Write up #10

Parametric Curves

by Kaori Tabeta

Graph of is as following;

It is circle with center of origin and radious is 1.

Let's try to change the equations to explore other graphs!

Investigation the equations

Let's try to investigate the equations for various a and b !

When a=1 and b=1, then the graph of the equations and above graph are same shape (circle) .

Let's try to change the a for various number in the case of b (b=1) is fixed !




It seems the number of a concern with the nimber of rings. How about decimal?


a=2.3 , b=1

a=2.5 , b=1

a=2.9 , b=1


Click here for movie file of In the case of.

Let's try to change the b for various number in the case of a (a=1) is fixed !

a=1, b=2

a=1 , b=3

a=1, b=4

a=1, b=5


Concerning with the number of rings is when b is odd number. When b is even number, it seems the number of b concern with the number of concave. It seems a-1.

In the case of

In the case of , let's try to conparasol two equations and !

a=1 ,b=3

Look at above graph !

a=2 ,b=6

a=4, b=12

a=5, b=4

a=10, b=8

It seems that the graphs are same in the case of .