__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**