Technical Papers

These papers relate to the mathematics used in the implementation of QuickCalc BASIC.  It is not necessary to read these in order to use QuickCalc or to write programs in BASIC.  

Rotated Ellipses and their Intersections With Lines

This paper addresses the mathematical equations for ellipses rotated at any angle and how to calculate the intersections between ellipses and straight lines.  The formulas for calculating the intersection points are derived, and methods are given for plotting these ellipses on a computer.


In addition, techniques are shown for determining tangents to (rotated) ellipses, calculating the ellipse’s bounding box, and finding its foci.


Computing the Arctangent (in a reasonable amount of time)

The arctangent function, although easy to calculate, has historically been very slow to converge, especially near its limits of ±1.  This has led to many complex methods to calculate p = 4 arctan (1), due to the slowness of the arctangent function.  This paper will demonstrate a new technique for calculating the arctangent function for long-precision numbers with greatly improved speed – around 1 second for 10000 digits over the entire range of the function. 


Please address any comments or criticism regarding these papers to


(back to home page)