The mathematical shape “Alexander’s Horned Sphere”, which really freaks me out.

## Mission Control Depth

Apple’s “Mission Control” can be activated by swiping three fingers upward to shrink the current windows, allowing easier viewing of what you have open. But what if it wasn’t shrinking, but moving backwards in three-dimensional space? Sort of like this:

Linear perspective, following Euclidean geometry, lets us calculate the distance of an object based on its actual and apparent heights. With a few screenshots we can get the measurements.

A full-sized window on my laptop measures:

1746 pixels high @ 144 ppi (12.125 inches)

In Mission Control view, it measures:

1034 pixels high @ 144 ppi (7.181 inches)

Now, using this formula:

d = h*a

Where:

h = apparent height

a = actual height of object

d = distance

And given our measurements, we can calculate the Mission Control depth:

d = 7.181 * 12.125 = ~87" = ~7'3" (or about 2.2 meters)

Or about like this:

## Fraction Bars

A device for teaching fractions to the visually impaired, from the 1910 book “Der Blindenunterricht. Vorträge über Wesen, Methode und Ziel des Unterrichtes in der Blindenschule”, via Bitcraft Lab.

## 0s and 1s > Pyramid

A lot of math today: if all the zeros and ones on my hard drive weighed 1 gram, they would form a pyramid running from the center of the Earth to a base of 6.2cm and 5.5cm respectively. If tipped on its side, that would mean the pyramid would run from NYC to Torino, Leipzig, Berlin, Senegal, or La Paz.

Map radius calculations via: Free Map Tools

## Ratios of Important Things

Ratio of square/page in Malevich’s “Black Square”: ~3/4

Ratio of pupil/eyeball in average adult human: ~3/8

## Random Walk: Square Root of Two

Following yesterday’s experiments with the Random Pi Walk (hat tip Alex Bellos), I’ve upped the ante. The above image is the decimal expansion of the square root of two, following the first one million digits. The data is thanks to Stan Kerr via Project Gutenberg. Each decimal digit 0-9 results in a change of direction of 36 degrees and, in this case, travels 3 pixels in that direction.

The resulting image is MUCH larger than the previous visualizations – click here for the full resolution version.

## Kettle Drum and Tabla Diagram

Can’t say I really understand what they mean, but found these “ideal circular membranes” for tuned drums. The black number is the ideal value, plus kettle drum (red) and tabla (blue).

Via: +plus Magazine

## Physical Samples

Doing some Friday afternoon math about the audio files on my computer.

~22 days of music = 80,129,302,838 samples*

Sample values range from -32,768 – 32,768

If each value were to be cut using a standard CNC mill with 0.000125″ accuracy, the resulting object would be:

10,016,162.8″ = 834,680.2′ = 158.08 miles long, and only…

8.192″ tall!

* calculation from Adam Caprez at the Holland Computing Center; thanks Adam!

## Batman Equation

Via lots of sources today, the “Batman Equation”. Written out by ipi31415, the equation is:

((x/7)^{2} Sqrt[Abs[Abs[x] – 3]/(Abs[x] – 3)] + (y/3)^{2} Sqrt[Abs[y + (3 Sqrt[33])/7]/(y + (3 Sqrt[33])/7)] – 1)(Abs[x/2] – ((3 Sqrt[33] – 7)/112) x^{2} – 3 + Sqrt[1 – (Abs[Abs[x] – 2] – 1)^{2} ] – y) (9 Sqrt[Abs[(Abs[x] – 1) (Abs[x] – 3/4)]/((1 – Abs[x]) (Abs[x] – 3/4))] – 8 Abs[x] – y) (3 Abs[x] + .75 Sqrt[Abs[(Abs[x] – 3/4) (Abs[x] – 1/2)]/((3/4 – Abs[x]) (Abs[x] – 1/2))] – y) (9/4 Sqrt[Abs[(x – 1/2) (x + 1/2)]/((1/2 – x) (1/2 + x))] – y) ((6 Sqrt[10])/7 + (3/2 – Abs[x]/2) Sqrt[Abs[Abs[x] – 1]/(Abs[x] – 1)] – (6 Sqrt[10])/14 Sqrt[4 – (Abs[x] – 1)^{2} ] – y) == 0

Via: Boing Boing

## “Sorting Out Sorting”

Yes, a 30-minute video about sorting algorithms… and it’s amazing.