From: Mike Stay <metaweta@gmail.com> Subject: [math-fun] Embedding and curvature A sphere can be embedded into Euclidean 3-space. Can a lower-curvature space always be embedded in a space with higher curvature and more dimensions? I.e. could a hyperbolic surface with constant curvature 1 be embedded in a three-dimensional hyperbolic space with constant curvature 2? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
--you are confused: hyperbolic spaces would have curvature -2 and -1, note the minus signs. But anyhow: The "sphere at infinity" in hyperbolic space is Euclidean (curvature=0) and smaller spheres have every positive curvature. The "equidistant surfaces" from a hyperplane in hyperbolic space have got every constant negative curvature you could want (above the curvature of the mother space). So I think the answer to your intended question is yes.
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Message: 5 Date: Thu, 7 Apr 2016 18:56:05 +0200 From: Simon Plouffe <simon.plouffe@gmail.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] cubes passing thru holes in cubes Message-ID: <57069125.1010804@gmail.com> Content-Type: text/plain; charset=windows-1252; format=flowed
Hello,
I passed the number into the grinding machine : nothing found. 1.00083944685934978860193... = unknown to me.
I used the 'smart' lookup and even the super smart lookup, generalized expansion, LLL test: Nothing.
Best regards, Simon plouffe
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