# Google sketchup experiments

Oliver Knill

## 2013: Zeta function

### March 23: Youtube version

Here is a test done during spring break 2013 with importing graphs of functions to Google earth. You see the function f(x,y) = 1/|zeta(x+i y)| which has the poles at the zeros of the zeta function. The graph is placed in front of the Science Center. Click on a thumbnail to see 2000 x 1200 pictures. The color at a point (x,y) is the argument of zeta(z) and the chosen rectangle is -8≤ Re(z)≤ 8 and -90≤ Im(z) ≤ 90 or in which there are 50 roots of the zeta function on the critical line Im(z)=1/2. A second shot took the parameters -8≤ Re(z)≤ 8 and -150≤ Im(z) ≤ 150.
 The basic Mathematica command which plots the graph is ```Plot3D[1/Abs[Zeta[x+I y]],{x,-8,8},{y,-150,150}] ``` It produces a graph like seen here. .

The video shows some flight simulator shots with a slalom around the roots of the zeta function. (Higher quality Quicktime or low resolution Webm,Ogg) Music "Fading like a flower" by Roxette 1991.

Flight with 106 zeros (Higher quality Quicktime or low resolution Webm,Ogg) Music "North" by Jeff Grace. And here is an other take with 106 nontrivial roots of the zeta function on the critical line re(z)=1/2. The rectangle is [-8,8] x [-150.1,150.1] in the complex plane. It contains the following 106 zeros (where each one appears plus or minus 1: 14.1347, 21.022, 25.0109, 30.4249, 32.9351, 37.5862, 40.9187, 43.3271, 48.0052, 49.7738, 52.9703, 56.4462, 59.347, 60.8318, 65.1125, 67.0798, 69.5464, 72.0672, 75.7047, 77.1448, 79.3374, 82.9104, 84.7355, 87.4253, 88.8091, 92.4919, 94.6513, 95.8706, 98.8312, 101.318, 103.726, 105.447, 107.169, 111.03, 111.875, 114.32, 116.227, 118.791, 121.37, 122.947, 124.257, 127.517, 129.579, 131.088, 133.498, 134.757, 138.116, 139.736, 141.124, 143.112, 146.001, 147.423, 150.054.