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.

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 11:
r := 7:
a := sqrt(R*r):

b := 2:
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [R + 2*b + r, 0]), r]):
ellipse(p, (x - R - b)^2/b^2 + y^2/a^2 = 1):
draw([C1(color = yellow, filled = true), 
C2(color = red, filled = true), p(color = blue, filled = true), 
C1(color = black), C2(color = black), p(color = black)], 
axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained):
alpha := arctan((R - r)/(R + 2*b + r));
long := cos(alpha)*(R + 2*b + r);
evalf(%);
circle(C2, [point(P2, [long, r - R]), r]);
rotation(p1, p, alpha, 'clockwise');
detail(p1);
point(A, 0, -R);
point(B, long, -R);
line(L1, [A, B]);
point(cen, [(143*sqrt(5))/25, -(26*sqrt(5))/25]);
reflection(L2, L1, cen);
detail(L2);
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  L2

draw([C1(color = yellow, filled = true), C2(color = red, filled = true), p1(color = blue, filled = true), C1(color = black), C2(color = black), p1(color = black), L1(color = black)], axes = none, view = [-15 .. 35, -15 .. 15], scaling = constrained);
A Bug in reflection ? Why these error messages. Thank you.

I wonder if there is any way to use ArrayInterpolation with contourplot or similar effect?

N_data.xlsx 

Thank you in advance,

Download test1.mw

I do not know what is the problem with Using ImportMatrix. N_data.xlsx is in the same directory.

Any comment would be appreciated.

Download test1.mw

polysols(diff(u(x), x) = u(x)^2 - 1) produces no results, while it can be verified by direct observation that u(x) = 1 is a polynomial solution.

I can not spawn draw the circles C3 and C4

restart;
with(plots):
with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
R := 7:
point(A, [0, R]):
line(L1, y = sqrt(3)*x + R):
line(L2, y = -sqrt(3)*x + R):
line(L3, y = R/3):
intersection(B, L1, L3):
intersection(C, L2, L3):
detail(C):
triangle(ABC, [A, B, C]):
circle(C1, [point(P1, [0, 0]), R]):
circle(C2, [point(P2, [0, R/3 + (2*R)/9]), (2*R)/9]):
detail(C2):
center(C2), coordinates(center(C2)):
reflection(P3, P2, C):
detail(P3):
reflection(C3, C2, C);
detail(C3):
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  C3
circle(C3, [point(P3*[(28*sqrt(3))/9, 7/9]), (2*R)/9]):
Error, (in geometry:-point) wrong number of arguments
reflection(C4, C2, B);
detail(C4);
Error, (in geometry:-reflection) unable to compute coeff
Error, (in geometry:-detail) unknown object:  C4
circle(C3*[point(P3, [(28*sqrt(3))/9, 7/9]), (2*R)/9]);
Error, (in geometry:-circle) wrong number of arguments

draw([L1(color = blue), 
ABC(color = red, transparency = 0.5, filled = true), 
L2(color = blue), L3(color = blue), 
C1(color = blue, thickness = 3), C1(color = yellow, transparency = 0.8, filled = true), C2(color = blue, filled = true)], 
axes = normal,
 view = [-R .. R, -R .. R], 
scaling = constrained);
Why these error messages. Thank you veru much.

fig([L1(color = blue), L2(color = blue), L3(color = green), C1(color = black), C2(color = black), C3(color = orange), C4(color = orange)]);
point(oo, [0, 0]);
                               oo

rotation(fig1, fig, oo, Pi/2, 'counterclockwise');
Error, (in geometry:-rotation) wrong type of arguments why thos error ? Thank you;
 

What should I do to reduce evaluating time?

Download Negativity_v1.mw

I have the function: f(x)= sqrt(x) for x>=0; f(x)=1/x for x<0 and I would like to plot the function.

How exactly to implement this?

