Dome of Viviani Windows

A Viviani curve (or Viviani window) is generated by the intersection of a sphere and a cylinder that passes through the center of and is also tangent to . This Demonstration shows a dome made out of a variable number of Viviani curves as the cylinder is rotated.


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


The dome is made out of a variable number of Viviani curves generated by the intersection of the hemisphere and the moving cylinder. Depending on the number of curves you want to show on the hemisphere, each curve will be shown every radians.
The green curve is the intersection of the hemisphere and the cylinder at its current location.
A real-life application of this can be seen at the Osaka Maritime Museum [1].
[1] Wikipedia. "Osaka Maritime Museum." (Apr 7, 2017) en.wikipedia.org/wiki/Osaka_Maritime_Museum.
    • 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 © 2017 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+