The Ladder around the Corner Problem

This Demonstration visualizes a typical problem of constrained optimization: find the maximum length of a ladder that can be moved horizontally around the corner between two perpendicular corridors of different widths and .
The ladder touches the outer walls at the points and , and the corner at . In order for the ladder not to intersect the gray area, throughout the ladder's range of motion. That is, the red point must stay below the hyperbola (orange). Since the ladder has fixed length , the red point must be on the circle (blue).
The blue circle touching the orange hyperbola at the green point represents the largest such circle with radius . The coordinates of the green point are . The length of the ladder is then [1].
The Locator defines the corner at . The slider lets you move the ladder around the corner to verify the solution visually. The "test" button sets the ladder to its maximum length at its critical point.


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


[1] C. Rao, "The Ladder around a Corner Room," Chaitanya's Random Pages (blog). (Nov 7, 2010) ckrao.wordpress.com/2010/11/07/the-ladder-around-a-corner-problem.
    • 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+