This is an animation of the generation of "hyperboloids of revolution of one sheet" used by Gaudi in various vaults.  I'm afraid it will take a few moments to download - a price for its high quality!  The animation will run smoothly when this page is fully downloaded.

The diagrams below show where they are used in the vault of the Sagrada Familia.  You can see my photographs in the Photos section of this website (links below.)

This animation was constructed using the excellent 3-D Dynamic Geometry program Wingeom by Richard Parris.  It is free and you can download it from http://math.exeter.edu/rparris.  It has both 2-D and 3-D capabilities.

Click here to download the Wingeom data file that I used.  You can load it into Wingeom-3D and rotate the top circle relative to the bottom one to see the effect yourself.

Examples of hyperboloid vaulting in the Sagrada Familia:

Click for photographs of the vaulting looking up from ground level, and from above, showing construction detail.  (They will open in new windows, which you can close whenever you like.)