# The Last Word?

To develop a complete mind,

Study the science of art.

Study the art of science.

Learn how to see.

Realize that everything connects to everything else.

– Leonardo Da Vinci

We’re going to blend the last two posts and look at Da Vinci’s ‘Last Supper’ and the √4 rectangle.

Murals present problems both in the making and the analysis of the work. The painting (it’s not a fresco) measures 180 x 350 inches (4.57 x 8.89 meters). We’ll address the challenges of making a work at this scale below. One of the challenges in analyzing a work this size is that you can’t trust a single photo because the room is small and you have to be careful about lens distortion. It also incorporates preexisting architectural features such as arches and a doorway. So how does one go about understanding the possible design decisions?

Start by approaching the whole thing with an open mind and look at as many options as possible. First, look at and measure a lot of photographs. Look at photos of the whole room. Diagram 1

Look at photos of the full commissioned work. Diagram 2

Look at photos of the narrative focus of the work. Diagram 3

Look at what others have written and diagrammed about the work (there’s no shortage). Then forget all that and just look at the work itself. Every poet uses some rhythm whether obvious or subtle. But, it’s there and it’s what makes it poetry.

So let’s look at the narrative focus of the work and ignore the room for now. It does not take long to notice that the linear perspective lines where the walls meet the roof (within the painting) converge on the central figure and mark the horizon line of the landscape beyond. Diagram 4

If we extend this lines to the edges of the painting we see a √4 rectangle. Diagram 5

This is what we get if we subdivide this area based on the √4 rectangle. Diagram 6

This is what we get if we extend the perspective lines to the √4 subdivisions. Diagram 7

Many focus on the Φ ratios* that can be found independent of the whole composition. As we noted in the previous post, this can be accomplished with almost any image or object.

So why is the central figure not really centered on the composition? Well, take a look at this. Diagram 8

The perspective is centered on the room. The central figure is centered on the doorway which is not centered on the room.

Finally, the √4 rectangle divides in half and then again in half and so on (old carpenters trick). It would be much more manageable (especially with assistants) to simple run a string the length of the wall and simply fold it back to find the half way points and repeat as required. Calculating repeated Φ ratios, at this scale and without the use of calipers or projection, would be tedious if not begging for failure.

Is this the last word? Certainly not. There will be many more opinions and observations about Da Vinci’s ‘Last Supper’ and we’re just getting started with the content we plan to provide…

*We tried and could not find anything comprehensive