restart;
with(plots): with(geometry):
_EnvHorizontalName := 'x':
_EnvVerticalName := 'y':
a := 7:
point(E, 0, a*sqrt(3)/2):
point(B, -a/2, 0):
point(C, a/2, 0):
point(o, 0, a*sqrt(3)/6):
point(A, 0, a/2):
point(H, 0, 0):
R := (3-sqrt(3))*sqrt(2)*a/12:
point(J, 0, a*sqrt(3)/6 - R):
triangle(Tr1, [E, B, C]):
triangle(Tr2, [A, B, C]):
StretchRotation(E1, E, B, Pi/4, clockwise, sqrt(2)/2);
coordinates(E1);
StretchRotation(E2, E, C, Pi/4, counterclockwise, sqrt(2)/2);
coordinates(E2);
triangle(Tr3, [E, B, E1]);
triangle(Tr4, [E, C, E2]);
triangle(Tr5, [B, C, J]);
circle(cir, [point(P1,[0,a*sqrt(3)/6]), R]):
poly := Matrix([[0, a*sqrt(3)/2], [-7/4 + (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4], [0, a/2], [7/4 - (7*sqrt(3))/4, -7/4 + (7*sqrt(3))/4]], datatype = float);
pol1 := polygonplot(poly, colour = "Magenta", transparency = 0.7, gridlines);
tex := textplot([0.2, a*sqrt(3)/2, "zE"], 'align' = {'above', 'right'});
draw([Tr1(color = cyan),
Tr3(color = green),
tex,
cir(color=blue),
Tr2(color = red),
Tr4(color = grey),
Tr1(color=blue)],'view' = [-5 .. 5, 0 .. 7], 
axes = normal, scaling = constrained,size=[800,800]);
Error, (in geometry:-draw) the option must be of type equation or name
line(L1, [B, o]);
Equation(L1);
line(L1, -(7*x*sqrt(3))/6 + (7*y)/2 - (49*sqrt(3))/12 = 0);
reflection(J1, J, L1);
triangle(Tr6, [B, J1, E]);
line(L2, [C, o]);
Equation(L2);
line(L2, -(7*x*sqrt(3))/6 - (7*y)/2 + (49*sqrt(3))/12 = 0);
reflection(J3, J, L2);
triangle(Tr7, [C, J3, E]);
triangle(T1, [E, J1, A]);
triangle(T2, [E, C, E2]);
triangle(T3, [B, H, J]);
triangle(T4, [C, H, J]);

draw([cir(color = orange, filled = true, transparency = 0.1), pol1, Tr6(color = blue, filled = true, transparency = 0.2), Tr5(color = blue, filled = true, transparency = 0.2), Tr7(color = blue, filled = true, transparency = 0.2), T1(color = green, filled = true, transparency = 0.2), T2(color = green, filled = true, transparency = 0.2), T3(color = green, filled = true, transparency = 0.2), T4(color = green, filled = true, transparency = 0.2)], axes = none, scaling = constrained);
Error, (in geometry:-draw) the option must be of type equation or name
NULL;
NULL;

Why these errors messages ? Thank you.

Download U.m.mw

Hello im an amateur using maple for my hidraulics machines course at engineering school. Does anyone know how to use the degrees package on maple 2021, i called it out by using the short form. with(Degrees): and then try to use sind but it doesnt recognice the command.

Also when using RPMs the units that should be giving me m/s appear as m²/m*s(radious). I know that the software recognice it as angular speed but is there anyway to eliminate the (radious) so i can work with the speed as lineal?

with(geometry):
_EnvHorizontalName := x:
_EnvVerticalName := y:
a := 7:
b := a*(1/2 + 1/6*sqrt(45 - 24*sqrt(3)))^2:
r := b*sqrt(b)/(sqrt(a + b) + sqrt(a)):
point(A, -a, b): point(B, -a, -b):
point(C, a, -c): point(F, a, b):
Sq := square(Sq, [A, B, C, F]):
circle(C1, [point(P1, [r, 0]), r]):
circle(C2, [point(P2, [(1 + sqrt(3))*r, r]), r]):
circle(C3, [point(P3, [(1 + sqrt(3))*r, -r]), r]):
ellipse(E, x^2/a^2 + y^2/b^2 = 1, [x, y]):
solve({Equation(C1), x^2/a^2 + y^2/b^2 = 1}, {x, y}):
point(T, [5.349255162, 2.829908743]):
IsOnCircle(T, C1);
draw([E(color = cyan), C1(color = yellow, filled = true), T(symbol = solidcircle, symbolsize = 20, color = red), Sq, C2(color = red), C3(color = red),Sq(color=blue)], axes = normal, view = [-a .. a, -b .. b], scaling = constrained);
square: (196+(7*(1/2+(1/6)*(45-24*3^(1/2))^(1/2))^2+c)^2)^(1/2)-(196+196*(1/2+(1/6)*(45-24*3^(1/2))^(1/2))^4)^(1/2) = 0
square: (7/2)*(1/2+(1/6)*(45-24*3^(1/2))^(1/2))^2-(1/2)*c = 0
Error, (in geometry:-square) not enough information to define a square
                             false

Error, (in geometry:-draw) cannot determine the vertices for drawing .Why all these errors ? Thank you.

EqBIS := proc(P, U, V)
local a, eq1, M1, t, PU, PV, bissec1;
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;
EqBIS*([4, 5], [11, 7/3], [11, 5]);
why such a procedure gives no result Thabk you.

I have maplesim installed and I get the error "Error, `MapleSim` does not evaluate to a module" when I run A:=MapleSim:-LinkModel(); in a Maple worksheet.

Does anyone know how to solve this error?