What is cissoid equation?

From Encyclopedia of Mathematics. A plane algebraic curve of order three whose equation in Cartesian coordinates is. y2=x32a−x.

What is the meaning of cissoid?

: a plane curve with two branches meeting at a cusp at one end of a diameter of a fixed circle, each point of the cissoid being obtained by going from the cusp along any chord to its intersection when extended with the tangent diametrically opposite the cusp and then returning along the extended chord a distance equal …

What is an asteroid in math?

In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle as it rolls inside a fixed circle with four times the radius.

What is the root of the word cissoid?

The word “cissoid” comes from the Greek κισσοειδής kissoeidēs “ivy shaped” from κισσός kissos “ivy” and -οειδής -oeidēs “having the likeness of”. The curve is named for Diocles who studied it in the 2nd century BCE.

How do you find the parametric equation of astroid?

The point P=(x,y) is described by the parametric equation: {x=acos3θy=asin3θ where θ is the angle between the x-axis and the line joining the origin to the center of C1.

How is astroid length calculated?

Theorem. The total length of the arcs of an astroid constructed within a stator of radius a is given by: L=6a.

How do you find the area of folium of Descartes?

Consider the folium of Descartes F, given in parametric form as: {x=3at1+t3y=3at21+t3. The area A of the loop of F is given as: A=3a22.

What is the parametric equation of cycloid?

cycloid, the curve generated by a point on the circumference of a circle that rolls along a straight line. If r is the radius of the circle and θ (theta) is the angular displacement of the circle, then the polar equations of the curve are x = r(θ – sin θ) and y = r(1 – cos θ).