Difference between revisions of "TriangleCurve Command"

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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''.}}
 
{{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''.}}
 
{{Example|1=
 
{{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, A*C = 1/8]</code> creates a hyperbola such that tangent through A to this hyperbola splits triangle ABC in two parts of equal area.
 
}}
 
}}
  
 
{{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.}}

Revision as of 13:55, 26 August 2012


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 to this hyperbola splits triangle ABC in two parts of equal area.


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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