FredrikMeyer

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Math notation style and a question

You wrote:

The square root of two can also be used to approximate $\pi$:

$2^{m}{\sqrt {2-{\sqrt {2+{\sqrt {2+...+{\sqrt {2}}}}}}}}\to \pi \,$ as $m\to \infty \,$

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I changed it to read as follows:

The square root of two can also be used to approximate π:

$2^{m}{\sqrt {2-{\sqrt {2+{\sqrt {2+\cdots +{\sqrt {2}}}}}}}}\to \pi {\text{ as }}m\to \infty .\,$

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Style conventions state that:

• "Displayed" math notation, whether in TeX or not, should be indented by a preceeding colon;
• \dots or \ldots or \cdots should be used rather than "...". I used \cdots because it's between two binary operators, the two plus signs (this convention applies not just within Wikipedia but more generally).
• I put the word "as" within \text in TeX. This does not generally apply outside of Wikipedia, but text outside of the math tags often fails to align properly, or match in size, with the material within math tags. This may be browser dependent, so I don't know how these things appear on your browser. For a similar reason I used non-TeX notation for the pi on the previous line.
• I also added a period at the end of the sentence.

See Wikipedia:Manual of Style (mathematics) for more on such matters.

Now my question: What is the pattern under the radical? I presume the expression depends on m. I also don't know the pattern of plus and minus signs. Michael Hardy (talk) 18:41, 12 June 2009 (UTC)

OK, I've just done some numerical work and it seems to bear out the asserted limit. Can you cite a book or paper where one finds a proof? Michael Hardy (talk) 23:09, 15 June 2009 (UTC)