POLAR EQUATION OF INWARDLY SPIRALING SPIRAL
One such form would be
r = a e*(-b theta)
Whether the curve is spiraling in or out depends upon your point of view.
The "logartihmic spiral" a*e^(b theta) spirals outward as you move counterclockwise along it.
http://en.wikipedia.org/wiki/Logarithmic_spiral
To find the polar equation of an inwardly spiraling spiral, we can start with a general formula for a spiral and then modify it to get an inward spiraling shape.
A general form of a polar equation for a spiral is given by:
r = a + bθ
where:
- r represents the distance from the origin to a point on the spiral,
- a determines the starting distance from the origin,
- b controls the rate at which the spiral expands,
- θ is the angle made by the ray from the origin to the point on the spiral.
To make the spiral inwardly spiraling, we need to modify the equation so that the distance (r) decreases as we move along the spiral.
One way to achieve this is to introduce a negative sign for b:
r = a - bθ
This modified equation will give an inwardly spiraling spiral. The value of a determines the initial distance from the origin, and the value of b controls the tightness of the spiral.
By plugging in different values for a and b, you can create different inwardly spiraling spirals with varying characteristics.