<< Should I feel stupid ... >> Join the club! "Commutative diagram" remains a member of an exclusive fraternity of mathematical concepts which immediately send my mind out to lunch whenever encountered, despite multiple attempts by earnest colleagues to dispel the dissociation. "Category theory" is another ... In each case the root issue involves inability to grasp what purpose they are intended to advance: instead of eventually reconnecting with anything with which I was previously familiar, such notions appear to take off from secure ground before disappearing into orbit, never to return ... WFL On 11/9/19, Joerg Arndt <arndt@jjj.de> wrote:
* Bill Gosper <billgosper@gmail.com> [Nov 08. 2019 15:44]:
[...]] Kids: I somehow missed (or completely forgot) the cool integral for the area of the curve enclosed by {x(t),y(t)}: ½∲(x dy - y dx).
And for the discrete kids, one also has to mention https://en.wikipedia.org/wiki/Shoelace_formula
With this one and an automaton for the border of the twin-dragon ( see Example 4.4 in F.\ M.\ Dekking: {Recurrent Sets}, Advances in Mathematics, vol.~44, no.~1, pp.~78-104, (1982). http://dx.doi.org/10.1016/0001-8708(82)90066-4 (now open access) ) you should be able to compute good approximations of the area of the twin-dragon (you asked about it in another email, I seem to recall).
Best regards, jj
P.S.: Should I feel stupid because I cannot grasp the commutative diagram on page 79? (I really tried!)
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