Arc Length and Polygonal Approximations

This Demonstration shows polygonal approximations to curves in and and finds the lengths of these approximations. These lengths are approximations to the arc length of the curve. Increasing the value of (the number of subintervals into which the domain is divided) increases the accuracy of the approximation. To get started, choose a "mode" (the type of curve you want to explore). Choices are curves defined by a function , by a polar function , and parametrically defined curves in and . Then choose a particular curve from the dropdown menu. Pressing the "arc length formula" button displays the integral needed to find the exact arc length.
  • Contributed by: Marc Brodie
  • (Wheeling Jesuit University)


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


A typical arc length integral has an integrand that has no elementary antiderivative. However, most examples in this Demonstration were chosen so that the integral can be evaluated using the fundamental theorem of calculus. In these cases, an exact answer is provided together with a decimal approximation. Otherwise, only a decimal approximation is provided.


    • 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.

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 © 2018 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+