The following is a brief look into cycloid curves or a curve which is formed by a fixed point on a circle as it rotates along a straight line without slipping. We will go over some of the basic properties of the curve such as its period, arc length, and area underneath the curve. using GeoGebra and Desmos we will examine the parametric functions that make up the cycloid curve as well as observe what occurs when key values such as the radius of the circle are adjusted. We will also examine two variations of the cycloid curve the curtate and prolate cycloid. Particularly focusing on how the basic properties of a cycloid remain the same or are slightly changed. Finally, we will speak shortly about the Tautochrone and Brachistochrone Problems and how a cycloid curve is used in the solution for both as well as the properties of a cycloid curve these problems establish.
The presentation regarding this subject can be found here and the worksheet can be subsequently be found here
The presentation regarding this subject can be found here and the worksheet can be subsequently be found here