of a triangle ABC is the triangle with vertices at the midpoints of the triangle's sides AB, AC and BC.
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Midpoint
In geometry, the midpoint is the middle point of a line segment.
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Nagel point
In geometry, the Nagel point is a triangle center, one of the points associated with a given triangle whose definition does not depend on the placement or scale of the triangle.
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Nine-point circle
In geometry, the nine-point circle is a circle that can be constructed for any given triangle.
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Orthocentric system
In geometry, an orthocentric system is a set of four points on a plane, one of which is the orthocenter of the triangle formed by the other three.
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Orthocentroidal circle
In geometry, the orthocentroidal circle of a non-equilateral triangle is the circle that has the triangle's orthocenter and its centroid at opposite ends of a diameter.
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Perpendicular
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).
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Pitot theorem
In geometry, the Pitot theorem, named after the French engineer Henri Pitot, states that in a tangential quadrilateral (i.e. one in which a circle can be inscribed) the two sums of lengths of opposite sides are the same.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Power of a point
In elementary plane geometry, the power of a point is a real number h that reflects the relative distance of a given point from a given circle.
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Problem of Apollonius
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1).
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Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.
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Semiperimeter
In geometry, the semiperimeter of a polygon is half its perimeter.
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Splitter (geometry)
In plane geometry, a splitter is a line segment through one of the vertices of a triangle (that is, a cevian) that bisects the perimeter of the triangle.
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Steiner inellipse
In geometry, the Steiner inellipse,Weisstein, E. "Steiner Inellipse" — From MathWorld, A Wolfram Web Resource, http://mathworld.wolfram.com/SteinerInellipse.html.
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Symmedian
In geometry, symmedians are three particular geometrical lines associated with every triangle.
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Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.
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Tangent circles
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point.
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Tangent lines to circles
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior.
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Tangential polygon
In Euclidean geometry, a tangential polygon, also known as a circumscribed polygon, is a convex polygon that contains an inscribed circle (also called an incircle).
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Tangential quadrilateral
In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides are all tangent to a single circle within the quadrilateral.
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The Mathematical Gazette
The Mathematical Gazette is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Triangle center
In geometry, a triangle center (or triangle centre) is a point in the plane that is in some sense a center of a triangle akin to the centers of squares and circles, i.e. a point that is in the middle of the figure by some measure.
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Trilinear coordinates
In geometry, the trilinear coordinates x:y:z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle.
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Trillium theorem
In Euclidean geometry, the trillium theorem – (from лемма о трезубце, literally 'lemma about trident', теорема трилистника, literally 'theorem of trillium' or 'theorem of trefoil') is a statement about properties of inscribed and circumscribed circles and their relations.
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Vertex (geometry)
In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.
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Contact triangle, Escribed circle, Excenter, Excentral triangle, Excentre, Excircle, Excircles, Gergonne Point, Gergonne point, Gergonne triangle, Geronne triangle, In-center, In-radius, Incentral triangle, Incircle, Incircle & excircles of a triangle, Incircle radius, Inradius, Inscribed circle, Intouch triangle, Mandart circle.
References
[1] https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle
