## How do I determine the minimum distance required t...

Good day.

I am wrestling a simple network (maze-type) problem and I hope someone can assist.

Given a standard x-y framework with several nodes whose locations are known, I would like to visit each node by starting from the origin, (0,0), and returning to that same point, A. (see attached)

However, I am permitted only to move horizontally and vertically within the maze.

Given that restriction, is there a routine that allows me to visit all locations, B, C, D, and E, such that the rectilinear distance is a minimum?

If there is a solution to this problem, can the distance also be given and order of visits specified?

MaplePrimes_Path.mw

## How to fix a piecewise function that is not behavi...

I have created a simple piecewise function to represent the radius r(x) of a circular cylinder of length 2a and radius b with ellipsoidal end caps of length e << a and e << b to get a smooth transition of r(x) at the two ends for use in slender body theory. The piecewise function does not behave as I had expected, and this is the first time that I have used a piecewise function. What am I doing wrong? The attached (I hope) Maple worksheet shows both my expected behavior and the actual behaviort. Any help will be greatly appreciated. Thanks.

Neill Smith

Piecewise_Cylinder_Geom.mw

## how to draw these 3 lines and then project them on...

how to draw these 3 lines and then project them on the plans Oxy,Oxz,Oyz;
3 given lines a := [3*t-7, -2*t+4, 3*t+4]; b := [m+1, 2*m-9, -m-12];c:={x = -200/29-2*t, y = 114/29+3*t, z = 119/29+4*t}, how to show these lines and the projections on the 3 planes ? Thank you.

## how to use results from "solve"...

I solve a system of equations, and am having difficulty 1) understanding what I"m seeing, 2) using the results.

At (21), I get the solution to the system of equations.  I then want to use substitute a value for xC1 that supports the solution, and plug it into the other variables that are solved in terms of it.  However, I can't figure out how to do this.  I keep getting errors like:

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received {Rsrc = .9640102828*xC1^2+0.2570694087e-2*(140625.*xC1^4-151321.*xC1^2)^(1/2), xC2 = -0.1333333333e-2*(281250.*xC1^3+750.*xC1*(140625.*xC1^4-151321.*xC1^2)^(1/2)+51018750.*xC1^2+136050.*(140625.*xC1^4-151321.*xC1^2)^(1/2)-151321.*xC1)/(375.*xC1^2+(140625.*xC1^4-151321.*xC1^2)^(1/2)), xC1 <= -363.3194071}

please see attached file.

I assume I'm getting 2 solutions.  I'm picking the first one and trying to then solve for the other variables once I pick a value for xC1.

Thank you,

substitution_help.mw