Did you know that Fibonacci had a golden retriever who inspired his spiral aptly called “Golden Spiral”? (Hey, I am joking!)
The Fibonacci spiral is frequently regarded as an approximation to the “golden spiral”, which is a logarithmic spiral whose growth factor is ø, the golden ratio.
The Reuleaux triangle is a curious geometric shape: it looks like a rounded triangle, yet it has a remarkable property. Each side is an arc drawn from the opposite vertex, and together these arcs form a curve of constant width. In other words, no matter how you measure it—between two parallel lines—the width always remains the same.
Because of this property, a curve of constant width can act as a rotor inside a square. As it turns, the shape remains in contact with all four sides of the square at every moment, tracing a continuous motion while never leaving the boundary.
Mechanisms based on intermittent motion appeared early in mechanical engineering. One of their first practical uses was in sewing machines, where motion had to advance in precise steps rather than continuously. Today similar mechanisms are widely used in devices that move film frame by frame—such as cameras, projectors, and film-processing equipment—where controlled, stop-and-go motion is essential.
This wavy floor is actually a mind-boggling optical illusion that discourages people from running down the hallway (in fact, the floor is a completely flat surface!).
Manchester firm Casa Ceramica used a neat combination of black and white tiles to make the floor along the hallway look as though it is uneven making the tiles appear to slope away into a dip.
The illusion only works in one direction, so you will be perfectly safe on the way out.
The making of the floor.
Many visual illusions have already been used to try and slow down traffic like this 3D-painted zebra crossing trialed in Iceland that provides an illusory effect of white blocks floating over the road.
Klein quartic has 24 symmetries forming a group isomorphic to the rotation/reflection symmetry group of a tetrahedron. Algebraically speaking, this group is S4: the permutations of 4 things.
Pattern with Arabesque paths moving in a linear fashion induces rotational motion to a hexagonal device.
Hexagonal-section structure made with pencils.
