@acer 

Thanks acer, I am going to figure out what I can do with this.
I'm not  used to Plot Component but I think it's an option I can get by with

@Stretto 

A new version of my first file
Animated_path_along_a_tree_V2.mw

@tomleslie 

`Sorry for my mistaje.

PS: I like the way you did it with geom3d

@vv @tomleslie

S... you are right

thousand apologies to  @yangtheary ​​​​​​​

 @Stretto

A variant of my last procedure where vertices and edges are highlighted and whose color is made persistent or not
Variant_1.mw

@one man 

Thanks.

For the first plot:  the deconstruction of the form not the opposite of its construction.
It seems like a bug in animate for if you advance frame by frame (use the cursor in the animate panel) the phenomenom doesn't occur.
Just like  animate wouldn't have time to display the complete surface when the frames follow one another.

Look at the begining of the deconstruction: the cross section has a closed eight shape while it is an open shape at the end of the construction.

@Mac Dude 

Right, see my reply to @gkokovidis
I didn't read the question carefully: I read that Carrie had invested $4000 at the age of 25 and waited 30 years to get it back.
I have edited my answer.

Also, as I told the OP, I am not familiar with English financial terms, like you I guess there is a  procedure in the Finance package that does the job, but it's hard to put the finger on it

@MKAP 

Two types of plots:

• u versus t for a given x
• u versus x for a given t

aaaa.mw

I don't think that 3D plots are readable, but tiy can do them by yourself if you want

This serie doesn't converge for any values of lambda and t.
What are the conditions toy put on them?
Where does x come from un U(x,t)?

@vv 

Thanks, I understand better the meaning of "false" now

@tomleslie 

Hi, I don't understand where the problem is.
Here is the original file loaded and executed in Maple 2015 (only a modification concerning an ambiguity between epsilon and  varepsilon in eq2 and eq3)

I have no spurious zeroes at all ???
Fuly_bonded_updated_2015.mw

@JAMET

I keep thinking that geom3d is the easiest way to handle this kind of problem in general situations (easiest in the sense that it requires no specific mathematical knowledge [a lazy person's opinion], even if a more concise way, look @vv, can bee proposed).

Here is a procedure which treats:

• intersecting planes
  • returns the intersection of their intersection with the line in case they are not the same
• prallel unconfounded planes
• confounded planes

Download Point_Line_Plane.mw

@vv 

Just a remark about your procedure EQSYS 

• it returns an error when the two planes are parallel and unconfounded
• it responds "false" if the planes are confounded and the line belongs to each of them
  (assuming that the intersection of two confounded planes is these same planes and that each line in these latter can thus be considered as a particular intersection among many; thus "true" seems to be a better answer, even if geom3d syays that the planes do not intersect ... maybe a definition of the intersection of two planes?)
   

sys1 :={16*x-2*y-11*z=0, 14*x-y-10*z=3}:
sys1a:={16*x-2*y-11*z=0, 32*x-4*y-22*z=0}: #confounded planes
sys1b:={16*x-2*y-11*z=0, 32*x-4*y-22*z=1}: #parallel uncounfounded planes 

sys2:={(x-2)/3=(y-5)/2, (y-5)/2=(z-2)/4}:

EQSYS(sys1 , sys2);  # answer is true
EQSYS(sys1a, sys2);  # answer is false but the line is in the plane
EQSYS(sys1b, sys2);  # error

In cases sys1a and sys1b geom3d would respond
 

plane(P1, ...., [x,y,z]);
plane(P2, ...., [x,y,z]);
line(L1, [P1,P2]);


P1 = sys1a --> intersection: the two planes P1 and P2 are the same
               Error, (in geom3d:-line) the two given planes are parallel

P2 = sys1b --> intersection: the two planes P1 and P2 are parallel
               intersection: the given objects do not intersect

@JAMET 

Of course...
But in a general situation you must distinguish several cases for the two planes (which may intersect or not):

• Let a*x+b*y+c*z+d the equation of a plane and a'*x+b'*y+cC'*z+d' the equation of the second one
• if a'/a=b'/b=c'/c=d'/d then P and P' are identical
• if a'/aA=b'/b=c'/c then Pand P' are parallel
• if at least one of the three equalities a'/a=b'/b, b'/b=c'/c, a'/a=c'/c  is not true then P and P' intersect along a line D
  In this case the elementary way to obtain the solution is:
  • to consider that one of the unknown (x or y or z) is a "parameter" t (for instance x=t) and solve a system of two equations in the two remaining unknowns.
  • to solve a system of two equations in the two remaining unknowns, for instance 
    solve({a*tx+b*y+c*z+d=0,  a'*t+b'*y+cC'*z+d'}, {y, z})

For your case this gives (for instance)
 

restart
e1 := 16*s-2*y-11*z:
e2 := 14*s-y-10*z-3:

# Set x as a parameter "s"
E0 := [x=s, solve({e1, e2}, {y, z})[]]
               [           2     11      4     2]
               [x = s, y = - s + --, z = - s - -]
               [           3     3       3     3]

# verify that this line is the one geom3d finds
with(geom3d):
plane(P1, 16*x-2*y-11*z, [x,y,z]):
plane(P2, 14*x-y-10*z-3, [x,y,z]):
line(L1, [P1,P2]):
E1 := [x, y, z] =~ Equation(L1,'t');
              [    1                             ]
              [x = - + 9 t, y = 4 + 6 t, z = 12 t]
              [    2                             ]

# as the parameterization can be different, express s as a finction of t
# and use this to re-parameterize E0 in terms of E1 to verify that E0 and 
# E1 are indeed identical

solve(rhs(E0[1])=rhs(E1[1]), s);
eval(E0, s=%);
                            1      
                            - + 9 t
                            2      
              [    1                             ]
              [x = - + 9 t, y = 4 + 6 t, z = 12 t]
              [    2                             ]

So to answer your question "Is it possible showing without geom3d ?", just do 

E0 := [x=s, solve({e1, e2}, {y, z})[]]

And now to verify if your two lines are the same :

X := s:
Y := solve((y-5)/2=(s-2)/3, y):
Z := solve((z-2)/4=(s-2)/3, z):
[x, y, z] =~ [X, Y, Z]

You might think it's shorter than using geom3d, but for general planes this doesn't work (look at the different situations in the beginning of this reply).
Why did I use geom3d? Just because I didn't know if your two planes where confounded, parallel or secant.
 

PS: I EDITED MY PREVIOUS REPLY
      It contained an error