SymPy Geometry Module - Documentation

from sympy.modules.geometry import *
x = Point(0, 0)
y = Point(1, 1)
z = Point(2, 2)
zp = Point(1, 0)
Point.are_collinear(x, y, z)
True
Point.are_collinear(x, y, zp)
False
t = Triangle(zp, y, x)
t.area
1/2
t.medians[x]
Segment(Point(1, 1/2), Point(0, 0))
m = t.medians
intersection(m[x], m[y], m[zp])
[Point(2/3, 1/3)]
c = Circle(x, 5)
l = Line(Point(5, -5), Point(5, 5))
c.is_tangent(l)
True
l = Line(x, y)
c.is_tangent(l)
False
intersection(c, l)
[Point(-25/2*2/25**(1/2), -25/2*2/25**(1/2)), Point(25/2*2/25**(1/2), 25/2*2/25**(1/2))]

LinearEntity
Properties	Methods
	[static] are_concurrent(l1, l2, ..., ln) [static] are_parallel(l1, l2) [static] are_perpendicular(l1, l2) parallel_line(self, p) perpendicular_line(self, p) perpendicular_segment(self, p) projection(self, p)

Line (inherits from LinearEntity)
Properties	Methods
coefficients (a tuple of the coefficients a,b,c in ax + by + c = 0) points (the points that originally defined this line) slope	arbitrary_point(self) equation(self, xaxis_name='x', yaxis_name='y') random_point(self)

Ray (inherits from LinearEntity)
Properties	Methods
source	random_point(self)

Segment (inherits from LinearEntity)
Properties	Methods
length midpoint	random_point(self) perpendicular_bisector(self, p=None)

Ellipse
Properties	Methods
horizontal_radius vertical_radius center area circumference	tangent_line(self, p) is_tangent(self, o) arbitrary_point(self) random_point(self) equation(self, xaxis_name='x', yaxis_name='y')

Circle (inherits from Ellipse)
Properties	Methods
radius

Polygon
Properties	Methods
area centroid perimeter sides vertices

RegularPolygon (inherits from Polygon)
Properties	Methods
apothem center circumcircle exterior_angle incircle interior_angle radius

Triangle (inherits from Polygon)
Properties	Methods
altitudes (returns a dictionary of [point, segment] pairs) orthocenter circumcenter circumradius circumcircle bisectors (returns a dictionary of [point, segment] pairs) incenter inradius incircle medians (returns a dictionary of [point, segment] pairs) medial	[static] are_similar(t1, t2) is_equilateral(self) is_right(self)

Module Level Functions

Example Usage