Hyperbolic

He showed that the figure-eight knot complement could be decomposed as the union of two regular ideal hyperbolic tetrahedra whose hyperbolic structures matched up correctly and gave the hyperbolic structure on the figure-eight knot complement.

Andrey Korotayev and others argue that historical hyperbolic growth curves can be attributed to feedback loops that ceased to affect global trends in the 1970s, and thus hyperbolic growth should not be expected in the future.

Hyperbolic functions for complex numbers Since the exponential function can be defined for any complex argument, we can extend the definitions of the hyperbolic functions also to complex arguments.

Indeed, hyperbolic space can have more than two dimensions and one can "stack up" copies of hyperbolic space to get higher-dimensional models of anti-de Sitter space.

Relationships to ordinary trigonometric functions are given by Euler's formula for complex numbers: : so: : Thus, hyperbolic functions are periodic with respect to the imaginary component, with period ( for hyperbolic tangent and cotangent).

The figure-eight knot and the (−2,3,7) pretzel knot are the only two hyperbolic knots known to have more than 6 exceptional surgeries, Dehn surgeries resulting in a non-hyperbolic 3-manifold; they have 10 and 7, respectively.

Thurston proved that in fact most Dehn fillings on a cusped hyperbolic 3-manifold resulted in hyperbolic 3-manifolds.

According to President Tinubu: “The hyperbolic character of the forgoing allegations was exposed by the petition itself, which had no facts in support thereof.

Admittedly this is all hyperbolic.

Much of the commentary I have seen on this proposal has seemed a bit hyperbolic.

Ninja is known for his hyperbolic takes from time to time, and this is a harsh one, but it’s odd that he doesn’t even seem to be aware of the game’s key controversy.

These statements might be a bit hyperbolic, but Schaefer points out the declining effectiveness of traditional marketing and advances in technology as drivers of brand communities.

Could be I instead read that in the articles itself though, as those sometimes do cover online consensus as well (even if it's hyperbolic at times).

In recent months, the project has faced outlandish, hyperbolic attacks.

It would not be hyperbolic to describe ’ portrayal of Daniel Plainview in as the greatest acting performance of all time.

Listening to the somewhat hyperbolic praise which Mr Swinney showered upon her may have given Ms Forbes a slight touch of the boak, given his behaviour in last year’s leadership contest when the woodpecker was doubtless pecking at his stump.

So, I don’t believe the hyperbolic warnings that Trump will be a dictator.

Still kinda hyperbolic imho, but I get ya.

The activists then worked to “buttonhole” administration officials at conferences and meetings around the world, pressuring them to freeze the process based on flimsy, hyperbolic climate alarm arguments similar to those behind the case against ExxonMobil.

The Republican nominee’s choice words for the industry are often extremely hyperbolic: He has said that electric cars will “kill” America’s auto industry, and lead to an “assassination” of jobs.