The Math Behind the Cap – A Captive of History and Geometry

Perhaps you have noticed the black hat that Sir Rowland Hill is wearing in his portrait, which sets his head into a kind of tilted square.

We have seen and heard it called a:

• Geneva Cap
• John Knox Soft Cap
• Oxford (ladies’) soft cap

Portrait of Sir Rowland Hill, Mercer’s Copy. Note his hat.

As a tribute to Old Sir Rowland’s significant role in shaping the identity of Soulton, we preserve a John Knox cap at Soulton Hall. It rests near his Chair of Estate, a constant reminder of his intellectual pursuits and the academic traditions he championed.

Oxford soft cap/John Knox hat kept near Old Sir Rowland’s Chair.

It is related to the more commonly seen mortarboard, a square academic cap with a flat top and tassel, a symbol of learning and achievement.

Mortarboards being thrown in the air in celebration at a moment of transformation: graduation.

Their origins connect to medieval European universities, where it was worn by scholars as a sign of their status. Today, it remains a ubiquitous sight at graduation ceremonies worldwide, marking the culmination of years of hard work and dedication.

You can still see the John Knox cap being worn in UK academic settings, such as in this video of the ancient Encaenia at University of Oxford.

The John Knox cap, with its distinctive tilted square, is believed to hold a deeper mathematical significance. An extension of the scholarship of James Wenn, would suggest that the shape of the cap is connected to the rhombic dodecahedron.

Vintage engraving portrait of John Knox, Scottish leader of the Protestant Reformation and founder of the Presbyterian denomination. Engraved by Henry Thomas Ryall (1811 – 1867) after a painting by an unknown artist. Published in 1835 in a collection of English portraits.

This complex geometric figure, when projected onto a flat surface, creates a shadow that resembles the tilted square of the cap. When worn with the sun behind, the shadow cast by the cap aligns with one of the projections of the rhombic dodecahedron, suggesting a deliberate mathematical design. This design may be seen as a reminder to the wearer of the privileges and responsibilities associated with a pursuit of knowledge, akin to Plato’s concept of the Guardians.

Rotation of a rhombic dodecahedron

This connection between the cap and the rhombic dodecahedron offers a fascinating glimpse into the historical and mathematical significance of this academic headwear.