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dbr:Conway_triangle_notation
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Conway-driehoeknotatie Conway triangle notation
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Bij berekeningen in een driehoek ABC wordt vaak gebruikgemaakt van Conway-driehoeknotatie, geïntroduceerd door John Conway. Startend met S voor de dubbele oppervlakte van de driehoek schrijft hij .In het bijzonder * * * * waarin zoals gebruikelijk a, b en c voor de lengtes van de zijden staan. Bovendien staan A, B en C voor de hoeken van de driehoek, en voor de hoek van Brocard.Verder geldt de conventie . In geometry, the Conway triangle notation, named after John Horton Conway, allows trigonometric functions of a triangle to be managed algebraically. Given a reference triangle whose sides are a, b and c and whose corresponding internal angles are A, B, and C then the Conway triangle notation is simply represented as follows: where S = 2 × area of reference triangle and in particular where is the Brocard angle. The law of cosines is used: . for values of where Furthermore the convention uses a shorthand notation for and Hence: Some important identities: Some useful trigonometric conversions:
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Conway Triangle Notation
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ConwayTriangleNotation
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Bij berekeningen in een driehoek ABC wordt vaak gebruikgemaakt van Conway-driehoeknotatie, geïntroduceerd door John Conway. Startend met S voor de dubbele oppervlakte van de driehoek schrijft hij .In het bijzonder * * * * waarin zoals gebruikelijk a, b en c voor de lengtes van de zijden staan. Bovendien staan A, B en C voor de hoeken van de driehoek, en voor de hoek van Brocard.Verder geldt de conventie . In geometry, the Conway triangle notation, named after John Horton Conway, allows trigonometric functions of a triangle to be managed algebraically. Given a reference triangle whose sides are a, b and c and whose corresponding internal angles are A, B, and C then the Conway triangle notation is simply represented as follows: where S = 2 × area of reference triangle and in particular where is the Brocard angle. The law of cosines is used: . for values of where Furthermore the convention uses a shorthand notation for and Hence: Some important identities: where R is the circumradius and abc = 2SR and where r is the incenter, and Some useful trigonometric conversions: Some useful formulas: Some examples using Conway triangle notation: Let D be the distance between two points P and Q whose trilinear coordinates are pa : pb : pc and qa : qb : qc. Let Kp = apa + bpb + cpc and let Kq = aqa + bqb + cqc. Then D is given by the formula: Using this formula it is possible to determine OH, the distance between the circumcenter and the orthocenter as follows: For the circumcenter pa = aSA and for the orthocenter qa = SBSC/a Hence: This gives:
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