「sympyで、座標面上の三角形の内角の計算」を調べた。

パイソニスタの方へ
・(1)のPolygonで、dict?を使わずにできますか？　return1文だけです。

普通は？余弦定理、内積だろ。私は勉強中です。

(1) Polygonのanglesで

The internal angle at each vertex.
https://docs.sympy.org/latest/modules/geometry/polygons.html#sympy.geometry.polygon.Polygon.angles

# (1) Polygonのanglesで
from sympy import *
var('AB',real=True,poitive=True)
def myTriangleRad(myT):
    P1=myT.args[0]
    P2=myT.args[1]
    P3=myT.args[2]
    myPol=Polygon(P1,P2,P3)
    return myPol.angles[P1],myPol.angles[P2],myPol.angles[P3]
AB=10
tr=Triangle(Point(0,AB),Point(AB,0),Point(AB,AB))
print("#",myTriangleRad(tr)[0],deg(myTriangleRad(tr)[0]))
print("#",myTriangleRad(tr)[1],deg(myTriangleRad(tr)[1]))
print("#",myTriangleRad(tr)[2],deg(myTriangleRad(tr)[2]))
# pi/4 45
# pi/4 45
# pi/2 90
tr=Triangle(Point(0,AB),Point(AB,AB),Point(AB,0))
print("#",myTriangleRad(tr)[0],deg(myTriangleRad(tr)[0]))
print("#",myTriangleRad(tr)[1],deg(myTriangleRad(tr)[1]))
print("#",myTriangleRad(tr)[2],deg(myTriangleRad(tr)[2]))
# pi/4 45
# pi/2 90
# pi/4 45

(2) Lineのangle_betweenで

Return the non-reflex angle formed by rays emanating from the origin with directions the same as the direction vectors of the linear entities.
https://docs.sympy.org/latest/modules/geometry/lines.html#sympy.geometry.line.LinearEntity.angle_between

# (2) Lineのangle_betweenで
from sympy import *
var('AB',real=True,poitive=True)
def myTriangleRad(myT):
    return Line(myT.args[0],myT.args[1]).angle_between(Line(myT.args[0],myT.args[2])), \
           Line(myT.args[1],myT.args[2]).angle_between(Line(myT.args[1],myT.args[0])), \
           Line(myT.args[2],myT.args[0]).angle_between(Line(myT.args[2],myT.args[1]))
AB=10
tr=Triangle(Point(0,AB),Point(AB,0),Point(AB,AB))
print("#",myTriangleRad(tr)[0],deg(myTriangleRad(tr)[0]))
print("#",myTriangleRad(tr)[1],deg(myTriangleRad(tr)[1]))
print("#",myTriangleRad(tr)[2],deg(myTriangleRad(tr)[2]))
# pi/4 45
# pi/4 45
# pi/2 90
tr=Triangle(Point(0,AB),Point(AB,AB),Point(AB,0))
print("#",myTriangleRad(tr)[0],deg(myTriangleRad(tr)[0]))
print("#",myTriangleRad(tr)[1],deg(myTriangleRad(tr)[1]))
print("#",myTriangleRad(tr)[2],deg(myTriangleRad(tr)[2]))
# pi/4 45
# pi/2 90
# pi/4 45

(3) 余弦定理で

(勉強中)

(4) 内積で

(勉強中)

作図

(省略)