Parametric Curves

by Molly McKee

Other things worth exploring

What happens when a and b are both prime?

What happens when either a or b are not whole numbers?

What happens when a and b are both fractions?

When a=b the parametric equation is a circle centered around the origin.

Investigate

with varying a and b

a = 2, a = 3, a = 4, a = 5

b = 1

a = 1

b = 2, b = 3, b = 4, b = 5

Investigate

with varying a and b

Also notice that when a=12 and b=3 the graph looks similar to when a=4 and b=1.

Hypothesis

If a is greater than b and a = bk, where k is an integer then the graph of

will be identical to the graph of

And if b is greater than a and b = ak, where k is an integer then the graph of

will be identical to the graph of