Songs For Beginners: Pascal’s Triangle

(:={
):=}

**********************************
()

{0 \choose 0} = 1

(),(a)

{1\choose0}=1, {1\choose1}=1

(), (a) (b), (a.b)

{2 \choose 0} = 1, {2\choose 1} = 2, {2\choose 2} = 1

(),(a)(b)(c),(b.c)(a.c)(a.b),(a.b.c)

{3\choose0}=1,{3\choose1}=3,{3\choose2}=3,{3\choose3}=1

*******************************
X
|\
0+

()
(),(a)
(),(b),(a),(b.a)
(),(c),(b),(c.b),(a),(c.a),(b.a),(c.b.a)
***********************************
{n+1\choose k} = {n\choose k} +{n\choose k-1}

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  1. I don’t ‘get’ the first verse.

  2. i’m replacing the usual “{”
    and “}”… for ease of typing…
    with “(” and “)” [and lightly
    mocking myself with a little
    “ain’t type fun” stab-at-humor;
    it looks like a smily, see?!
    ;0
    oh well.].

    the symbol “:=”
    means “equals by definition”.
    the actual handwritten notes
    occur in the context of
    *more instances* of this
    same symbol.

    readers of the zines are (implicitly)
    invited to guess what the heck
    anybody would want to go and do anything
    like put a colon in front of an equal sign for.

    [
    actually in practice, there’ll very likely be
    somebody standing by that can hardly wait
    to tell ’em. anyhow this has been the case
    in the few instances that’ve taken place so far…

    and it was very clearly the case here again.
    thanks for asking (and now aren’t you sorry).
    ]

    “lectures without words”.
    the trick is to get stuff that *seems almost*
    to explain itself. get ’em hooked…
    get ’em *talking*…

  3. vlorbik

    “A good line drawing
    has the minimum number
    of lines still adequate
    for recognition. It is,
    in a sense, the best
    for mathematical illustration
    because it leaves the most
    space for decorations to be
    applied by the user.”

    http://www.scribd.com/doc/14009839/George-K-Francis-A-Topological-Picture-Book-1988-213p-0387964266




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