98100701 ICM Officina Machina model 2110i35
2000.10.07 12:18
nonEuclidean geometry
NonEuclidean geometry, that term oftused but not exactly understood by many of today's nonorthogonally 'inclined' architects and theorists, stems from the many ageold 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 nonEuclidean 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 nonorthogonal surfaces and forms, resorted to 'descriptive geometry'.
2000.10.07 17:03
Re: geometry notes
Could it be that human perception of space may be nonEuclidean, but that human imagination has evolved (so far) in a very Euclidean manner?
051007a plans of domestic architecture
051007b tallest.db with Empire State building corrected
 
2014.10.07 21:39
7 October
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).
