# Parametric Function Plotter

Description| How it works| GalleryThis app plots the parametric equation specified by x = f(t) and y = g(t).

Note - a newer version of this tool is the Graphing Calculator.

## Download

.xls file (93 KB) or .zip file (25 KB)## How to use

The use of this app is quite similar to the Single Variable Calculus
Tool. Key in the functions x(t) and y(t) in the the cells B5 and B6
respectively. The equal to sign must be used so that the cells
display the value corresponding to t = min(t).Key in the range of t
in the cells B10 and B11.

For example, to plot the curve given by x(t) = sin(t) and y(t) =
cos(t), the screen would look like this if the entries are made
correctly.

These equations are the parametric equations of a circle.
The entire circle is plotted if the range of t equals or exceeds
2*pi, otherwise a part of the circle is plotted.

As another example, keying in x(t) = t^2 and y(t)=2*t with t ranging
from -10 to 10 gives us a parabola (see figure below). A parabola
belongs to a class of curves known as conic sections, which are
formed by the intersection of a cone and a plane surface. Other
conic sections are circles, ellipses and hyperbolas. (Parameteric
equations for these are available at
this Wikipedia
page.)

## "Squaring the circle"

User Alexander Weiner has kindly shared some very interesting work he has done with the various apps on this site. He has sent me his work which he calls "Squaring the circle". This is based on the parametric formula of a circle. The picture below shows what this does. The file from Alex can be downloaded here.

Alex has also pointed out to me the following YouTube video describes the interesting mathematics behind this. Thanks Alex!

## Also See:

Animated ChartsDigital Rain

Oscilloscope / Function Generator Simulator

Psychedelic Mandelbrot Set

3 Wheel Spirograph

Simulation of Pendulum Waves