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The Geometry of the Last Supper

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The Triangle #2

From the Geometry of the Last Supper by Raphaël Mouterde. It shows the triangle on the grid and the arc created by the rotation of the triangle's base. The arc intersects the grid and gives the height of the windows and the cornice. It is also tangent to the pediment.

Starting from the centre of the grid (see the mini-series on the grid if you haven’t yet read it), and following Jesus’ open arms, we can draw a triangle with a base of 4 and a height of 2.

In my previous post, I claimed that the triangle was the key to the geometry of The Last Supper. This new mini-series aims to show why. I hope you enjoy it.

We’ve seen that the grid establishes the general proportions of the dining room and guides the placement of the groups of disciples in the composition. Yet, some elements of the back wall remain unaccounted for, seemingly escaping the order of the grid.

So, we shall look for a geometry that, while rooted in the grid, allows us to move beyond its rigidity.

📐 Let’s grab an imaginary drawing compass, plant it on N, and rotate the triangle’s base upward. With that gesture, we draw an arc that inevitably interacts with the grid. As we follow this movement, several things happen:

  1. As the base rotates, the arc first meets one of the vertical grid lines. This intersection aligns precisely with the top of the window opening.

  2. Higher up, the arc becomes tangent to the decorative pediment.

  3. The arc intersects with the grid a final time at the height of the cornice, just below the ceiling.

This is quite remarkable: in a single movement, our compass reveals three major clues, each one bringing us closer to understanding the underlying harmony of this extraordinary composition.


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