Squaring the Circle
Quadratura circuli
The impossible figure of the whole.
Squaring the Circle: what does it mean in analytical psychology?
For the geometers it could not be done; for the alchemists it was a figure of the work. Jung called the squaring of the circle one of the many archetypal motifs of wholeness, and found it in his patients’ mandalas, where a square and a circle hold one another about a centre.
Michael Maier’s Atalanta fugiens (1617) shows a philosopher drawing it, with the instruction: make a circle of a man and a woman, then a square, then a triangle, then a circle, and you will have the philosophers’ stone.
Squaring the Circle: where does it appear in myth and tradition?
The ground-plans of temples and cities; Leonardo’s Vitruvian man in square and circle; the heavenly Jerusalem, foursquare, with the Lamb its light.
From the Sources
Jung says the reader will recognise in the vision the famous medieval problem of squaring the circle, which belongs to alchemy.
“He will also easily recognize the famous mediaeval problem of the squaring of the circle which belongs to the sphere of alchemy.”
C. G. Jung, M.D., LL.D., Two Essays on Analytical Psychology, Part II, Chapter III, p. 247, commenting on a patient's vision. Authorized translation by H. G. and C. F. Baynes; London: Bailliere, Tindall and Cox, 1928 (Internet Archive OCR text). The text, read in part
Muir writes that to prove the same proposition of π is to prove that a Euclidean construction for squaring the circle is impossible.
“To prove the same proposition regarding π is to prove that a Euclidean construction for circle-quadrature is impossible.”
Thomas Muir, Encyclopædia Britannica, eleventh edition: Circle, 'Circle', section 'Squaring of the Circle', on Hermite and Lindemann. The 1911 Encyclopædia Britannica, as transcribed on Wikisource. The text, read in part
Each passage is quoted from the text named, which the press fetched and read, and was checked word for word against a fresh copy of it; the link opens that copy. Passages are given as printed, without the editors’ footnote numbers, and with words broken across lines joined.
Where to Read
- Psychology and Alchemy, CW 12
- Michael Maier, Atalanta fugiens (1617), emblem XXI
Jung’s writings are cited by the volume of the Collected Works (CW), Bollingen Series / Princeton, 1953–79.
Related Symbols
In the Glossary: Self, philosophers’ stone.
Also among Shapes
“Learn as much as you can about symbolism; then forget it all when you are analysing a dream.”
Cite This Entry
“Squaring the Circle.” In Symbols of the Psyche, the Symbolarium. The Thinking Press, 2026. https://thethinkingpress.org/symbolarium/psyche/squaring-the-circle.
Symbols That Share Its Terms
The Self (Das Selbst) · The Orphan (The abandoned one) · The Anthropos (The cosmic man) · The Centre (Axis mundi) · The Sphere (The round, the rotundum) · The Quintessence (The fifth essence) · The Treasure Hard to Attain · Gold (Aurum)
Nearby in the alphabet: The Spiral: Returning to the same place, a little higher. The Stag: The fleeing spirit of the wild, crowned with antlers. The Star: A light in the dark: guidance and destiny.