How to create formatted math formulas that contain formatted strings?

Question

I would like to create some formulas with short sentences as the variables. A minimal example follows.

$$\text{Area[Rectangle]} \times \frac{\text{Points in Circle}}{\text{Total Number of Points}}$$

In Mathematica

"Area[Rectangle]" ( "Points in Circle")/("Total Number of Points")

returns

And

Inactivate["Area[Rectangle]" ( "Points in Circle")/("Total Number of Points"), Times]

Comes out worse

How do I go about creating a general function that I can pass in the formula of these string variables and get something like what is rendered above? Preferably without unprotecting any built-ins or loading 3rd-party packages.

Answer 1

I think that for the notebook/CDF applications the use of the cells, such as DisplayFormula or DisplayFormulaNumbered are best of all. I only would like to turn your attention to the point that these cells look awfully in the default notebook, but quite good if you use the JournalArticle StyleSheet. Alternatively you may create your own StyleSheet with the desired format of the formulae.

Another story is the presentation. Here you need to show the formulas large and, eventually, spectacular. Below I give two codes for functions helping to represent formulas in a presentation.

The function Ac dynamically accentuates the expression in question. The expression wrapped by the Ac changes its color from black to a desired one and in addition blinks few times. All this is upon clicking. The function Pl simply represents the expression with a desired size and color.

Ac[expr_, color_, size_] :=
  DynamicModule[{c1 = 0},
                  EventHandler[     
                   Dynamic[ 
                                        If[c1 == 0, 

      Style[expr, Black, Plain, size, Italic] // ExpressionCell,

      Dynamic@If[Clock[1, 0.7, 2] < .5,

         Style[expr, Gray, Plain, size, Italic] // ExpressionCell,

         Style[expr, color, Bold, size, Italic]] // ExpressionCell
                                             ]
                                  ],                                  \

    {"MouseDown" :> (c1 = c1 /. {0 -> 1, 1 -> 0})}
                                          ]
                    ];

and

Pl[expr_, color_, size_] := 
 ExpressionCell[Style[expr, color, Plain, size, Italic]]

Now to make it comfortable I would first define other functions in which I determine the desired colors and sizes:

acc1[expr_] := Ac[expr, Blue, 28]
acc2[expr_] := Ac[expr, Red, 28]
pl[expr_] := Pl[expr, Black, 28]

Done. Now it is easy to represent any formula. Here is yours, for example

Row[{"Area[Rectangle]" // acc1, "\[Times]" // pl, 
  "\!\(\*FractionBox[\(Points\\\ in\\\ Circle\), \(Total\\\ Number\\\ \
of\\\ Points\)]\)" // acc2}]

on your screen it will look as follows:

The result is

After you click on the word "Area" you get this:

After you click on "Points in Circle" you get this:

If you click on the "Area" again you get this:

After you once more click on "Points..." you return to the initial black image.

There are few other ways of doing all this. The function Acalso provides some blinking. In the case of a dislike, one can do the accentuation, but without blinking, which is in a way easier.

I hope it helps. Have fun!