On the literature of descriptive geometry

Oliver Knill

Descriptive geometry (or darstellende Geometry as it is called in German) is a tool to solve problems in three dimensional space constructively in the plane. My own high school teacher Roland Staerk is an expert in that subject and has written a book (PDF) about it. While already at the time when I was in high school, the course "Darstellende Geometrie" was replaced with more traditional geometry. Our class actually had some special lectures about this from Staerk. The subject lives on: it is now part of classical geometry, projective geometry, linear algebra as well as multivariable calculus. It is also important in computer science related areas like computer vision, technical drawing, computer assisted design or game development. It is also relevant for art and design like in architecture, painting or sculpting or data visualizations.

As one can see from the book selection below, descriptive geometry has flourished during last century. It seems less relevant today due to the fact that computers can deal with three dimensional space directly. But as everybody teaching multivariable calculus or linear algebra can tell, geometric intuition and skills have become less proficient today and the explanation is obvious: new courses in high school like programming, CAD, game development, movie editing or 3D printing and of course calculus do not leave much time any more for traditional geometry like planimetry with ruler and compass and descriptive geometry. It would be silly to lament about this. Time moves on, subjects bloom and go, but by collecting some books on the subjects here, I hope to help to see the historical relevance of the subject. When looking at this documents, one can also marvel at the beauty of the drawings and see some of the masters in geometry excel in pedagogical skills. The geometer Marcel Grossmann might be familiar to many as he was helping Einstein with his theory of general relativity. The first book source below is by Albert E. Church who taught at West Point. Also notable of course is Alfred North Whitehead who is known best for his work Principia Mathematica written together with Bertrand Russell. Gaspard Monge is the one of the Monge-Ampere equations.

Albert Church Elements of descriptive Geometry, American Book Company, 1864 PDF
Gaspard Monge Darstellende Geometrie, Engelmann Verlag, 1900PDF
Alfred North Whitehead The axioms of descriptive geometry, Cambridge University Press, 1907PDF
Marcel Grossmann Darstellende Geometrie, Springer, 1922PDF
Karl Keiser Angewandte darstellende Geometrie, Springer, 1925PDF
Ludwig Eckhart Konstruktive Abbildungsverfahren, Springer, 1926PDF
Fritz Rehbock Darstellende Geometrie, Springer, 1956PDF
Karl Strubecker Vorlesungen ueber darstellende Geometrie, Vanderhoeck-Ruprecht, 1967PDF
Emil Mueller and Erwin Kruppa Lehrbuch der darstellenden Geometrie, Springer, 1961PDF
Minor Hawk Descriptive Geometry, Schaum, 1962 PDF
Eduard Stiefel Lehrbuch der Darstellenden Geometrie, Springer, 1971PDF
Roland Staerk Darstellende Geometrie, Schoeningh, 1978PDF

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