the Dark ages

Just for fun, before i started uding Rhino to draft these projects, I was doing the math longhand in a notebook. here are some shots of that process.

This is the image where i used the formula for elipses to define the profile curve of an elipse which was 3x4.


Once i had the coordinaates for various points along the curve, the distance formula is used to calculate (surprise) the distance between them.

From there the diameter of the elipsoid shape is determined at said points along the lines. and from that a circumferance ratio for lattitudes parrallel to the equator is determined.
These ratios are used with the desired dimensions and number of gores to create a model templates . here is one for a piece with 16 gores which is 1 meter wide at the equator and 1.3 meters long. (a 3:4 Parabolic measurement)
Show your work.
the fun part about all of this is the fact that the texts that i used to research this loved to use the phrase basic high school mathematics dictate that ...

kind of a blow to the ego, but at least feel prepared for the SATs now.