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Because the two periods are not related by an integer but are incommensurate, the system does not flow toward a closed path but instead orbits without converging on the surface of the torus.
There are three classical attractors, a point which characterises a steady state system, a closed loop which characterises a periodic system, and a torus which combines several cycles.
The Clifford torus is generated by a family of circles.
In the formula of the curve given above the torus is formed from a circle of radius a whose centre is rotated along a circle of radius r.
‘In other words, each solution could be drawn on the surface of a torus,’ he notes.
All the quasi-fuchsian subgroups correspond to pairs of once-punctured tori, but as one tends to the boundary a certain curve on one of the tori may get squeezed to a point.
A bagel can serve as a physical model for a mathematical surface called a torus.
‘And it stands to reason that they would have other toruses dotting the quadrant,’ Maria speculated.
The surface area of the inside portion of a torus can be obtained by integrating Eq. 4, which yields
A small patch of a sphere or torus surface looks almost like a piece of a flat plane and has area rather than volume.
Into how many pieces can one cut a torus using two planes?
Intuitively, this is a consequence of the fact that two lineages can be functionally separated by a greater distance in a rectangle than in a torus.
The surface of a sphere is a good example, as is a torus (the mathematical name for the shape of the surface of a quoit, or a ring-shaped doughnut).
To be rigorous, the hole is not actually in the torus: the torus is the surface and the hole is in the space around the surface.
You can see a movie of a flat surface becoming a torus at this page about Paper Strip Activities.
We can also represent the flat hexagonal torus as a tiling of flat space, as in fig.9.
The resulting surface is a two-manifold called a torus.
I found there that the solution of Archytus involves three surfaces - torus, cylinder, and cone.
‘It appears the torus is rotating like a wheel,’ she continued.
To avoid edge effects, the lattice is represented on a circle for a one-dimensional model or a torus for a two-dimensional model.
A long cylindrical bar of orange-painted steel evokes a tori (temple gate) and serves as a balustrade.
One stand has a torus molding with red-painted triglyph and metopal sections, while a lower register has alternating black and white sections.
The gadrooned flattened torus moulding, shown on the shelf or footrest of the stand in the engraving also appears on the stretchers of the Blenheim stands.