Difference between revisions of "TriangleCurve Command"

From GeoGebra Manual
Jump to: navigation, search
Line 7: Line 7:
 
{{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.
 
}}
 
}}
  
 
{{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 15:29, 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 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.


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.
© 2024 International GeoGebra Institute