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nLab > Latest Changes: trig & pi

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  1.  
    • CommentRowNumber1.
    • CommentAuthorMichael Hardy
    • CommentTimeMay 6th 2010
    trigonometric identities and the irrationality of pi

    I created this new page. I'm new here and I have no idea whether this sort of thing belongs in a place like this.

    -- naively.....
    • CommentRowNumber2.
    • CommentAuthorMichael Hardy
    • CommentTimeMay 6th 2010
    .....and if something like this should be here, then an obvious question is which other articles should link to it?
    • CommentRowNumber3.
    • CommentAuthorAndrew Stacey
    • CommentTimeMay 6th 2010

    I guess it depends what you want to do with it!

    Whether this was your intention or not, the way you’ve written it makes me want to define an algebraic theory (Lawvere theory) based on these operations and identities. (That’s always a danger with adding something to the nLab, before you know it someone’s either turned it into an algebraic theory or an infinity-category.)

    PS I tidied up your code a little, putting a few things in \aligned environments.

    PPS Your “bug-to-post” ratio is alarmingly high! The title of this discussion broke one of the extensions.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2010
    • (edited May 6th 2010)

    Michael,

    how about that Wikipedia rule that no reader who has read the first few sentences of an entry should be left wondering what it is about? I read half-way through it and still don’t really know! :-)

    Then what about saying “I know” in an entry? How does the reader know who is speaking here? After five other users have edited the entry? If you want to speak personally, better use a query box. See HowTo.

    Maybe have a look at our template page. I gather your page is more a question than an exposition of something (??) but maybe the template page is still good as an inspiration

    • CommentRowNumber5.
    • CommentAuthorMichael Hardy
    • CommentTimeMay 6th 2010
    Urs,

    I've brought the article a bit closer to the desiderata that you suggest. I haven't yet fit it into the template, but I'll think about that. The page as a whole does amount to a question.

    Andrew: Would your proposed Lawvere theory make trigonometric identities into algebra, for which sinusoidal waves would be inessential, or perhaps only one of many special realizations?
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2010

    Michael,

    I added some sections and some hyperlinks. (Most of the hyperlinks currently unsaturated…) Have a look to see what you think.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2010

    Where you speak in first person in the query box, I added your (linked) name.

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