Positive Curvature: Maximum Area of Equilateral Triangle

AI Thread Summary
The maximum area of an equilateral triangle on positive curvature is a topic of mathematical interest, specifically in the context of geometry on curved surfaces. Participants express confusion about the relevance of this topic to physics and cosmology, indicating a desire for clarity on the mathematical principles involved. The discussion highlights the need for understanding how geometry differs in curved spaces compared to flat surfaces. Questions arise about the specific calculations and theories that apply to determining the area of such triangles in positive curvature. Overall, the conversation centers on the intersection of geometry and its implications in broader scientific contexts.
randa177
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what's the maximum area of an equilateral triangle that can be drawn on a positive curvature?
 
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Sounds like math, not cosmology.
 
I signed on to this forum as a physics and Math help forum, did I read it wrong? Yes I would also like to know the max area on curved space?

milt
 
Abstract The Event Horizon Telescope (EHT) has significantly advanced our ability to study black holes, achieving unprecedented spatial resolution and revealing horizon-scale structures. Notably, these observations feature a distinctive dark shadow—primarily arising from faint jet emissions—surrounded by a bright photon ring. Anticipated upgrades of the EHT promise substantial improvements in dynamic range, enabling deeper exploration of low-background regions, particularly the inner shadow...
https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.

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