Just a note to self, so I don't lose some of these sites I've found.

I've been looking at algorithms to calculate π (pi) recently. I've not actually installed and learned anything like GMP, MAPM, MPFR, or other so-called "bignum" libraries, so I'm pretty much limited to the digits that can be stored in a double. *sniff* Well, I'll get around to it eventually, eh?

So, the major algorithms I've found are as follows:

• Archimedes' iterative algorithm for approximating Pi
  • Archimedes' Algorithm for Pi
  • Archimedes' Approximation of Pi
  • http://physics.weber.edu/carroll/Archimedes/pi.htm
  • Archimedes and the Computation of Pi
  This algorithm starts off with a circle inscribed in a square, and a square inscribed in that circle. The perimeters of the squares quite obviously set upper and lower bounds for the diameter of the circle, and the diagonal of the inner square equals the diameter of the circle; so upper and lower bounds for π (pi) can be calculated. Given relationships between regular polygons, each n-gon (starting with the square, or 4-gon) can yield a 2n-gon, ad infinitum. The only limitation is the precision with which you can store numbers, in particular the square root of two (as your initial calculation of the diameter, given a 1×1 inscribed square).
• The Bailey, Borwein, and Plouffe (BPP) formula
  • BPP Formula
  • Bellard's Formula
  • http://oldweb.cecm.sfu.ca/projects/pihex/index.html
  • PiHex on Wikipedia
• Series expansions and Fibonacci numbers
  • Pi and the Fibonacci Numbers (Talks about several series-expansion algorithms such as arctangent, Gregory's series, and Machin's formula.)

I've implemented Aristotle's algorithm and Gregory's series, and filled a double with accurate values for π (pi) fairly quickly. Actually, the expansion of Gregory's series rand several orders of magnitude faster. I suppose now I should install GMP and play with actual numbers instead of these piddly little doubles.

See also: History of numerical approximations of pi on Wikipedia

I debated entitling this "Erotology and Calliology" or "Aphrodology and Bellology," but declined. You may refer to it as such if you wish . . . I rather like the term "calliology", and may continue using it.

Anyhow, I'm trying to keep a few reference pages available to which I may direct people when certain topics come up in conversation. I find it saves words and time, as well as ensures consistency on my part, if I'm able to cite what I've actually written down.

The following entries are those which have some bearing on my philosophies of love and beauty. Since you're able to read it all right here, I'm not going to rant on the topic now. I'll save that for what I've already written.

Suffice it to say that I worship women . . .

• All Things Feminine: "Careless of being crushed by beauty, I would ride high on the gales of Her mischance until, swept into the face of Wonder, I live, crippled by sweetness, forever."
• A Note to the Hunters and Acolytes of Women: Yes, I admit that I pursue women, but if she's not a goddess worthy of worship (and I don't just mean physically beautiful), she's not even worth chasing.
• Necessary Irreverence: Sometimes speaking to a woman is irreverent to the very concept of beauty. Sometimes such irreverence is necessary.
• Commentary on Ezra Pound's "The Garden": My analysis of the poem, from both socioeconomic and philosophical bases.
• Commentary on A.E. Coppard's "The Higgler": "The Higgler" is just a piece of great literature (not sappy) on love.
• Sir: The way to my heart is to call me "Sir."
• Boxes and Hinds: What does anyone look for?
• High Standards and Perfect Sisters: Why I look for what I look for.

I have a ponderous list of movies I’ve been assigned by various friends and enemies:

I've been told . . .

• Dangerous Liaisons: Also from CD. Apparently there is some underlying artistic necessity to my watching it.
• A Beautiful Mind: Yeah, the crazy-mathematician movie. That’s my kind of main character.

Might I Recommend . . .

• A River Runs Through It
• Casablanca
• The Spanish Prisoner
• The Hitchhiker’s Guide to the Galaxy

I watched . . .

• Lion in Winter: CD assigned this one to me. It’s got Patrick Stewart in it, who is actually a much more skilled actor than he was ever required to be on Star Trek. I finally watched it. Highly recommended!