The Math of Lovecraft

[Acutely decayed]

I think i see ...cross sections of the interior of a sphere would still be parallel.. parallel lines wouldn't diverge .. but it isn't so much a saddle as an extended bowed plane.. anywhere on it would look like a saddle (?) but it doesn't have an end (?)...always had problems with hyperbolic in the descriptions when trying to read into this..appreciate your reply

still haven't really got a handle if anyone comes across a good visual depiction or vid...i think i have to think about lines of sight rather than the shape maybe...

I think I can imagine the divergenece or convergence of lines extended from parallell starting positions irrespective of the shape...but need to think of them making the shape.

sorry, just something that has been bugging me in this area

[waffles]

Quote Originally Posted by Acutely decayed

I think i see ...cross sections of the interior of a sphere would still be parallel.. parallel lines wouldn't diverge .. but it isn't so much a saddle as an extended bowed plane.. anywhere on it would look like a saddle (?) but it doesn't have an end (?)...always had problems with hyperbolic in the descriptions when trying to read into this..appreciate your reply still haven't really got a handle if anyone comes across a good visual depiction or vid...i think i have to think about lines of sight rather than the shape maybe... I think I can imagine the divergenece or convergence of lines extended from parallell starting positions irrespective of the shape...but need to think of them making the shape. sorry, just something that has been bugging me in this area

Thanks for asking. I haven't thought about this stuff for years and am very rusty.

Another book that comes to mind - and is very accessible with lots of hel[full illustrations - is

https://www.amazon.com/Shape-Space-Textbooks-Mathematics/dp/1138061212/ref=sr_1_1?crid=UCHDFUXVSWL3&keywords=the+shape+of+space&qid=1657758635&s=books&sprefix=the+shape+of+space%2Cstripbooks%2C170&sr=1-1

 

https://www.amazon.com/Shape-Space-Textbooks-Mathematics/dp/1138061212/ref=sr_1_1?crid=UCHDFUXVSWL3&keywords=the+shape+of+space&qid=1657758635&s=books&sprefix=the+shape+of+space%2Cstripbooks%2C170&sr=1-1

[Acutely decayed]

Thanks again, think fig 15.1 from edition 2 (which i tracked down) helps my understanding a section through hyperbolic space is a hyperbolic plane...makes more sense to me than the saddle analogy...it is like saddles everywhere - my spatial visualisation is rubbish...anyway sorry if derailed thread or came across as Colin Robinson - genuinely interested



"densely coiled layers of illusion"