The elliptic hyperboloid is a beautiful quadratic surface that is “doubly ruled,” meaning that the surface, although curved, contains two straight lines through each point. This property allows it to be used in architectural applications where designers wish to achieve an elegant curve using cost-effective straight stock.

Here it is applied to the design of a walk-through archway in the teaching garden at the University of British Columbia in Vancouver. Thank you to the many students, staff and faculty who participated in its construction.

Related:

More videos from the Mathematical Impressions series.

This twisted construction seems to mimic the trabecular patterns found in mature long bones. These bones ossify and twist on a cartilaginous matrix both in utero and after birth. It seems reasonable that these bone ossify in an approximately linear configuration before osseus rotation.

I was always intrigued by the ‘modhas’ (pretty comfortable seats made from the thin but strong straight stems of a grass like plant, whose name I forget!) because of this shape resulting from just tying up straight sticks, but never bothered to investigate. Good to know more! Thanks.

This is as fascinating as Elliptical coordinate systems where curved ellipsis and hyperbolae intersect orthogonally (at right angles) at every point.

See https://en.wikipedia.org/wiki/Elliptic_coordinate_system