Parametric Function Plotter

Description| How it works| Gallery



This app plots the parametric equation specified by x = f(t) and y = g(t).

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 Charts

Digital Rain

Oscilloscope / Function Generator Simulator

Psychedelic Mandelbrot Set

3 Wheel Spirograph

Simulation of Pendulum Waves