Simple programming techniques / tricks in Mathematica for making graphics for the math book?

Question

(Closed). This question needs to be more focused. It is not currently accepting answers. question from:https://stackoverflow.com/questions/8748294/simple-programming-techniques-tricks-in-mathematica-for-making-graphics-for-th

Answer 1

Here is a simple/basic way to do the first one:

Graphics[{

 (* The dashed circle segment *)
 {
  Dashing[{.04, .01}], 
  Darker[Orange], 
  AbsoluteThickness[2], 
  Circle[{0, 0}, 1, {1, 2 [Pi]}]
 },

 (* The solid circle segment *)
 {
  Orange, 
  AbsoluteThickness[2], 
  Circle[{0, 0}, 1, {0, 1}]
 },

 (* The radial lines and the small circle segment *)
 Line[{{0, 0}, {1, 0}}],
 Line[{{0, 0}, {Cos[1], Sin[1]}}],
 Circle[{0, 0}, .2, {0, 1}],

 (* Various text labels *)
 {
  Text[Style["[Theta]", 24], .3 {Cos[.5], Sin[.5]}], 
  Text[Style["s", 24], 1.1 {Cos[.5], Sin[.5]}], 
  Text[Style["r", 24], {.5, -.1}]
 }
}]

The following is the exact same thing, but wrapped in Manipulate and parameterized on the angle alpha:

Manipulate[
 Graphics[{
  {Dashing[{.04, .01}], Darker[Orange], AbsoluteThickness[2], 
  Circle[{0, 0}, 1, {[Alpha], 2 [Pi]}]},
  {Orange, AbsoluteThickness[2], Circle[{0, 0}, 1, {0, [Alpha]}]},
  Line[{{0, 0}, {1, 0}}],
  Line[{{0, 0}, {Cos[[Alpha]], Sin[[Alpha]]}}],
  Circle[{0, 0}, .2, {0, [Alpha]}],
  {Text[Style["[Theta]", 
  24], .3 {Cos[[Alpha]/2], Sin[[Alpha]/2]}], 
  Text[Style["s", 24], 1.1 {Cos[[Alpha]/2], Sin[[Alpha]/2]}], 
  Text[Style["r", 24], {.5, -.1}]}
 }],
{{[Alpha], 1}, 0, 2 [Pi]}]

If you move the slider, the content will change accordingly: