By ICAA Education
April 20, 2022
Architect and author Steve Bass presents the first part of his Constructive Geometry course, originally taught in-person at the ICAA but made available here in digital format for the first time. This is the first part of a four-part course. Part II is available here. Parts III and IV will be available soon.
Constructive geometry is an ancient science, dating to the origins of civilization itself, and its logic establishes the basis of geometrical architecture. As viewers will learn in this hands-on course, constructive geometry is a method of drawing angles and polygons using only the mathematical relationships between fundamental elements, rather than measuring units in a coordinate system using rulers or protractors. In fact, it is only through this mathematical logic that formal definitions can be made for the fundamental elements, such as points, lines, angles, and polygons, which underlie the sciences of architecture and engineering.
In this course, viewers will learn the mathematical basis for common geometrical constructions, beginning with lines and angles and progressing to polygons. Later sessions in this series will then relate these foundational constructions to elements of classical architecture, such as the construction of moulding profiles.
Physically drawing these geometric constructions will help the viewer to understand these mathematical relationships. Viewers are encouraged to download the accompanying booklet below and actually draw the constructions demonstrated in the video. Only a straightedge and a compass are required to draw the constructions. Rulers, protractors, and triangles are not necessary, though they may be useful for checking one’s work.
Constructive geometry is a useful method for measuring the mathematical relationships between physical forms, but it is more than a system of measurement. Early thinkers realized that because constructive geometry utilizes the method of logic, it also stimulates intellectual clarity. This allows the designer to make rationally based choices with awareness of alternatives and possible outcomes.
As Plato asserted,
[The study of geometry, when] "pursued for the sake of knowledge ... compels us to contemplate reality rather than the realm of change." Since " ... the objects of [geometrical] knowledge are eternal and not liable to change and decay", such study "will tend to draw the mind to the truth and direct the philosophers' reason upwards ..."
By including examples that appear in the work of Serlio, Palladio, and others, this presentation may also be seen as preparation for approaching the canonical literature of classical architecture.
Click on the chapter markers in the video above to jump to each section. The chapter topics are listed here for reference.
Use the label number of each exercise to locate it in the course booklet. Not all exercises in the booklet are covered in this video.
[00:20] Introduction and Course Description
[01:04] Download the course booklet and commentary
[01:36] Why study geometry?
[04:06] Construction 1.1 - Bisect a line
[13:36] Construction 1.2 - Construct a perpendicular on a line
[17:22] Construction 1.3 - Construct a perpendicular off a line
[19:52] Construction 1.4 - Bisect an angle
[22:15] Construction 1.5 - Construct a line parallel to given line
[25:45] Construction 1.6 - Equilateral triangle given a side
[28:38] Construction 1.7 - Equilateral triangle given the altitude
[33:41] Construction 3.2 - Hexagon within a given circle
[40:48] Construction 3.1 - Hexagon given a side
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