Kitonum

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12 years, 68 days

MaplePrimes Activity


These are replies submitted by Kitonum

@janhardo I think it is useful to know the physical meaning of this curvilinear integral: if  2*x+y^2  is the linear density at the point  (x,y) of the segment, then the value of the integral is the mass of this segment. 

@Preben Alsholm  Thank you for the improvement.

@ActiveUser  See the corrected answer.

You have already built it. cos(Pi/4)  is a constant. And what is the question?

@Scot Gould You're right. Using  add  instead of  sum  avoids many problems. 

@sunit  You are not required to apply the command to every equation. Build a system and apply the command to this system as in the example:

convert({1.0*x+0.3*y=1,2*x-1.0*y=3}, rational);

                              

@nguyenhuyenag 

This is also written in the help.

Solution for your example:

restart;
bl:=sqrt(2)-1>0:
evalb(evalf(bl));

                               true

@Carl Love  Thanks. The  seq  is my favorite command in Maple. Owners of older versions of Maple (< Maple 13 or 14) , who do not know about  zip ,  can simply write this:

A:=[1,2,3]:
B:=[7,8,9]:
[seq(f(A[i],B[i]),i=1..nops(A))];


The  seq  command can completely replace map, zip, and ~  (which of course make the code a little shorter).

Here's another animation in which the ellipse of a given shape (defined by the parameter  k ) rotates around a given triangle:


 

restart;
Eq:=(x-x0)^2/a^2+(y-y0)^2/b^2=1:
b:=k*a: k:=2/3:
Eq1:=subs([x=x*cos(alpha)+y*sin(alpha),y=-x*sin(alpha)+y*cos(alpha)],Eq);
T:=[[0,0],[2,3],[6,0]]:
R:=[seq([x,y]=~t,t=T)];
Sys:=map(p->eval(Eq1,p),R);
Sol:=solve(Sys,{a,x0,y0}, explicit)[1];
eval(Sol,alpha=Pi/4);
F:=t->plots:-implicitplot(eval(Eq1,[eval(Sol,alpha=t)[],alpha=t]), x=-3..10, y=-10..10, gridrefine=3);
plots:-animate(F,[t], t=0..Pi, frames=90, background=plots:-display(plottools:-polygon([[0,0],[6,0],[2,3]],color="LightBlue", thickness=2)), scaling=constrained);

(x*cos(alpha)+y*sin(alpha)-x0)^2/a^2+(9/4)*(-x*sin(alpha)+y*cos(alpha)-y0)^2/a^2 = 1

 

[[x = 0, y = 0], [x = 2, y = 3], [x = 6, y = 0]]

 

[x0^2/a^2+(9/4)*y0^2/a^2 = 1, (2*cos(alpha)+3*sin(alpha)-x0)^2/a^2+(9/4)*(-2*sin(alpha)+3*cos(alpha)-y0)^2/a^2 = 1, (6*cos(alpha)-x0)^2/a^2+(9/4)*(-6*sin(alpha)-y0)^2/a^2 = 1]

 

{a = (1/72)*(31625*sin(alpha)^6-25500*cos(alpha)*sin(alpha)^5-11850*sin(alpha)^4-5700*cos(alpha)*sin(alpha)^3+40605*sin(alpha)^2+11760*cos(alpha)*sin(alpha)+56260)^(1/2), x0 = (5/4)*sin(alpha)^2*cos(alpha)+3*cos(alpha)-(85/24)*sin(alpha)^3+(49/24)*sin(alpha), y0 = -(85/54)*sin(alpha)^2*cos(alpha)+(49/54)*cos(alpha)-(5/9)*sin(alpha)^3-(22/9)*sin(alpha)}

 

{a = (1/576)*630565^(1/2)*8^(1/2), x0 = (187/96)*2^(1/2), y0 = -(281/216)*2^(1/2)}

 

proc (t) options operator, arrow; plots:-implicitplot(eval(Eq1, [(eval(Sol, alpha = t))[], alpha = t]), x = -3 .. 10, y = -10 .. 10, gridrefine = 3) end proc

 

 

 


Edit.

Download ells2.mw

@one man  There are infinitely many such ellipses, and their family also depends on two parameters. The simple animation below is made for ellipses with one axis parallel to one of the sides of the triangle:


 

restart;
Sol:=solve({x0^2/a^2+y0^2/b^2=1,(2-x0)^2/a^2+(3-y0)^2/b^2=1,(6-x0)^2/a^2+y0^2/b^2=1}, explicit);
sol:=simplify(Sol[1]);

{a = (1/3)*6^(1/2)*((15+(64*b^2+81)^(1/2))/(4*b^2-9))^(1/2)*b, b = b, x0 = 3, y0 = ((3/2)*(15+(64*b^2+81)^(1/2))/(4*b^2-9)-2)*(4*b^2-9)/(15+(64*b^2+81)^(1/2))}, {a = -(1/3)*6^(1/2)*((15+(64*b^2+81)^(1/2))/(4*b^2-9))^(1/2)*b, b = b, x0 = 3, y0 = ((3/2)*(15+(64*b^2+81)^(1/2))/(4*b^2-9)-2)*(4*b^2-9)/(15+(64*b^2+81)^(1/2))}, {a = (1/3)*(-6*(-15+(64*b^2+81)^(1/2))/(4*b^2-9))^(1/2)*b, b = b, x0 = 3, y0 = -(-(3/2)*(-15+(64*b^2+81)^(1/2))/(4*b^2-9)-2)*(4*b^2-9)/(-15+(64*b^2+81)^(1/2))}, {a = -(1/3)*(-6*(-15+(64*b^2+81)^(1/2))/(4*b^2-9))^(1/2)*b, b = b, x0 = 3, y0 = -(-(3/2)*(-15+(64*b^2+81)^(1/2))/(4*b^2-9)-2)*(4*b^2-9)/(-15+(64*b^2+81)^(1/2))}

 

{a = (1/3)*6^(1/2)*((15+(64*b^2+81)^(1/2))/(4*b^2-9))^(1/2)*b, b = b, x0 = 3, y0 = (-16*b^2+3*(64*b^2+81)^(1/2)+81)/(30+2*(64*b^2+81)^(1/2))}

(1)

plots:-animate(plots:-implicitplot,[eval((x-3)^2/a^2+(y-y0)^2/b^2=1,sol), x=-10..15,y=-10..10, color=red], b=1.55..4, frames=60, background=plots:-display(plottools:-polygon([[0,0],[6,0],[2,3]],color="LightBlue", thickness=2)), scaling=constrained, size=[900,500], axes=none);

 

 


 

Download ells.mw

@Liiiiz 

restart; with(plots): 
A := inequal({am2 < 0.34+3.6*dt}, dt = 0 .. 0.1, am2 = 0 .. 0.7, color = "SkyBlue", numpoints = 8000): 
B := textplot([seq(seq([x, y, "+"], y = 0.03 .. 0.33+3.6*x, 0.03), x = 0.004 .. 0.096, 0.0046)], font = [times, bold, 14]): 
display(A, B);

                

@nm  This is not strange and is the usual way in different situations, for example

restart;
solve(sin(x)=1/2, allsolutions);

                         

@vv  Great idea!  Vote up.

@anthonyfl  I have been working with Maple for about 18 years.

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