# Question:Hoùology matrice

## Question:Hoùology matrice

Maple 2021

what is the homology matrix that plates the ABCE square on the NPCM square
I think it may bi find out with the rotation angle, the vector of translation and the homothety ratio.
restart;
with(geometry):
with(plots):
_EnvHorizontalName = 'x':  _EnvVerticalName = 'y':

point(A, 0, 1):
point(B, 1, 1):
point(C, 1, 0):
point(E, 0, 0):
square(Sq, [A, B, C, E]):
Phi := (1 + sqrt(5))/2:
point(N, (2 - Phi)/(Phi - 1), 1):
line(BE, [B, E]):
MakeSquare(s1, [N, C, 'diagonal']):
point(M, (3 - sqrt(5))/(2*sqrt(5) - 2), (3 - sqrt(5))/(2*sqrt(5) - 2)):
point(P, (1 + sqrt(5))/(2*sqrt(5) - 2), (3*sqrt(5) - 5)/(2*sqrt(5) - 2)):
T:=<simplify(coordinates(midpoint(O1,E,B))-coordinates(midpoint(O2,M,P)))>:
simplify(distance(O1,O2)):
line(MN,[M,N]):eq:=Equation(%,[x,y]):sol:=solve(eq,y):
Ang:=Pi/2-arctan(diff(sol,x)):
r:=simplify(distance(N,M)):
line(MP,[M,P]):eq:=Equation(%,[x,y]):subs(y=0,%):point(Q,solve(%,x),0):
line(PQ,[P,Q]):
homology(Sq1, Sq, C, Ang, 'clockwise', r):

display(draw([A(color = black, symbol = solidcircle, symbolsize = 12),
B(color = black, symbol = solidcircle, symbolsize = 12),
C(color = black, symbol = solidcircle, symbolsize = 12),
E(color = black, symbol = solidcircle, symbolsize = 12),
N(color = black, symbol = solidcircle, symbolsize = 12),
Sq(color = red, filled = true, transparency = 0.9),
BE(color = green),
PQ(color = black),
Sq1(color = black),
s1(color = red, filled = true, transparency = 0.8)]),
textplot([[coordinates(A)[], "A"],
[coordinates(B)[], "B"],
[coordinates(E)[], "E"],
[coordinates(N)[], "N"],
[coordinates(P)[], "P"],
[coordinates(M)[], "M"],
[coordinates(Q)[], "Q"],
[coordinates(C)[], "C"]],
align = [above, right]), view = [-0.6 .. 1.5, 0 .. 1], axes = none);

﻿