Posts Tagged Geometry
A “divine and cosmic” geometric shape—practical and pleasing
Posted by mark in architecture, geometry on April 15, 2024
The Venice Beach Pavilion—just a short walk away from my winter home in Florida—features a distinctive hyperbolic paraboloid roof dating back 50 years. I love its elegant wavy shape that sails into the sky. Therefore, I am rooting that the City succeeds in getting this iconic structure—characteristic of the Sarasota School of Architecture—registered as an historic landmark, thus enabling funding for badly needed repairs.
Check out an overhead view of the Pavilion here. It is far more impressive when seen from below. There’s no better place to enjoy a fried shrimp basket at a shady mid-century modern, round-concrete table being cooled by the ocean breeze and soothed by the sounds of crashing waves.
The best way to describe the hyperbolic paraboloid is it being the shape of a Pringles potato chip. It’s easy to create in Stat-Ease software by setting up a full three-level response surface design on two factors and then entering a quadratic equation via its simulation tools. The 3D view below stems from a model that includes only a two-factor interaction term, which creates the simple, but pleasing, twisty surface similar to the Venice Pavilion. However, the colors may be a bit much. ; )
“The hyperbolic paraboloid has been seen as a representation of the divine and the cosmic. Its symmetry (one axis but no center of symmetry) and balance have been seen as a reflection of the inherent order and beauty of the universe.”
Nick Stafford, Pringles, A Reflection of the Order and Beauty of the Universe
Getting straight to the point via the word for today
Posted by mark in Basic stats & math on January 25, 2010
Today I learned a new aspect of geometry – the “symmedians” of a triangle. This esoteric term showed up in a review by Wall Street Journal writer Mark Laswell of a book on personal ads.* Here’s the appeal for a companion that caught my eye:
“Apparently the Three Symmedians aren’t a novelty Bosnian folk troupe. Rubbish mathematician (M 37).”
This diagram and detailing by Wolfram Mathworld tells you how to draw symmedians on a triangle and locate the symmedian point, which is the “isogonal conjugate” of the centroid.
It turns out that the centroid is a vital point for mixture design of experiments aimed at optimizing product formulations, as explained in this primer that I co-authored.
So that explains how the symmedian is an interesting ‘counter-point’ for me. However, I wonder if the self-styled “rubbish mathematician” attracted an isogonal conjugate with his play on geometry.
*(“Lonely Hearts, Like Minds The eccentric personal ads of ‘romantically awkward eggheads”)