How many circles in an Apollonian gasket?
The table lists the curvatures of the largest circles in the gasket. Only the first three curvatures (of the five displayed in the table) are needed to completely describe each gasket – all other curvatures can be derived from these three….Integral Apollonian gaskets.
| Beginning curvatures | Symmetry |
|---|---|
| −15, 32, 32, 33, 65 | D1 |
Who discovered the Apollonian gasket?
The mathematics tools used to solve the problem are known since René Descartes, and were re-discovered by Frederick Soddy, who published his solution in 1936 in the form of a poem in Nature [3]. Computing Apollonian gaskets is an interesting and not so difficult programming exercise.
When was the Apollonian Gasket discovered?
The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles.
What is the difference between Apollonian and Dionysian?
Apollo represents harmony, progress, clarity, logic and the principle of individuation, whereas Dionysus represents disorder, intoxication, emotion, ecstasy and unity (hence the omission of the principle of individuation).
What are Apollonian qualities?
According to Nietzsche, the Apollonian attributes are reason, culture, harmony, and restraint. These are opposed to the Dionysian characteristics of excess, irrationality, lack of discipline, and unbridled passion.
What is the purpose of Sierpinski triangle?
The Sierpinski triangle activity illustrates the fundamental principles of fractals – how a pattern can repeat again and again at different scales and how this complex shape can be formed by simple repetition. Each students makes his/her own fractal triangle composed of smaller and smaller triangles.
How many triangles are in the Sierpinski triangle?
three triangles
This leaves us with three triangles, each of which has dimensions exactly one-half the dimensions of the original triangle, and area exactly one-fourth of the original area.