Let's try to change the equations to explore other graphs!
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=3
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 , let's try to conparasol two equations and !
Look at above graph !
It seems that the graphs are same in the case of .