Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don't apply: angles of a triangle add up to less than 180 degrees and Euclid's parallel postulate ...

Those curves -- an example of a high-level geometry concept called the hyperbolic plane -- were not even defined by geometry theorists until the 19th century.

Hyperbolic geometry, conceived by mathematician Carl Gauss in 1816, is stranger still. Like planar geometry, it posits that the shortest distance between two points is a straight line. And hyperbolic ...

“The first time I saw a print of ‘Circle Limit III,’ I said to myself, ‘that is the most beautiful example I have ever seen of the Poincaré circle model for hyperbolic geometry,'” says ...

For example, the Internet only requires D = 7 dimensions to be mapped into the hyperbolic space of our model, whereas this name is multiplied by six and scales to D = 47 in one of the most recent ...

Hyperbolic geometry is radical because it violates one of the , which long stood as a model for reason itself. The fifth and final axiom of Euclid’s system – the so-called parallel postulate ...

In Math 3404: Advanced Topics in Geometry, they worked on deeper versions of the same projects, as well as some additional topics like using geometry for data visualization and understanding Escher’s ...

Bending the Rules of GeometryBending the Rules of Geometry By VI HART, HENRY SEGERMAN, ELISABETTA MATSUMOTO, M EIFLER, ANDREA HAWKSLEY and SAMANTHA QUICK • August 27, 2017 ...

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