Difference between revisions of "TriangleCurve Command"

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<noinclude>{{Manual Page|version=4.2}}</noinclude>{{betamanual|version=4.2}}
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}}
{{command|geometry}}
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;TriangleCurve( <Point P>, <Point Q>, <Point R>, <Equation in A, B, C> )
;TriangleCurve[<Point P>,<Point Q>,<Point R>,<Equation in A,B,C>]
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:Creates implicit polynomial, whose equation in [[w:Barycentric_coordinate_system_(mathematics)|barycentric coordinates]] with respect to points ''P'', ''Q'', ''R'' is given by the fourth parameter; the barycentric coordinates are referred to as ''A'', ''B'', ''C''.
:creates implicit polynomial, whose equation in [[w:Barycentric_coordinate_system_(mathematics)|barycentric coordinates]] with respect to points P, Q,R is given by the fourth parameter; the barycentric coordinates are refered to as A,B,C.
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:{{Example|1=If ''P'', ''Q'', ''R'' are points, <code>TriangleCurve(P, Q, R, (A - B)*(B - C)*(C - A) = 0)</code> gives a cubic curve consisting of the medians of the triangle ''PQR''.}}
 
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:{{Example|1=
{{Example|1=If ''P,Q,R'' are points, <code>TriangleCurve[P,Q,R,(A-B)*(B-C)*(C-A)=0]</code> gives a cubic curve consisting of the medians of the triangle ''PQR''.}}
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<code>TriangleCurve(A, B, C, A*C = 1/8)</code> creates a hyperbola such that tangent, through ''A'' or ''C'', to this hyperbola splits triangle ''ABC'' in two parts of equal area.}}
{{Example|1=
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:{{Example|1=
<code>TriangleCurve[A,B,C,A*C=1/8]</code> creates a hyperbola such that tangent to this hyperbola splits triangle ABC in two parts of equal area.
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<code>TriangleCurve(A, B, C, A² + B² + C² - 2B C - 2C A - 2A B = 0)</code> creates the [[w:Steiner_inellipse|Steiner inellipse]] of the triangle ''ABC'', and <code>TriangleCurve(A, B, C, B C + C A + A B = 0)</code> creates the [[w:Steiner_ellipse|Steiner circumellipse]] of the triangle ''ABC''. }}
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{{Note|The input points can be called ''A'', ''B'' or ''C'', but in this case you cannot use e.g. ''x(A)'' in the equation, because ''A'' is interpreted as the barycentric coordinate.}}
 
{{Note|The input points can be called ''A'', ''B'' or ''C'', but in this case you cannot use e.g. ''x(A)'' in the equation, because ''A'' is interpreted as the barycentric coordinate.}}

Latest revision as of 09:44, 11 October 2017


TriangleCurve( <Point P>, <Point Q>, <Point R>, <Equation in A, B, C> )
Creates implicit polynomial, whose equation in barycentric coordinates with respect to points P, Q, R is given by the fourth parameter; the barycentric coordinates are referred to as A, B, C.
Example: If P, Q, R are points, TriangleCurve(P, Q, R, (A - B)*(B - C)*(C - A) = 0) gives a cubic curve consisting of the medians of the triangle PQR.
Example: TriangleCurve(A, B, C, A*C = 1/8) creates a hyperbola such that tangent, through A or C, to this hyperbola splits triangle ABC in two parts of equal area.
Example: TriangleCurve(A, B, C, A² + B² + C² - 2B C - 2C A - 2A B = 0) creates the Steiner inellipse of the triangle ABC, and TriangleCurve(A, B, C, B C + C A + A B = 0) creates the Steiner circumellipse of the triangle ABC.


Note: The input points can be called A, B or C, but in this case you cannot use e.g. x(A) in the equation, because A is interpreted as the barycentric coordinate.
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