Dayton History Books Online

This site is a collection of historical documents for Dayton, Ohio. Strangely fascinating, at least a couple of them. I found it searching for information on the 1913 flood, and this report by National Guard General George H. Wood gives a real participant's perspective.

Also interesing is this early history of Dayton.

Random walk encircles point with probability zero

Ivars Peterson reports on the Yi Sun's winning project for the Intel Science Talent Search, in which Yi Sun

...worked out the expected number of steps it takes a walker on a two-dimensional grid to encircle a given point (origin). One such circuit corresponds to a winding number of 1.

Yi discovered that the expected number of steps to complete such a circuit in two dimensions is infinite. He also derived an explicit (very complicated) formula for the expected value of the winding number after n steps.

That is a pretty interesting result. The projects for the STS always seem really interesting, which brings me to an ongoing peeve with the STS: the reports are not published in detail anywhere that I have found.

Build your own TI-59

This Design News story doesn't give much information about 'Daniel', who has evidently emulated a TI-59 with a PIC microprocessor. Unfortunately, most of the links seem to be broken as well. At least this Make magazine blog entry gives a few more pictures.

The multicolor LEDs are kind of an interesting touch, and what's the deal with that LCD display? Debugging? I am certainly in a pretty weak position to be critical of the utility of other peoples' free-time projects, but why a TI-59? It was a decent calculator for its time, but it is fairly easy to find one on Ebay, replace the inevitably dead & corroded batteries and have a working version of the real thing. Still, a pretty neat project.

The Trouble with the Turing Test

Mark Halpern has written a fascinating article examining the current state of AI with respect to the Turing test. Never heard of Turing? Don't worry. Mr. Halpern explains it all, and goes farther to claim that even a computer which passes the Turing test may or may not be acually thinking. Too many articles on this topic devolve into fluttering gibberish, but Mr. Halpern stays fully grounded. Highly recommended.

Perimeter of an ellipse

Define an ellipse as

x^2/a^2 + y^2/b^2 = 1

then the perimeter P is calculated with

P = 4*a*E(e)

where E() is the complete elliptic integral of the second kind, and the eccentricity e is

e = sqrt(1 - b^2/a^2)

The complete elliptic integral of the second kind can be defined as an integral:

E(z) = integral( sqrt( 1 - z*(sin(x))^2), x, 0, pi/2 )

There are a variety of numerical methods to find E(z), but just using the v200 nInt() function for numerical integration works fairly well because the integrand is well-behaved with no discontinuties. Calculating E(z) with nInt() executes in about 2 seconds, with an RMS error of 1.8E-11 for 11 samples of z on [ -1, -0.8, ... , 0.8, 1 ].

For a lot of ellipse information and relationships see the Mathworld entry. You can calculate E(z) at the Wolfram formula page. A minor cottage industry seems to have sprung up for simple functions to estimate the ellipse perimeter, the most complete overview is here.