Re: Notation of very large numbers

From: Jukka K. Korpela (jkorpela@cs.tut.fi)
Date: Mon Jan 23 2006 - 01:27:44 CST

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    On Mon, 23 Jan 2006, Philippe Verdy wrote:

    > * the number "n in a triangle":
    > denotes "n to the power of n" (representation is possible
    > within existing Unicode plain-text),
    > i.e. n^n;

    By representation within existing Unicode plain-text, do you mean the
    notation n^n literally (it's just an attempt at denoting n to the power n
    in ASCII), or n followed by U+207F SUPERSCRIPT LATIN SMALL LETTER N,
    or n followed by U+20E4 COMBINING ENCLOSING UPWARD POINTING TRIANGLE?

    > * the number "n in a square":
    > denotes "n within n triangles" (impossible to represent within
    > existing Unicode plain-text),

    If n in a triangle is n followed by U+20E4, then n in a square would be
    n followed by U+20DE COMBINING ENCLOSING SQUARE.

    > * the number "n in a circle" (or pentagon):
    > denotes "n within n squares";

    Similarly, this could, in theory, be written in Unicode as
    n followed by U+20DD COMBINING ENCLOSING CIRCLE. Alternatively,
    the character U+24DD CIRCLED LATIN SMALL LETTER N could be used.

    > * the number "n in a hexagon":
    > denotes "n within n circles" (or pentagons);
    >
    > * etc (generalized to polygons with growing number of vertices)

    Unicode currently has no combining enclosing hexagon, not to mention
    "higher" polygons.

    > Such notation cannot be strictly represented as such within Unicode
    > (but upper-layer mathemetical layout syntaxes may be used).

    Some of the notations you mention _can_ be written in Unicode plain text,
    when the symbol that is to appear in a triangle, square, or circle is a
    single character.

    Whether this is a feasible approach is very questionable, since in
    contexts where you would use such notations, you probably need
    higher-level tools (such as a formula editor, a mathematical markup
    language, or some TeX-based system) anyway, and then you get much better
    rendering for these notations, too.

    -- 
    Jukka "Yucca" Korpela, http://www.cs.tut.fi/~jkorpela/
    


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