Difference between revisions of "TriangleCurve Command"
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− | ;TriangleCurve | + | ;TriangleCurve( <Point P>, <Point Q>, <Point R>, <Equation in 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 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 referred to as ''A'', ''B'', ''C''. | ||
:{{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''.}} |
Revision as of 17:17, 7 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, andTriangleCurve[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.