EasyGeometry::D2::Triangle

A polygon with three vertices and three sides. Line inherit from Linear Entity.

#is_similar?(other)

Description

Is another triangle similar to this one.

Signature

Parameters:
    other - EasyGeometry::D2::Triangle

Returns:
    boolean (true or false)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [4, 4], [0, 4])
t2 = EasyGeometry::D2::Triangle.new([0, 0], [0, 1], [1, 1])

t1.is_similar?(t2) # true

#is_equilateral?

Description

Are all the sides the same length?

Precision - 10e-13

Signature

Parameters:

Returns:
    boolean (true or false)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [4, 4], [0, 4])
t2 = EasyGeometry::D2::Triangle.new([0, 0], [1/2r, Math.sqrt(3)/2], [1, 0])

t1.is_equilateral? # false
t2.is_equilateral? # true

#is_isosceles?

Description

Are two or more of the sides the same length?

Precision - 10e-13

Signature

Parameters:

Returns:
    boolean (true or false)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [4, 4], [0, 4])
t2 = EasyGeometry::D2::Triangle.new([0, 0], [1/2r, Math.sqrt(3)/2], [1, 0])

t1.is_isosceles? # true
t2.is_isosceles? # true

#is_scalene?

Description

Are all the sides of the triangle of different lengths?

Precision - 10e-13

Signature

Parameters:

Returns:
    boolean (true or false)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [4, 4], [0, 4])
t2 = EasyGeometry::D2::Triangle.new([0, 0], [1/2r, Math.sqrt(3)/2], [1, 0])

t1.is_scalene? # false
t2.is_scalene? # false

#is_right?

Description

Is the triangle right-angled.

Signature

Parameters:

Returns:
    boolean (true or false)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [4, 4], [0, 4])
t2 = EasyGeometry::D2::Triangle.new([0, 0], [1/2r, Math.sqrt(3)/2], [1, 0])

t1.is_right? # true
t2.is_right? # false

#altitudes

Description

The altitudes of the triangle.

An altitude of a triangle is a segment through a vertex, perpendicular to the opposite side, with length being the height of the vertex measured from the line containing the side.

Signature

Parameters:

Returns:
    Hash(The hash consists of keys which are vertices and values which are Segments.)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [5, 0], [0, 5])

t1.altitudes # {
             #    Point(0, 0): Segment(Point(0, 0), Point(5/2, 5/2)),
             #    Point(5, 0): Segment(Point(5, 0), Point(0, 0)),
             #    Point(0, 5): Segment(Point(0, 5), Point(0, 0)),
             # }

#orthocenter

Description

The orthocenter of the triangle.

The orthocenter is the intersection of the altitudes of a triangle. It may lie inside, outside or on the triangle.

Signature

Parameters:

Returns:
    EasyGeometry::D2::Point
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [5, 0], [0, 5])

t1.orthocenter # Point(0, 0)

#circumcenter

Description

The circumcenter of the triangle.

The circumcenter is the center of the circumcircle.

Signature

Parameters:

Returns:
    EasyGeometry::D2::Point
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [1, 0], [0, 1])

t1.circumcenter # Point(0.5, 0.5)

#circumradius

Description

The radius of the circumcircle of the triangle.

Signature

Parameters:

Returns:
    Numeric
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [2, 0], [0, 2])

t1.circumradius # Math.sqrt(2)

#bisectors

Description

The angle bisectors of the triangle.

An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half.

Signature

Parameters:

Returns:
    Hash(each key is a vertex (Point) and each value is the corresponding bisector (Segment).)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [5, 0], [0, 5])

t1.altitudes # {
             #    Point(0, 0): Segment(Point(0, 0), Point(5/2, 5/2)),
             #    Point(5, 0): Segment(Point(5, 0), Point(0, 585786437626905/282842712474619)),
             #    Point(0, 5): Segment(Point(0, 5), Point(585786437626905/282842712474619, 0)),
             # }

#incenter

Description

The center of the incircle.

The incircle is the circle which lies inside the triangle and touches all three sides.

Signature

Parameters:

Returns:
    EasyGeometry::D2::Point
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [1, 0], [0, 1])

t1.incenter # Point(1 - Math.sqrt(2)/2, 1 - Math.sqrt(2)/2)

#inradius

Description

The radius of the incircle.

Signature

Parameters:

Returns:
    Numeric
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [4, 0], [0, 3])

t1.inradius # 1

#exradii

Description

The radius of excircles of a triangle.

An excircle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two.

[1] http://mathworld.wolfram.com/Exradius.html

[2] http://mathworld.wolfram.com/Excircles.html

Signature

Parameters:

Returns:
    Hash
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [5, 0], [0, 5])

t1.exradii # {
             #    Segment(Point(0, 0), Point(5, 0)): 3.5355339059327373,
             #    Segment(Point(5, 0), Point(0, 5)): 8.535533905932738,
             #    Segment(Point(0, 5), Point(0, 0)): 3.5355339059327373,
             # }

#medians

Description

The medians of the triangle.

A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas.

Signature

Parameters:

Returns:
    Hash(each key is a vertex (Point) and each value is the median (Segment) at that point.)
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [1, 0], [0, 1])

t1.medians # {
             #    Point(0, 0): Segment(Point(0, 0), Point(0.5, 0.5)),
             #    Point(1, 0): Segment(Point(1, 0), Point(0, 0.5)),
             #    Point(0, 1): Segment(Point(0, 1), Point(0.5, 0)),
             # }

#medial

Description

The medial triangle of the triangle.

The triangle which is formed from the midpoints of the three sides.

Signature

Parameters:

Returns:
    EasyGeometry::D2::Triangle
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [1, 0], [0, 1])

t1.medial # Triangle(Point(0.5, 0), Point(0.5, 0.5), Point(0, 0.5))

#eulerline

Description

The Euler line of the triangle.

The line which passes through circumcenter, centroid and orthocenter.

Signature

Parameters:

Returns:
    EasyGeometry::D2::Line 
    or EasyGeometry::D2::Point for equilateral triangles in which case all centers coincide
    
Errors:

Example

t1 = EasyGeometry::D2::Triangle.new([0, 0], [1, 0], [0, 1])

t1.eulerline # Line(Point(0, 0), Point(0.5, 0.5))