#hyperboloids

[lindahall]

Vladimir Shukhov – Scientist of the Day

Vladimir Grigoryevich Shukhov, a Russian structural engineer, was born Aug. 28, 1853. 

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[upstairsdownstairsandinbetween]

"Kärven", Naturum, Getterön, Sweden,

Courtesy: White Arkitekter

[pesura]

album stream: Bad Zu - Bad Luck (Hyperboloid, 2023)

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[kvetch19]

[wikipediagrams]

[ithisatanytime]

(Hyperboloid Records)

[thetaizuru]

(Hyperboloid Records)

[misilevich]

Hyperboloid Records logo visuals

[260khorsepower]

Soon i will make a hyperboloid

[homotexas]

bonus: naively taking the intersection of two ultraparallel lines under this interpretation gives you their common perpendicular

only just realized how useful the notion is that (k+1)-vectors in n-dimensional homogeneous coordinates act not only as k-flats but also as centers/axes for all (n−k−1)-dimensional curves of constant curvature. it works out super nicely in non-euclidean cases.

e.g. in 2D elliptic geometry, every vector in ℝ³ (except the origin) is mapped to a point, which corresponds to all lines/circles in elliptic geometry having point centers within the space. euclidean projective geometry additionally has vectors mapped to points at infinity unique only up to direction, which serve as the centers for lines. hyperbolic projective geometry maps vectors on the null cone to points at infinity for the centers of horocycles, but also for each line a ‘point beyond infinity’ (at what would be a space-like vector in Minkowski space) which serves as the ‘center’ for it and its hypercycles.

further, for each of these, you can find the centers for lines (more generally (n−1)-flats) through a point p by taking as a point any vector tangent to the projective surface at p. in elliptic, this means all lines through p have centers on the great circle around p. in euclidean, since you're projecting to a plane, these are always the points at infinity. and in hyperbolic since the gradient on the hyperboloid is always more vertical than horizontal this will always be an ellipse of those ‘points beyond infinity’. neat!

[milksockets]

'hyperboloid 3' by bud latven, 2007 in against the grain: wood in contemporary art, craft + design - museum of arts and design (2012)

[transcendental-dustpan]

OH STARS MY GIRLFRIEND JUST CALLED MY BREAST [HALF] A HYPERBOLOID OF TWO SHEETS

MY DAY HAS BEEN MADE

[soup-mother]

hyperboloid cooling tower you are a beautiful girl to me

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[julsipi]