The Geometry of the Last Supper

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Uncover the hidden mathematical beauty behind Leonardo da Vinci’s masterpiece – at the intersection of art, geometry, and symbolism.

Leonardo da Vinci's "The Last Supper" overlaid with a geometric grid and perspective lines. Bright yellow perspective lines suggested by the top of the tapestries, originate from the upper corners and converge at the vanishing point on Jesus’s head. A blue triangle with its sides on the diagonals of the grid and its apex at the centre. Two white semi-circular arcs show the rotations of the triangle's sides. The perspective lines are tangent to the arcs, as if resting on them. The angle between the hands of James and Thomas is the same as the angle of the arc.
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 side of the triangle to the vertical. The main perspective line suggested by the top of the tapestries has the same slope than the diagonal of the grid and is tangent to the arc.
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 side of the triangle to the vertical. The angle covered by the arc is the same as the angle formed by the hands of James and Thomas.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows the triangle on the grid and the arcs created by both rotations of the triangle's base. The outer edge of the pediment is given by the circle of radius 1 (module of the grid) coming into contact with the arcs at a tangent.
The window of the All Good Bookshop in London, Turnpike Lane. The book called The George of the Last Supper by Raphael Mouterde is presented in the window.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows a close-up of Jesus and the first group of disciples seated next to him on either side. There is an overlay of the grid with the triangle of base 4, height 2 and its apex at the centre of the grid. The open arms of Jesus suggest such a triangle, key to the geometry of the Last Supper.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows the Last Supper with an overlay of the 12x6 grid and elements of the composition that don't fall on the grid, i-e: the perspective, the pediment and the openings of the windows and the door with its decorative pediment.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows the Last Supper with an overlay of the 12x6 grid and elements of the composition that don't fall on the grid, i-e: the perspective, the pediment and the openings of the windows and the door.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows the circle used to define the outer edge of the pediment above the door. The centre of the circle is not aligned with the vanishing point of the perspective. It sits slightly higher. In the circle are Jesus and two hands–one from James the Greater and one from Thomas.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows a close up of Jesus from Leonardo da Vinci's Last Supper. Behind Jesus is a door and the decorative semi-circular pediment above it, only faintly visible due to the degradation of the painting.
The cover of Cathédrales, Le Verbe Géométrique by Thierry de Champris and published by Guy Trédaniel.
From The Geometry of the Last Supper by Raphaël Mouterde. This picture shows a close up of the triangle of base 4 (and height 2) with its apex at the centre of the grid. It is the key that will open the geometry for the composition of the Last supper.
From the Geometry of the Last Supper by Raphaël Mouterde. It shows the Leonardo's Last Supper with the 12x6 grid on it and how the three openings, the pediment above the door and the perspective lines suggested by the tapestries defy the rule of the grid. And this is where the geometry comes in.
From the Geometry of the Last Supper by Raphaël Mouterde. A close up of Jesus and the door behind him, with the decorative circular pediment above it.
From The Geometry of the Last Supper by Raphael Mouterde. It shows the 12x6 grid superimposed to a picture of Leonardo da Vinci’s Last Supper. The apostles are grouped and confined within 5 modules of the grid on the left and on the right. This leaves 2 modules in the centre for the calming presence of Christ.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows the 12x6 grid of the Last Supper superimposed to the two groups of the disciples on the left of Jesus. The median passes through the head of the disciples. Only Judas is situated below the line.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows Thomas, James and Philip and the 12x6 grid. They are confined to 2 modules of the grid and Thomas's hair and beard touches the limit of their dedicated space.
From The Geometry of the Last Supper by Raphaël Mouterde. It shows the 12x6 grid on the Last Supper and how the two groups of disciples on the left of Jesus and the two groups on the right are confined within the grid in this manner: 3-2-2-2-3 modules.
From The Geometry of the Last Supper by Raphael Mouterde. It shows a grid of 12x6 which commands the composition. The 3 walls are the size of 4 modules of the grid.
From The Geometry of the Last Supper by Raphael Mouterde. It show the Leonardo da Vinci’s Last Supper and how the centre of the circle used to draw the decorative pediment above the door (behind Jesus) is placed above the vanishing point of the perspective.
From The Geometry of the Last Supper by Raphael Mouterde. It shows how the dimension of the floor of the dining room is too small, if we assume that the back wall goes all the way down to the table.
Peter reaches above Judas’ shoulder to ask John something… The Geometry of the Last Supper by Raphael Mouterde
The cover of the book The Geometry of the Last Supper by Raphaël Mouterde