9722

Arc Length of Cycloid

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.
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 .

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

RELATED LINKS

    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+