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LETTERS

Random Triangle

Congratulations and many thanks for the excellent Mathematica Journal, with the new Trott's Corner! Trott's article about random triangle (RT) in square (v7i2) is a real gem! Amazed and inspired by his cunning ability in Mathematica,  I've spent two weeks looking for a more simple solution and found one.  But was the figure 11/144 known before or is Trott the first who found it?  This is not clear from his paper. Is it possible to find the probability function for the square of RT (not only mean value)?  Is it possible to solve the same problem in a circle, a triangle, or rectangle? These (and other) questions clearly demonstrate how seminal both Trott's paper and its author are. 

One request-suggestion. As millions of math lovers all over the world can't subscribe to TMJ,  is it possible to put in the electronic edition more information (abstracts or full papers, at least for previous issues)?

Dr. Zakir F. Seidov
PhysDept
Ben-Gurion University
Ber-Sheva, Israel


The editors reply: 
We are preparing all back issues for access online. As for abstracts of current articles,  these will be available to non-subscribers even when the full article is not. 

Columnist Michael Trott (mtrott@wolfram.com) replies:
Crofton first calculated the value 11/144 around 1890. The distribution function of the area of a RT in a square is known.  There are known solutions of the problem of RT in a circle, rectangle,  (right) triangle, etc. For details see the references of my articles, as well as books about integral geometry. The known methods to solve these problems are not based on integration, but rather on reformulating the problem as a differential equation (Crofton's formulas). So if you are able to express the problem as single integrals, this would surely be of interest. The first open problem is a random tetrahedron in a cube. The result is conjectured to be 1/58. If your method could solve this problem, this would be a great success.


Using the Journal Stylesheet

Recently, increasingly frustrated by exporting formulas to Microsoft Word, etc., I have started urging colleagues in international projects who do not use Mathematica themselves for writing reports, to download MathReader, and they seem to be impressed by the seamless joints between mathematical work and text. I like the way the articles are displayed in The Mathematica Journal, and I would like to use the style sheet for my own purposes. How can I get rid of the headers (author and article names) and footers (The Mathematica Journal, vol:issue (year))?

Werner Holländer
Fraunhofer Institute of Toxicology and Aerosol Research
Hannover, Germany


Compositor Glenn Scholebo (glenn@wolfram.com) replies: The PageHeaders and PageFooters are set by the "Notebook Options" in the stylesheet TMJv4Style.nb. The style sheet is available for download at http://www.mathematica-journal.com/submissions/TMJv4Style.nb. PageHeaders and PageFooters settings can also be controlled by File->Printing Settings->Headers and Footers which can be applied to individual notebooks.


Evaluating Expressions in TraditionalForm

I received the latest copy of The Mathematica Journal and was trying to run the "Tricks of the Trade" Complex Conjugation example on pp. 253; i.e., a+Ib/.Complex(a_, b_):->Complex(a, -b) and I keep receiving the notice, "Syntax::sntxb: Expression cannot begin with "Complex (a_, b_):->Complex(a, -b)". I tried using square brackets, italicized letters, etc. This appears to be a traditional input. What am I doing wrong?

Doug Cook
cookdr@ix.netcom.com


Paul Abbott  replies: You are correct that this is a TraditionalForm expression. In Mathematica InputForm, In[1] of 'Complex Conjugation' reads a + I*b /. Complex[a_, b_] :> Complex[a, -b] and if you input this, it should work fine. Note that I use TraditionalForm for input and output in both my journal columns (see below). If you feel more comfortable with StandardForm (the default) or even InputForm, simply select the cell(s) you want to convert and use the following menu command: Cell -> Convert To -> StandardForm or Cell -> Convert To -> InputForm

You can, of course, simply run (and edit) the Notebook version of the Journal columns as is. Alternatively, you can also copy expressions from these notebooks into your own Notebooks. In this case, since I would guess that you are using, by default, StandardForm, it is best to convert the input cells to StandardForm before running them. 

For readers who are new to TraditionalForm Expressions, some background may be helpful. In Version 2.2, the default input FormatType was InputForm and the default output FormatType was OutputForm. In Version 3.0 (and 4.0) the default input and output FormatType are both set to StandardForm. StandardForm provides good readable two-dimensional typeset input and output and is mathematically unambiguous because the user inputs expressions using Mathematica syntax.

Nevertheless, many users would like their input and output to be presented more attractively and to correspond to mathematical syntax as far as this is consistently possible. To this end Version 3.0 (and 4.0) provides TraditionalForm. TraditionalForm can be selected as the default input and output format via Default Input FormatType and Default Output FormatType under the Cell menu.

Since TraditionalForm is, with some slight reservations, the most attractive input and output format, I have decided to use it in these columns. Also, where required, the Utilities`Notation` package will be used.

It may not always be obvious how to input typeset expressions in TraditionalForm. Probably the easiest way is to type the expression in a TraditionalForm cell using normal syntax and then use Cell -> Convert To -> TraditionalForm on the cell.