# Pendulum Wave Derivation and Bill of Materials I posted a while ago that I had worked out some of the math for a pendulum wave. Attached are PDF files detailing the derivation of my specific variation of the pendulum wave and the corresponding bill of materials.

Pendulum Wave Tutorial (PDF)

Pendulum Wave Bill of Materials (PDF)

There is small problem with the bill of materials. On page 6 (arm dimensions), I have only one of the two arm types shown. Looking from the assembly drawing on the first page, it should be clear that the cut and grooved side of the arm alternates for each pendulum. The first and last arms should have inward-facing grooves.

# An Iterative Solution for Pi Using Pythagorean’s Theorem

Pythagoras, “Father of the Shortcut”, is honored every time someone diagonally traverses their campus lawn rather than taking perpendicular sidewalks to class.

Using Pythagorean’s Theorem and High School-level algebra, I will show you a simple derivation I found for an iterative expression of pi. (Yes, it was once again during a long, boring summer internship with nothing to do.)

Before we begin, we must define pi so that we will know how to find it. Pi (π) is a constant which relates the diameter of a circle to its circumference. In other words, if we know both the diameter and circumference of a circle, dividing the latter by the former will yield pi. Continue reading

# Spherical Configuration of Rounded Gears – A Derivation

Introduction

While sitting at my desk one day, I wondered how to model a spherical configuration of rounded gears (SCORG). Where does each gear need to be positioned? How should each gear be sized in such a way as to share the same diametral pitch with all other gears? How does the size of each gear affect the overall dimensions? Crappy sketches