L’éventail de la Geisha

restart:with(plots):with(geometry):

NULL;

_EnvHorizontalName := 'x':

_EnvVerticalName := 'y':

NULL;

EqBIS := proc(P, U, V)

local a, eq1, M1, t, PU, PV, bissec1;

description "P est le sommet de l'angle dont on chercche la bissectrice" ;

a := (P - U)/LinearAlgebra:-Norm(P - U, 2) + (P - V)/LinearAlgebra:-Norm(P - V, 2);

M1 := P + a*t; eq1 := op(eliminate({x = M1[1], y = M1[2]}, t));

RETURN(op(eq1[2])); end proc:

with(plottools);

with(plots);

r1 := 1/2;

r2 := r1/2;

R := r1*(21 - 12*sqrt(3));

21 (1/2)

R := -- - 6 3

2

a := arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6);

b := arc([0, 0], r1, Pi/6 .. (5*Pi)/6);

with(geometry);

eq := EqBIS(<sqrt(3)/2, 1/2>, <0, 0>, <0, 1/2>);

line(bis, eq);

(1/2)

eq := 2 3 y - 2 x + 4 y - 2

bis

OpT := 2*sqrt(r1*R);

line(lv, x = OpT);

intersection(Omega, bis, lv);

coordinates(Omega);

evalf(%);

(1/2)

OpT := 2 3 - 3

lv

Omega

[ / (1/2) \]

[ (1/2) 2 \3 - 1/]

[2 3 - 3, --------------]

[ (1/2) ]

[ 2 + 3 ]

[0.464101616, 0.3923048456]

retarrt;

with(plots);

with(plottools);

[cos((5*Pi)/6), sin((5*Pi)/6)];

[ 1 (1/2) 1]

[- - 3 , -]

[ 2 2]

a := arc([0, 0], 2*r1, Pi/6 .. (5*Pi)/6);

b := arc([0, 0], r1, Pi/6 .. (5*Pi)/6);

NULL;

A:=[cos(Pi/6), sin(Pi/6)];

B:=[cos(5*Pi/6), sin(5*Pi/6)];

Oo:=[0,0];

Op:=[0,1/2];

poly:=[A,B,Oo];

R := r1*(21 - 12*sqrt(3))

[1 (1/2) 1]

A := [- 3 , -]

[2 2]

[ 1 (1/2) 1]

B := [- - 3 , -]

[ 2 2]

Oo := [0, 0]

[ 1]

Op := [0, -]

[ 2]

[[1 (1/2) 1] [ 1 (1/2) 1] ]

poly := [[- 3 , -], [- - 3 , -], [0, 0]]

[[2 2] [ 2 2] ]

21 (1/2)

R := -- - 6 3

2

Omega := [2*sqrt(3) - 3, 2*(sqrt(3) - 1)/(2 + sqrt(3))];

Omega1 := [3 - 2*sqrt(3), 2*(sqrt(3) - 1)/(2 + sqrt(3))];

[ / (1/2) \]

[ (1/2) 2 \3 - 1/]

Omega := [2 3 - 3, --------------]

[ (1/2) ]

[ 2 + 3 ]

[ / (1/2) \]

[ (1/2) 2 \3 - 1/]

Omega1 := [-2 3 + 3, --------------]

[ (1/2) ]

[ 2 + 3 ]

r3 := 3/16;

EF := sqrt(r3);

3

r3 := --

16

1 (1/2)

EF := - 3

4

r := (150 - 72*sqrt(3))/193*1/2;

alpha := -5/3*r + 1/2*1/2;

p := sqrt(3)/3*1/2 - sqrt(3)/18*r;

75 36 (1/2)

r := --- - --- 3

193 193

307 60 (1/2)

alpha := - --- + --- 3

772 193

1 (1/2) 1 (1/2) /75 36 (1/2)\

p := - 3 - -- 3 |--- - --- 3 |

6 18 \193 193 /

p2 := textplot([[A[], "A"], [B[], "B"], [Oo[], "O"]], align = ["above", "right"]);

display(a, b, p2, polygonplot(poly, thickness = 3, color = blue, transparency = 0.3), circle(Omega, R, color = blue, filled = true), circle(Omega1, R, color = blue, filled = true), circle([0, 3/4], 1/4, color = yellow, filled = true), circle([EF, 1/2 + r3], r3, color = green, filled = true), circle([-EF, 1/2 + r3], r3, color = green, thickness = 5), circle([p, 3/4 + alpha], r, color = red, thickness = 5), circle([-p, 3/4 + alpha], r, color = red, thickness = 5), axes = none, scaling = constrained, size = [500, 500]);

how to put color inside circles ? Thabk you.