## 15202 Reputation

12 years, 70 days

## Physical meaning...

@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.

## Thanks...

@Preben Alsholm  Thank you for the improvement.

## ?...

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

## Re...

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

## Apply the command to the system...

@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);

## Re...

This is also written in the help.

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

true

## seq...

@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).

## Another animation...

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);
 >

Edit.

## Ellipses circumscribed around a triangle...

@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]);
 (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);
 >

## Re...

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);

## Usual way...

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

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

## Nice...

@vv  Great idea!  Vote up.

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