Abstract

A real-valued function of one variable consists of two things: (1) a set of real numbers called the domain of definition and (2) a rule for associating one and only one real number with each number in the domain of definition. The set of number pairs defined by a function ƒ, used as coordinates of points in the plane, constitute the graph of ƒ. Stated otherwise, the graph of ƒ is the graph of the equation: y = ƒ(x). There are many cases in which it is convenient to express the coordinates of points on a curve in terms of a third variable. This third variable is called a parameter. A common situation in which a parametric representation is particularly useful is the one in which the position of a particle moving along a curve depends upon time. This chapter presents two examples in which a parametric representation is derived from the geometric properties of the curve. A cycloid is a curve generated by a fixed point on a circle as it rolls without slipping along a straight line. The chapter discusses the way to derive a parametric representation for it.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.