Hyperbolic

Mirzakhani’s work is considered to be ‘pure mathematics’, involving theoretical understanding of the symmetry of curved spaces and hyperbolic objects, but her findings may also have practical implications in quantum physics.

At the risk of being slightly hyperbolic, the fourth season of The Simpsons is the greatest thing in the history of the universe.

Using the techniques already explored, we can contrive to activate a coding triplet in any one of those four extremal corners. If one fixates at length on a pale blue-green stimulus, as in Figure 18, and then refixates on an already maximally saturated orange surface, then the resituated f/p vector will yield an activation triplet within the farthest corner of the cube, beyond the limits of the classical spindle. The H–J theory of our internal color representations entails that one should there find a circular after-image of a hyperbolic orange, an orange that is more "ostentatiously orange" than any (non-self-luminous) orange you have ever seen, or ever will see, as the objective color of a physical object. Row 1 of Figure 19 will allow you, once more, to test such a prediction for yourself.

In this configuration the on-axis image is produced at the real hyperbolic focus (fₛ₂) but off-axis performance suffers.

The hyperbolic cosine of zero is one.

There is a universal constant m_0>0 such that every hyperbolic surface R has an embedded hyperbolic disk with radius greater than m_0.

A hyperbolic isometry f has two (distinct) fixed points on ∂ℋ.

Exactly one hypercycle is a hyperbolic geodesic, and this is called the axis A_f of f.