Triangle Functions

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Triangle Functions Support

The Fractal Science Kit fractal generator Triangle functions are associated with the Triangle object:

Object Triangle { A : B : C }

The fields A, B, and C are the triangles vertices. The Triangle functions calculate various metrics, points, vectors, triangles, or circles related to the triangle.

The following example illustrates how you would define a Triangle object using the object's constructor:

Triangle t = Triangle(A, B, C)

This example assigns a triangle to the variable t. The triangle is defined by the arguments: A, B, and C, passed to the constructor.

Complex Triangle.CollinearPoints(Triangle t)

Triangle.CollinearPoints returns True if the triangle points are collinear and do not in fact represent a triangle. Many of the Triangle functions require that the triangle points are not collinear so if there is a possibility of this occurring, you should call Triangle.CollinearPoints before calling the function and take appropriate action if it returns True.

Complex Triangle.LengthSideA(Triangle t)
Complex Triangle.LengthSideB(Triangle t)
Complex Triangle.LengthSideC(Triangle t)
Complex Triangle.AngleA(Triangle t)
Complex Triangle.AngleB(Triangle t)
Complex Triangle.AngleC(Triangle t)
Complex Triangle.Perimeter(Triangle t)
Complex Triangle.Area(Triangle t)
Complex Triangle.TrianglePower(Triangle t)
Complex Triangle.CirclePower(Triangle t)
Complex Triangle.TangentAB(Triangle t)
Complex Triangle.TangentBC(Triangle t)
Complex Triangle.TangentCA(Triangle t)
Complex Triangle.MollweideA(Triangle t)
Complex Triangle.MollweideB(Triangle t)
Complex Triangle.MollweideC(Triangle t)
Complex Triangle.NewtonA(Triangle t)
Complex Triangle.NewtonB(Triangle t)
Complex Triangle.NewtonC(Triangle t)

These functions provide access to several metrics including the length of the sides, the vertex angles in radians, the perimeter, and the area. Triangle.CirclePower returns the circle power of the incenter with respect to the circumcircle.

For additional details see:

Eric W. Weisstein. "Triangle Power."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Circle Power."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Mollweide's Formulas."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Newton's Formulas."

From MathWorld--A Wolfram Web Resource.

 

Complex Triangle.MedianAFoot(Triangle t)
Complex Triangle.MedianBFoot(Triangle t)
Complex Triangle.MedianCFoot(Triangle t)
Complex Triangle.AltitudeAFoot(Triangle t)
Complex Triangle.AltitudeBFoot(Triangle t)
Complex Triangle.AltitudeCFoot(Triangle t)
Complex Triangle.AngleBisectorAFoot(Triangle t)
Complex Triangle.AngleBisectorBFoot(Triangle t)
Complex Triangle.AngleBisectorCFoot(Triangle t)

These functions provide access to the feet of the triangle's medians, altitudes, and angle bisectors.

For additional details see:

Eric W. Weisstein. "Triangle Median."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Angle Bisector."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Altitude."

From MathWorld--A Wolfram Web Resource.

 

Vector Triangle.SideA(Triangle t)
Vector Triangle.SideB(Triangle t)
Vector Triangle.SideC(Triangle t)
Vector Triangle.MedianA(Triangle t)
Vector Triangle.MedianB(Triangle t)
Vector Triangle.MedianC(Triangle t)
Vector Triangle.AltitudeA(Triangle t)
Vector Triangle.AltitudeB(Triangle t)
Vector Triangle.AltitudeC(Triangle t)
Vector Triangle.AngleBisectorA(Triangle t)
Vector Triangle.AngleBisectorB(Triangle t)
Vector Triangle.AngleBisectorC(Triangle t)

These functions return vectors for the triangle's sides, medians, altitudes, and angle bisectors.

For additional details see:

Eric W. Weisstein. "Triangle Median."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Angle Bisector."

From MathWorld--A Wolfram Web Resource.

 

Eric W. Weisstein. "Altitude."

From MathWorld--A Wolfram Web Resource.

 

Complex Triangle.Centroid(Triangle t)
Complex Triangle.OrthoCenter(Triangle t)
Complex Triangle.InCenter(Triangle t)
Complex Triangle.ExCenterA(Triangle t)
Complex Triangle.ExCenterB(Triangle t)
Complex Triangle.ExCenterC(Triangle t)
Complex Triangle.CircumCenter(Triangle t)

These functions return a few of the triangle's centers.

For additional details see:

Eric W. Weisstein. "Triangle Centers."

From MathWorld--A Wolfram Web Resource.

 

Triangle Triangle.MedialTriangle(Triangle t)
Triangle Triangle.OrthicTriangle(Triangle t)
Triangle Triangle.IncentralTriangle(Triangle t)
Triangle Triangle.IntouchTriangle(Triangle t)
Triangle Triangle.EulerTriangle(Triangle t)
Triangle Triangle.ReflectedTriangle(Triangle t)
Triangle Triangle.CevianTriangle(Triangle t, z)
Triangle Triangle.DoubleCevianTriangle(Triangle t, z)
Triangle Triangle.PedalTriangle(Triangle t, z)
Triangle Triangle.DoublePedalTriangle(Triangle t, z)

These functions return several related triangles.

For additional details see:

Eric W. Weisstein. "Special Triangles."

From MathWorld--A Wolfram Web Resource.

 

Circle Triangle.InCircle(Triangle t)
Circle Triangle.ExCircleA(Triangle t)
Circle Triangle.ExCircleB(Triangle t)
Circle Triangle.ExCircleC(Triangle t)
Circle Triangle.CircumCircle(Triangle t)
Circle Triangle.MedialCircle(Triangle t)
Circle Triangle.IncentralCircle(Triangle t)
Circle Triangle.ReflectedCircle(Triangle t)
Circle Triangle.CevianCircle(Triangle t, z)
Circle Triangle.PedalCircle(Triangle t, z)
Circle Triangle.DoublePedalCircle(Triangle t, z)

These functions return several related circles.

For additional details see:

Eric W. Weisstein. "Triangle Circles."

From MathWorld--A Wolfram Web Resource.

 

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