We compare the hausdorff measures and dimensions with respect to the Euclidean and Heisenberg metrics on the first Heisenberg group. The result is a dimension jump described by two inequalities. The ...
Annals of Mathematics, a distinguished journal of research papers in pure mathematics, was founded in 1884. Annals of Mathematics is published bimonthly with the cooperation of Princeton University ...
THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an abstract ...
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Star system demonstrates extreme gravitational lensing
In an extraordinary testament to the predictive power of Einstein’s theory of general relativity, a star system has been ...
I was randomly musing the other day about how the planning and zoning process can completely change the character of a city. I look at American cities and see the Euclidean system in use a lot, which, ...
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