Platonic Esoteric Geometry

Let none but geometers enter here

While Plato was publishing his dialogues, his Academy was researching and teaching sacred arithmetic and geometry. This explains the constant references to mathematics in the dialogues.

At the Platonic Academy of Melbourne we believe that a full understanding of Plato’s philosophy is only achieved by seeing and experiencing just how it was informed by the mystical mathematics practiced at Plato’s original Academy. This is why this very special course mixes discussion of the philosophical teaching with hands-on geometric drawing.

Join us for six small-group weekly sessions consisting of a talk, a discussion and then some drawing with compass and ruler.

For geometry beginners. But not for beginners with Plato, who should be Reading Plato first.

Instructors: Bernie Lewin and Nabeel Kahn


from Tuesday, 2 Feb, 2021, 6:30 – 8.30pm


Course Outline

Week 1 | Overview of the Platonic arts

Philosophy: The medieval quadrivium (arithmetic, geometry, music, astronomy) from Plato Republic
Activity: Introduction to compass & ruler by drawing polygons

Week 2 | The shape of numbers: gnomic expansions

Philosophy: the hierarchy of numbers linear, plane and solid.
Activity: Gnomonic expansions of squares, triangles and lines

Week 3 | Ratio and proportion

Philosophy: the 4-term proportion, the 3-term continuous proportion & musical proportions
Activity: width-length geometric expansion and logarithmic spiral

Week 4 | Doubling of the square and the diagonal

Philosophy: Plato’s theory of learning-as-remembering
Activity: Doubling the square; √2 expansion; Spiral of Theodorus 

Week 5 | Two-term proportion: the Golden Ratio

Philosophy: the Republic’s ‘Divided Line’
Activity: Finding the Golden Ratio in the line, Pentagon & Pentagram

Week 6 | Platonic solids, sacred geometry and Islamic design

Philosophy: The Platonic solids + Christian and Islamic design
Activity: A selection of sacred geometric designs