## What is a limaçon graph?

In geometry, a limaçon or limacon /ˈlɪməsɒn/, also known as a limaçon of Pascal, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius.

## What is a Limacon with inner loop?

When the value of a is less than the value of b, the graph is a limacon with and inner loop. r = 5 + cos 4θ When the value of a is greater than the value of b, the graph is a dimpled limacon. r = 5 –2 sin θ When the value of a is greater than or equal to the value of 2b, the graph is a convex limacon.

**What is a limacon with inner loop?**

### Why is it called a limacon?

Description. Limacon of Pascal was discovered by Étienne Pascal (father of Blaise Pascal) and named by another Frenchman Gilles-Personne Roberval in 1650 when he used it as an example of his methods of drawing tangents i.e. differentiation. The name ‘limacon’ comes from the Latin limax meaning ‘a snail’.

### How do you find the region inside cardioid r 1 cos θ and outside the circle r 3 cos θ?

Use a double integral to find the area of the region inside the cardioid r=1+cosθ and outside the circle r=3cosθ Bookmark this question.

**What do A and B represent in a 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.

## How do you tell if a Limacon has an inner loop?

When the value of a is less than the value of b, the graph is a limacon with and inner loop. When the value of a is greater than the value of b, the graph is a dimpled limacon.

## What do A and B represent in a Limacon?

**How do you find the area enclosed by two polar curves?**

To get the area between the polar curve r=f(θ) and the polar curve r=g(θ), we just subtract the area inside the inner curve from the area inside the outer curve. If f(θ)≥g(θ), this means 12∫baf(θ)2−g(θ)2dθ.

### Why is a Limacon called a Limacon?

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.