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by Mitch McEwen

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    Geometry doesn't have to be white - on Descartes, Baldwin, and grids

    Mitch McEwen
    Feb 20, '17 1:39 PM EST

    Here's a mini-podcast on Descartes, whiteness, and grids.  Let's liberate geometry from empire.  Especially in honor of today's American holiday. 


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      wow! seriously, I've been wondering the same thing (about the grid) since undergrad (nearly 2 decades now).  where does Descartes come up with the grid? My explanation on the differences of geometry (and not sure how founded it was) - Cartesian Geometry had reference and Euclidian was relative...own a french and english version of "The Geometry of Rene Descartes" which includes the writings you reference. I've flipped through it multiple times looking for the x,y,z bit and just did again - nope.  Also, never thought to correlate the meditations to the geometry.  20 year question solved in 10 minutes, thanks.

      Feb 20, 17 7:45 pm

      2007.04.09 23:29
      3DH Gallery
      The idea of this system was developed in 1637 in two writings by Descartes. In part two of his Discourse on Method Descartes introduces the new idea of specifying the position of a point or object on a surface, using two intersecting axes as measuring guides. In La Géométrie, he further explores the above-mentioned concepts. --wikipedia
      So let me rephrase...
      The xyz coordinate system is not necessarily the same thing as Cartesian rationalism.
      The work, La Géométrie, was responsible for introducing the Cartesian coordinate system, which is a mathematical graph in which x is the horizontal line and y is the vertical line, and in which the positive numbers on the x line are on the right and the negative numbers on the left, and the positive numbers on the y line are on the top and the negative numbers are on the bottom, and specifically discussed the representation of points of a plane, via real numbers; and the representation of curves, via equations. --wikipedia
      So the system was not so much a rational cage, rather a method to represent curves?!

      also in 9 April

      Feb 20, 17 8:17 pm

      what page?

      Feb 20, 17 10:10 pm
      Featured Comment

      Don't trust the wikipedia. Read the actual Géométrie. I wish I could recommend a good English translation, but they all suck. The French is surprisingly fresh and readable, but admittedly I have only read thoroughly a few chapters and mostly studied the pictures (joke- they are very much not pictures in the Robin Evans sense). The Ethics of Geometey by Lachterman is great.

      Feb 20, 17 10:31 pm

      The surface is a cone, and the lines for x y and z don't even necessarily have to meet at 90 degrees. The main work of Géométrie is to use algebra on the problem, and 90 degrees keeps the algebra manageable for someone working with a pencil and paper.

      Feb 20, 17 10:35 pm

      Here's a useful summary of Descartes math (mostly from Geometrie)


      And a  good summary of the diagrams in French here -

      Feb 20, 17 10:51 pm

      thank you, have lots of reading to do. 

      Feb 20, 17 11:02 pm

      i love that modern geometry is based on a french guy staring at a fly on the ceiling while tripping on ergot spoiled grain

      Feb 24, 17 8:53 am
      CINEARCHITECTURE's comment has been hidden

      I have since 25 Years studied how female architects could express themself in for ex geometry in architecture.

      Theres an tradition in Vitruvius Palladio Le Corbusier.

      But where is Vitruvian Woman Most of my study is based on Le Corbusiers Le Modulor

      Read more


      Welcome to contact me if You interested in this issue  !

      Agneta Eriksson Hilden  arkitekt SAR MSA artist developer

      Mar 16, 17 5:10 am

      Found an excellent cheap paperbook version w/ original drawings, text, and English trans.

      Title: The Geometry of Rene Descartes
      Author: Rene Descartes; Marcia L. Latham (Translator); David E. Smith (Translator)
      List Price: $12.95
      Publisher: Dover Publications, Incorporated
      Date: 1954-06-01
      Binding: Trade Paper

      Sep 4, 17 9:23 pm

      Was into geometry, P. Scott Cohen etc. and all that while studying but totally lost interest in it the last couple of years, your blog has triggered something, I might give that Descartes guy a try. Thanks. Didn't yet listen to the podcast but will later :)

      Sep 5, 17 11:08 am

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About this Blog

Posts are sporadic. Topics span architecture, urban design, planning, and tangents from these. I sometimes include excerpts of academic articles. There is an evolving series of interviews with non-architects about subjects often discussed by architects (neighborhoods, social justice, style, etc). This blog started during my fellowship at Akademie Schloss Solitude in Stuttgart, Germany.

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