Arc Length of Cycloid

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

A polygon rolls on a line . The positions of a vertex when has a side flush with form a polygonal path (orange). The orange segments are the base sides of green isosceles triangles. When you drag the "combine" slider, the green triangles combine to form a right triangle with height , the diameter of incircle of the polygon. Hence, the length of the orange path is the sum of the height and the hypotenuse of this triangle.

[more]

As the number of sides goes to infinity, the orange path approaches a half cycloid and the hypotenuse of the triangle approaches . Hence the arc length of one arc of the cycloid is .

[less]

Contributed by: Okay Arik (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send