3 dominates π

3 dominates π, digital image

This work attempts to show the significance of the starting digits of pi. [Zoom in hundreds of times on the SVG image above to see all nine of the circles]. Over short distances, it is the 3 that dominates.

C = π2r

So for a small circle you can roughly approximate the relationship between the circumference and the diameter (2r) as three. You will be wrong, but only .14159265359… wrong. Round it to 3.1 and you are less wrong (.04159265359… wrong).

Pi is irrational, not like a two year old having a tantrum, but in the mathematical sense where it cannot be represented by a ratio (fraction) because it has a infinite non-repeating decimal expansion. With infinite digits after the decimal point, the best we can do is approximate pi to the number of digits we know. [Currently pi to about 12 trillion digits has been calculated].

For calculating the distances and sizes of far off galaxies, the decimals of pi take on more significance and more precise estimates of pi are needed.

So how much pi is necessary? In Scientific American’s blog: How Much Pi Do You Need?, the answer is 32 significant digits for use with the fundamental constants of the universe and 15 or 16 for everyday things like space station and GPS navigation.

Happy pi day!