“The history of pi is a quaint little mirror of the history of man.”- Petr Beckmann
Denoted by the lowercase Greek letter π, the mathematical constant that is defined as the ratio of the circumference of a circle to its diameter (in Euclidean or planar geometry ) has captured the imagination of Mathematicians and Scientists, right from the dawn of civilisation and in more recent times, of the general public too. Maybe it is the nature of this constant-irrational, transcendental yet natural- or because it is so ubiquitous in its occurrence when it comes to natural sciences and mathematics that both the scientific as well as non-scientific community have a certain interest as well as reverence for. π (Pronounced /pai/) has spawned many myths, an ongoing contest amongst enthusiasts to calculate as well as memorise its non-recurring, non-repeating & never ending digits to the nth decimal place and of course the much celebrated “Pi Day” that falls every year on March, 14 (3,14 as in approx. of pi=3.14).
To commemorate this year’s Pi Day, we printed this quirky Illumination of Pi on our 3D printer and you can too by downloading the required files from here. I’ll share my experience about printing it out, along with suggestions on how to set up the LED to light your printed sculpture.
A mathematical technique warps the cutouts on the curved sides of the cylinder such that an unwarped shadow is cast on the floor. The digits of pi swirl along the arm of an Archimedes spiral; the length of the sequence before it fades a measure of your printer’s ability to capture fine details. I used a .15 resolution, but you could go lower if you want to illuminate to more decimal places. Used an infill of 20% and PLA filament. I would recommend using Black or any other dark colour for the filament, since the red, slightly translucent filament I used does not give as crisp an illumination as a dark filament would. Another point to note is to use no rafts and print the sculpture at a low speed so as to ensure the cut outs are well-formed.
Once the sculpt was printed, I used a camera flash light to check how well the resolution of the digits turned out to be; you could very well skip this step, but it does give a good idea if you will have to clean the print or redo it at a lower resolution if the length of the sequence is not to your satisfaction. Next step is setting up the LED.
I used a 5 W, high power LED that work 9 volts. You could use any other configuration as long as the light source is bright enough. I attached a heat sink before mounting the LED as high power ones tend to heat up pretty good. Mounting the LED is again important in deciding the quality of your illumination in terms of how crisp/faded it turns out to be. Adjust the height of the LED as per the requirements of your illumination. I lit up the LED using a standard Power Supply, controlling the voltage to see how the brightness affects the illumination. In the end, used a 9V battery to power my set up.
So here you have it, Illumination of Pi. If you are still not curious about why this mathematical constant is so special, I’ll leave you here with wise words of Simon Newcomb:
“Ten decimal places of pi are sufficient to give the circumference of the earth to a fraction of an inch, and thirty decimal places would give the circumference of the visible universe to a quantity imperceptible to the most powerful microscope.”
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