Difference between revisions of "TriangleCurve Command"
From GeoGebra Manual
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<noinclude>{{Manual Page|version=4.2}}</noinclude> | <noinclude>{{Manual Page|version=4.2}}</noinclude> | ||
{{command|geometry}} | {{command|geometry}} | ||
| − | ;TriangleCurve[<Point P>, <Point Q>, <Point R>, <Equation in A, B, C>] | + | ;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''. |
| − | + | :{{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, through ''A'' or ''C'', to this hyperbola splits triangle ''ABC'' in two parts of equal area.}} |
| − | <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= |
| − | }} | + | <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''. }} |
| − | {{Example|1= | ||
| − | <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 | ||
| − | }} | ||
{{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 13:40, 28 June 2013
- 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.
