def circle_plot(self):
pts = []
pi = RR.pi()
for angle in self.angles:
angle = RR(angle) * pi
c = angle.cos()
s = angle.sin()
if abs(s) < 0.00000001:
pts.append((c, s))
else:
pts.extend([(c, s), (c, -s)])
P = points(pts, size=100) + circle((0, 0), 1, color='black')
P.axes(False)
P.set_aspect_ratio(1)
return encode_plot(P)
def circle_plot(self):
pts = []
pi = RR.pi()
for angle in self.angles:
angle = RR(angle)*pi
c = angle.cos()
s = angle.sin()
if abs(s) < 0.00000001:
pts.append((c,s))
else:
pts.extend([(c,s),(c,-s)])
P = points(pts,size=100) + circle((0,0),1,color='black')
P.axes(False)
P.set_aspect_ratio(1)
return encode_plot(P)
def circle_plot(self):
pts = []
pi = RR.pi()
for angle in self.angles:
angle = RR(angle) * pi
c = angle.cos()
s = angle.sin()
if abs(s) < 0.00000001:
pts.append((c, s))
else:
pts.extend([(c, s), (c, -s)])
P = circle((0, 0), 1, color="black", thickness=2.5)
P[0].set_zorder(-1)
P += points(pts, size=300, rgbcolor="darkblue")
P.axes(False)
P.set_aspect_ratio(1)
return encode_plot(P, pad=0, pad_inches=None, transparent=True, axes_pad=0.04)
def regular_polygon(self, n, base_ring=QQ):
"""
Return a regular polygon with `n` vertices. Over the rational
field the vertices may not be exact.
INPUT:
- ``n`` -- a positive integer, the number of vertices.
- ``base_ring`` -- a ring in which the coordinates will lie.
EXAMPLES::
sage: octagon = polytopes.regular_polygon(8)
sage: len(octagon.vertices())
8
sage: polytopes.regular_polygon(3).vertices()
(A vertex at (-125283617/144665060, -500399958596723/1000799917193445),
A vertex at (0, 1),
A vertex at (94875313/109552575, -1000799917193444/2001599834386889))
sage: polytopes.regular_polygon(3, base_ring=RealField(100)).vertices()
(A vertex at (0.00000000000000000000000000000, 1.0000000000000000000000000000),
A vertex at (0.86602540378443864676372317075, -0.50000000000000000000000000000),
A vertex at (-0.86602540378443864676372317076, -0.50000000000000000000000000000))
sage: polytopes.regular_polygon(3, base_ring=RealField(10)).vertices()
(A vertex at (0.00, 1.0),
A vertex at (0.87, -0.50),
A vertex at (-0.86, -0.50))
"""
try:
omega = 2*base_ring.pi()/n
except AttributeError:
omega = 2*RR.pi()/n
verts = []
for i in range(n):
t = omega*i
verts.append([base_ring(t.sin()), base_ring(t.cos())])
return Polyhedron(vertices=verts, base_ring=base_ring)
def regular_polygon(self, n, base_ring=QQ):
"""
Return a regular polygon with `n` vertices. Over the rational
field the vertices may not be exact.
INPUT:
- ``n`` -- a positive integer, the number of vertices.
- ``base_ring`` -- a ring in which the coordinates will lie.
EXAMPLES::
sage: octagon = polytopes.regular_polygon(8)
sage: len(octagon.vertices())
8
sage: polytopes.regular_polygon(3).vertices()
(A vertex at (-125283617/144665060, -500399958596723/1000799917193445),
A vertex at (0, 1),
A vertex at (94875313/109552575, -1000799917193444/2001599834386889))
sage: polytopes.regular_polygon(3, base_ring=RealField(100)).vertices()
(A vertex at (0.00000000000000000000000000000, 1.0000000000000000000000000000),
A vertex at (0.86602540378443864676372317075, -0.50000000000000000000000000000),
A vertex at (-0.86602540378443864676372317076, -0.50000000000000000000000000000))
sage: polytopes.regular_polygon(3, base_ring=RealField(10)).vertices()
(A vertex at (0.00, 1.0),
A vertex at (0.87, -0.50),
A vertex at (-0.86, -0.50))
"""
try:
omega = 2 * base_ring.pi() / n
except AttributeError:
omega = 2 * RR.pi() / n
verts = []
for i in range(n):
t = omega * i
verts.append([base_ring(t.sin()), base_ring(t.cos())])
return Polyhedron(vertices=verts, base_ring=base_ring)