Saturday, March 21, 2015

Barn Raising in Santa Cruz

Santa Cruz, California
The new Cowell Ranch hay barn at UC Santa Cruz replaces the 150-year old original with a traditionally-built timber frame barn in the same location. The barn will house the Farm and Garden program at UCSC.


Buenos Aires, Argentina

Buenos Aires, Argentina
Buenos Aires runs on its buses, and each line has its own color scheme, so you can see from a distance if your bus is coming.

Wednesday, March 18, 2015

Go, pi

I have a friend who used to know \(\pi\) to about 50 places. I can barely remember nine. But on pi day last weekend, I wrote a little Go program that approximates \(\pi\) by calculating many terms of an infinite series (Nilakantha's Series).

You can express Nilakantha's series as: $$\pi = 3 + \frac{4}{2\times3\times4} - \frac{4}{4\times5\times6} + \frac{4}{6\times7\times8} - \frac{4}{8\times9\times10} + \dots$$

Here's the Go program:

  package main

  import (

  const ndefault = 10000

  func main() {
          // How many iterations?
          n := ndefault
          if (len(os.Args) > 1) {
                  n,_ = strconv.Atoi(os.Args[1])
          if n == 0 { n = ndefault }
          fmt.Println("n =", n)

          pi := 3.0
          s  := 1.0    // Sign for alternating terms

          // Nilakantha series.
          for i := 2.0; i <= float64(n*2); i += 2 {
                  pi = pi + s * (4 / (i * (i + 1) * (i + 2)));
                  s = -s
          fmt.Printf("%1.20f\n", pi)

Not perfect, but not bad (maybe I'm doing something wrong):
                     going off
                     rails here.
  approx: 3.14159265358953820879
  actual: 3.141592653589793238462643383279502884197
If you really want to know more about the history and the mathematics, there's a nice paper here from the Mathematical Association of America: The Discovery of the Series Formula for \(\pi\). And the Wikipedia page on \(\pi\).

Pi, a few days late

Everyone knows this one:
$$ A_{circle}=\pi{r^2}$$
But this one is a great wonder:
$$e^{i \pi} = -1$$