# JānisL

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bio website jlazovskis.com location Waterloo, Canada age member for 1 year, 11 months seen Apr 12 at 4:45 profile views 45

# 47 Actions

 Aug31 comment Regional Mathematics Olympiad(RMO-India) Geometry Problem Watch your assertions there, guy. I have zilch idea of what level your competition is at; there are competitions where this type of language is used to mask a simple problem, i.e. one where any specific situation simplifies to the general case. Aug31 comment Regional Mathematics Olympiad(RMO-India) Geometry Problem My bad, I'm not familiar with the RMO-India question setup. Questions posed in this way in competitions I've gone to can be solved in this way. Aug31 answered Regional Mathematics Olympiad(RMO-India) Geometry Problem May27 comment What is the metric tensor on the n-sphere (hypersphere)? Great, thanks for the step-by-step explanation. Although what you've written is fairly clear, you can make it clearer by using the TeX environment, with the $ delimiters, like instead of g'rϕk, write $g'_{r\phi_k}$, which comes out as$g'_{r\phi_k}$. May27 accepted What is the metric tensor on the n-sphere (hypersphere)? May25 asked What is the metric tensor on the n-sphere (hypersphere)? May11 awarded Tumbleweed May9 accepted Spherical geometry - relating angles of lunes and segments of great circles May9 comment Spherical geometry - relating angles of lunes and segments of great circles @robjohn Indeed! Your answer is correct. May9 comment Spherical geometry - relating angles of lunes and segments of great circles @robjohn Regarding your answer below, the side$\varphi$should be$\varphi r$, and$\theta/2$should be$\theta r/2$. I am assuming (though not 100% sure) that will change your relation accordingly. Is that correct? May9 comment Spherical geometry - relating angles of lunes and segments of great circles @robjohn Yes, that's a better description May9 revised Spherical geometry - relating angles of lunes and segments of great circles added more clarification about geodesic May9 awarded Editor May9 revised Spherical geometry - relating angles of lunes and segments of great circles added clarification May9 asked Spherical geometry - relating angles of lunes and segments of great circles May4 asked Relation between triangle and its circumscribed circle, on the surface of a sphere. Generalizations to higher dimensions. May2 comment An explicit bijection between$R^n$and$S^n\setminus \{$point$\}$The reason why I wanted$n$-spherical coordinates is to see where an$n$-simplex on the surface of the$n$-sphere would map to in$R^n$, and I know how to express the$n$-simplex on$S^n$in$n$-spherical coordinates. But now I'm thinking stereographic projection might be just as easy, if I center the simplex at the south pole of the sphere (the pole opposite from which the projection is done). Hmmm. May2 asked An explicit bijection between$R^n$and$S^n\setminus \{$point$\}$May1 comment Curvature (Gaussian) of a hypersphere @BabakS.I see now - my question is wrong, as Gauss curvature applies to 2-dimensional surfaces, and its higher-dimensional analog is sectional curvature, which is indeed$1/r^2\$ at every point. May1 awarded Commentator