98100701 ICM Officina Machina model 2110i35
Non-Euclidean geometry, that term oft-used but not exactly understood by many of today's non-orthogonally 'inclined' architects and theorists, stems from the many age-old mathematical attempts to disprove one of Euclid's axioms:
"There was in particular one axiom, the axiom of parallels, which they disliked and attempted to eliminate. The axiom states that through a given point one and only one parallel can be drawn with respect to a given line; that is, there is one and only one line that does not ultimately intersect with a given line and yet lies in the same plane." (from H. Reichenbach, The Rise of Scientific Philosophy, 1951.)
With the discovery that light does not travel in a straight line, the notion that parallel lines can then (eventually) intersect seems to disprove Euclid's parallel axiom.
Another aspect of non-Euclidean geometry is that the sum of the angles inside a triangle can add up to more that 180 degrees, but such triangles only truly exist when the area of the triangle is extremely vast, say a triangle created by connecting three galaxies.
Basically, it is still Euclidean geometry that governs what architects on Earth are capable of building.
As an aside, I remember reading that Gehry's office, when first dealing with designs that collaged many non-orthogonal surfaces and forms, resorted to 'descriptive geometry'.
Re: geometry notes
Could it be that human perception of space may be non-Euclidean, but that human imagination has evolved (so far) in a very Euclidean manner?
051007a plans of domestic architecture 2080i12
051007b tallest.db with Empire State building corrected 2060i03
Spent a few hours today working on a model of Palais Savoye. Just about at the point now where the models of all the various Savoye derivatives can be placed within the skeleton Palais. I basically had to carve out a corner of the Palais's undulating roof plane, so, yes, lots of x, y and z manipulation.
Up to now I've just been manipulating 2D data to achieve these elevations:
And, of course, a model will enable much more interesting views (into an otherwise virtual museum of architecture).
15100701 SANAA Building at Grace Farms New Canaan
18100701 Acropolis of Contemporary Art model work 2473i04
19100701 iq32 Cubist ICM Plan Obus 2436i74
19100702 Louvre plan sections nts 207hi01