How do I know if I have cardioid or Limacon?

When the value of a is greater than the value of b, the graph is a dimpled limacon. When the value of a is greater than or equal to the value of 2b, the graph is a convex limacon. When the value of a equals the value of b, the graph is a special case of the limacon. It is called a cardioid.

What is A and B in Limacon?

|a| determines the length of the inner loop, or where it ends on the x-axis, while |b| determines the length of the outer loop, or where it ends on the x-axis. 4. When b is negative, the limacon curves is reflected over the y-axis.

Is a cardioid a special type of Limacon?

A famliy of related curves usually expressed in polar coordinates. The cardioid is a special kind of limaçon.

Can a Limacon be a circle?

approaches 0, the loop fills up the outer curve and, in the limit, the limaçon becomes a circle traversed twice.

How do you calculate cardioid?

If the radius of the circle that creates the cardioid is a, then we have the following:

1. The equation of a horizontal cardioid is r = a ± acosθ.
2. The equation of a vertical cardioid is r = a ± asinθ.

What is a cardioid curve?

Description. The cardioid, a name first used by de Castillon in a paper in the Philosophical Transactions of the Royal Societyin 1741, is a curve that is the locus of a point on the circumference of circle rolling round the circumference of a circle of equal radius. Of course the name means ‘heart-shaped’.

What does a limaçon look like?

Limaçon curves look like circles. They have various types depending on the values in their equations. In the image below, for example, the types of limaçon curves are: dimpled, cardioid, and looped (respectively).

What are the 4 different Limacons?

In the image below, for example, the types of limaçon curves are: dimpled, cardioid, and looped (respectively).

What is a limaçon curve?

: a plane curve whose equation in polar coordinates has one of the forms ρ = a cos θ ± b or ρ = a sin θ ± b and which reduces to a cardioid when a = b.

Is a convex limaçon a circle?

The limaçon is an anallagmatic curve. The limaçon is the conchoid of a circle with respect to a point on its circumference (Wells 1991).

Why are Limacons called Limacons?

The name ‘limacon’ comes from the Latin limax meaning ‘a snail’. Étienne Pascal corresponded with Mersenne whose house was a meeting place for famous geometers including Roberval.

What is A and B in cardioid?

for a=b, a>b, and a and when k is in integer values between 0 and 6.28 radians. Also, the x-intercepts of the cardioid are the ordered pairs (-(a+b),0) and (0,0). The cardioid has y-intercepts of (0,3) and (0,-3), the values for a and b and their opposites.