Class Series: Philosophy Through Geometry

Ancient authors tell us that, at the door to Plato’s Academy, there was a sign which read “Let no one who does not geometrize enter here.” Regardless of the literal truth of that story, the practice of geometry clearly held an important place in the Academy, and in the ancient Greek philosophical tradition more generally. Over the course of four weeks together, we explored some of the reasons why.

This exploration combined hands-on, practical, collaborative work in doing geometry, with philosophical reading and reflection on what we’re doing, and why it matters. This was not a “math class.”

Each and every week, we combined four different elements: Practical exercises in geometry, short readings from the dialogues of Plato, ideas drawn from other ancient philosophers like Aristotle, Euclid, Iamblichus, and Proclus, and lively & active conversation and collaboration, as a community of learners, exploring together the interplay of these philosophical and geometrical themes.

Detailed topics & handouts from each week are provided below, as well as supplementary readings & resources (downloadable as pdfs below).

Week 1

Tuesday, March 8th

Topic:  The Geometric Ethos

In-Class Readings: Selections from Plato’s Meno and Phaedo.

  • Learning as recollection.
  • Simple geometric constructions: circles, triangles, hexagons.


Week 2

Tuesday, March 15th

Topic: Limit and the Unlimited

In-Class Readings: Selections from Aristotle’s Metaphysics, Book I; and from Plato’s Philebus.

  • The Pythagorean “Table of Opposites”
  • Point, line, plane, and figure
  • Parallels and perpendiculars.


Week 3

Tuesday, March 22nd

Topic: The Divided Line and the Golden Section

In-Class Readings: Selections from Plato’s Republic, Book VI (and, time permitting, from Plato’s Timaeus).

  • Different kinds of “knowing”
  • Geometric and harmonic proportions


Week 4

Tuesday, March 29th

Topic: Traditional Methods of Proof

In-Class Readings: Selections from Plato’s Republic, Book VII; and from Euclid’s Elements, Book I.

  • The ordering of the various sciences
  • “Elements” in geometry and beyond

David Nowakowski


David is a philosopher and educator in the Helena area whose professional work is dedicated to helping people of all ages and backgrounds access, understand, and apply the traditions of ancient philosophy to their own lives.  Read full profile…

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Course Description

View, download, and print the course description here.  

Readings & Resources

View, download, and print readings & resources here.

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