The downloaded worksheet below displays 3 points on the unit sphere which define a solid angle with a triangular face. The sides of the solid angle's are red arcs on the surface of the sphere and red radii which outline the planar sides within the sphere.

Three questions:

1. Is there a way to make the surfaces of the solid triangle more apparent by filling them with color?

2. Is there a way to calculate the area of the face on the surface of the sphere?

3. Is there a way to calculate the volume of the solid triangle?

Download Mechanics;_irregular_solid_angle.mw

The following commands show that I have an existing archive containing one procedure.

Why do I receive the error message when I try to save a second procedure to the same archive. The procedure I am trying to save has been executed within the same worksheet where I issue the savelib command.

> LibraryTools[ShowContents]("C:\\Program Files\\Maple 15\\Earl.mla");

LibraryTools[WriteMode]("C:\\Program Files\\Maple 15\\Earl.mla");

savelibname := "C:\\Program Files\\Maple 15\\Earl.mla";

savelib('CreateCircleVector');

[["RotateDisplay.m", [2015, 10, 1, 16, 3, 22], 41984, 655]]
[["C:\Program Files\Maple 15\Earl.mla", "WRITABLE"]]
"C:\Program Files\Maple 15\Earl.mla"

Error, cannot lock repository, C:\Program Files\Maple 15\Earl.mla

Shading is not valid as an option in the command defining a plottools object e.g. a parallelepiped, and yet shading can be selected in the actual display of the object. Is there a way to code for shading when creating the object?

%piecewise(``, x+y-2*z = 1, ``, 2*x+y-3*z = 5, ``, -x+y+z = 1); What does % here do?

I can find no help page to explain the functionality of the percent sign in this command and removing it produces an error. Please explain this.

A procedure can be made available in many worksheets by copying its original commands to each such worksheet. Is there a better way to include and invoke such a procedure in multiple worksheets?