## 375 Reputation

6 years, 199 days

## Equation of an ellpise after rotation...

Maple 2021

restart:local D:
with(plots):
with(plottools):

a := 7;
b := a/2;
NULL;

r := b/2;
c := 2*sqrt(10)*r;
A := [c/2, c/2];
B := [c/2, -1/2*c];
C := [-c/2, (-c)/2];
D := [-c/2, c/2];
f := (x, y) -> x^2/a^2 + y^2/b^2 = 1;
Ell1 := rotate(implicitplot(f(x, y), x = -9 .. 9, y = -6 .. 6, color = blue), Pi/4);

g := (x, y) -> x^2/b^2 + y^2/a^2 = 1;
Ell2 := rotate(implicitplot(g(x, y), x = -10 .. 10, y = -10 .. 10, color = blue), Pi/4);

quadri := plot([A, B, C, D, A], x = -6 .. 6, y = -6 .. 6, filled = true, color = red, transparency = 0.7);
Cir1 := disk([c/2 - r, -c/2 + r], r, color = blue);
Cir2 := disk([-c/2 + r, -c/2 + r], r, color = blue);
Cir3 := disk([-c/2 + r, c/2 - r], r, color = blue);
Cir4 := disk([c/2 - r, c/2 - r], r, color = blue);
display([quadri, Ell1, Ell2, Cir1, Cir2, Cir3, Cir4], scaling = constrained, axes = normal);
how to find the equations of ellipses in order to fit them to discs and whiten the interior of ellipses ? Thank you.

## Difficultu with pointplot...

Maple 2021

restart;
with(LinearAlgebra);
with(plots);
NULL;

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;
NULL;
A := <4, 8>;
B := <4, 2>;
C := <1, 4>;
EqBIS(A, B, C);
NULL;

Cen := proc(M, N, R) local eq1, eq2, sol; eq1 := EqBIS(M, N, R) = 0; eq2 := EqBIS(N, M, R) = 0; sol := simplify(solve({eq1, eq2}, {x, y})); RETURN([subs(sol, x), subs(sol, y)]); end proc;
Cen(A,B,C):

CircleParm := t -> [(-t^2 + 1)/(t^2 + 1), 2*t/(t^2 + 1)];
P1 := Transpose(convert(CircleParm(1/4), Vector));

P2 := Transpose(convert(CircleParm(5), Vector));
P3 := Transpose(convert(CircleParm(-1/10), Vector));
P4 := Transpose(convert(CircleParm(-3/2), Vector));

C1 := Transpose(convert(Cen(P1, P2, P3), Vector));
Pts := [P1, P2, P3, P4, C1];

display(implicitplot([x^2 + y^2 - 1], x = -2 .. 2, y = -4 .. 2, colour = [blue], scaling = constrained), pointplot(Pts, symbolsize = 16));
Error, (in plots:-pointplot) incorrect number of coordinates in points data
NULL;Why this error. Thank you.

## resolution of the equation of degree 3...

Maple 2021

restart:
eq := a*x^3 + b*x^2 + c*x + d;
s := x1 + x2 + x3 = -b/a;
sp := x1*x2 + x1*x3 + x2*x3 = c/a;
p := x1*x2*x3 = -d/a;
sol:=solve({eq, p, s, sp}, {x1, x2, x3},explicit);
a := 1;
b := -5;
c := 6;
d := -1;
sol;

why is not successfull ?   Thank you.

## How to built a pentagon...

Maple 2021

restart;
with(plots);
with(plottools);
Vdot := proc (U, V)local i: add(U[i]*V[i], i = 1 .. 2) end proc:
dist := proc (M, N) sqrt(Vdot(expand(M-N), expand(M-N))) end proc:
ngon := n -> local i; [seq([cos(2*Pi*i/n), sin(2*Pi*i/n)], i = 1 .. n)]:
theta := (2*Pi)/5;
poly := [seq([cos(k*theta), sin(k*theta)], k = 1 .. 5), datatype = float];
Ii := [0, 1/2]:
H := [-1/4, 0]:
r := dist(Ii, H):
theta := (2*Pi)/5:
p1 := pointplot([seq([cos(k*theta), sin(k*theta)], k = 0 .. 5)], symbol = solidcircle, color = red, symbolsize = 10):
p2 := textplot([seq([cos(k*theta), sin(k*theta), cat("M", k)], k = 0 .. 4)], align = ["above", "right"]):
cir1 := circle([0, 0], 1/2, color = green,dashdot:):
cir2 := circle([-1/4, 0], r, color = black):
cir3:=circle([0,0],1,color=red):
display([p1, p2, cir1, cir2, cir3,polygonplot(poly, thickness = 5, color = blue, transparency = 0.95)], axes = normal);
Why this error , Thank you.

## Difficulty with concatenation and indexi...

Maple 2021

Why this error message ?
with(geometry);
vartheta := (2*Pi)/17;
x || k := cos(k*theta);
y || k := sin(k*theta);
xk := cos(k theta): yk := sin(k theta)
.M||k:=(point,x||k,y||k);
with(plots):
Points := pointplot([seq(M || k, k = 1 .. 16)], symbol = solidcircle, color = red, symbolsize = 10):
Error, (in plots:-pointplot) cannot convert data to an Array of datatype float[8]; Thank you for your answer..

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