Archive for category geometry
Don’t be a rube—build a snub cube
I am a fan of geometry, but beyond a tetrahedron for mapping out three components in a mixture design of experiment, things get too hyper (pun intended) for me as a practical matter. However, I greatly admire the genius chemists who assembled 12 helical macrocycles into a 2,712-atom polyhedral shape called a snub* cube. These “supramolecules,” the first to made in a stereoselective way—vital to human biology, could lead to crucial advances in pharmaceuticals.
If you are exceedingly interested in geometry, handy with scissors, and desire a very cool ‘sky lantern,’ follow the directions in the video for making a snub cube.
*As you may suspect, “snub” refers to a shape with the corners pushed inwards, similar to one’s ego after suffering from a rejection—some of the air gets taken out of you. ; )
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