## Raphael was one of three Master artists of the Renaissance

Raffaello Sanzio da Urbino, known as Raphael, was an Italian painter and architect of the High Renaissance and lived from 1483 to 1520. He is recognized as one of the three great masters of that period, accompanied by Michelangelo and Leonardo da Vinci. His work is admired for its form, composition, and visual achievement of the ideal of human grandeur.

One of his most famous works is *The School of Athens, *a fresco in the Apostolic Palace in the Vatican. It captures the spirit of the Renaissance, and is revered as his masterpiece. It was painted between 1509 and 1511.

## The School of Athens: Inspired by a union of art and mathematics

It was also in 1509 that Luca Pacioli published the book *De Divina Proportione (The Divine Proportion)*, with illustrations by Leonardo da Vinci. MonaLisa.org reports that *The School of Athens* *“incorporates many of the mathematical theories of Luca and Leonardo.”* “*Civilisation*” author Kenneth Clark is quoted there saying “*This union of art and mathematics is far from our own way of thinking, but it was fundamental to the Renaissance.”*

## Raphael made his use of the Golden Ratio obvious

If there’s any doubt that Raphael used the Golden Ratio in this painting’s composition, it can be eliminated with a good degree of confidence by the golden rectangle that was placed front and center in the painting. It’s as though Raphael made a small but undeniable statement to answer the question before it was asked. This small rectangle is about 18″ by 11.1″ and is a rather unusual feature. Perhaps it once bore the title or some description of the painting. Even the framed area immediately below it shows a framed that is in golden ratio proportion to the borders on its sides. Click on the images for full resolution:

## No other ratio would accomplish the same result in this composition

The painting has thousands of intricate lines, so some might say that finding golden ratios within it would be a simple exercise in pattern recognition. There are two ways to overcome that objection. You can test it for yourself by setting the Line Ratio in PhiMatrix (no cost trial) to any other ratio to see if you get the same abundance and consistency of results. Further, the golden ratios are very evident on the major elements of the composition alone. Note in the first image below (click to enlarge) that simple golden ratios of the width and height of the painting define the positions of the large wall of the first arch, the top of stairs at the floor and the top of the second arch. Other golden ratios define other key elements of the composition in the other images.

## The intricate application of the golden ratio is brilliant

To appreciate the intricacy and depth of Raphael’s planning and application of the dimensional proportions in this painting, consider the illustration below. This image includes four rectangles that overlay the painting:

- Each rectangle begins at the left side of the left column in the painting. This point represents the first architectural reference point of the actual school building as viewed through the arched portal of the fresco.
- Each extends to a prominent composition feature on the right side of the painting.
- Each is divided into one or more golden ratios (accurate to the pixel with PhiMatrix software).
- Each dividing line illustrates a golden ratio formed within another prominent feature of the composition.

Trace the four rectangles separately, each in its own color, following it until you see the golden ratios that are revealed. It may be easiest to look first at the rectangles as overlayed onto a black background, also shown below.

Raphael’s use of the golden ratio is not only clear and compelling, but quite brilliant in its execution. Do you agree? Your comments are welcome below.

References:

jim carlin says

the cochlea-for hearing

the chambered nautilus

& a spiral staircase with no nails

convinced me of a Good Orderly Direction

even if I didn’t underastand It

Peter Nockolds says

Around this time someone noted the relationship of the Fibonacci Sequence to the Golden ratio in a copy of Pacioli’s work. This represents a synthesis of Arithmetic and Geometry. The potential for this synthesis appears in the painting, one the left is Pythagroras with a slate signifying the two parts of the quadrivium associated with number: Arithmetic and Music, on the right are the two parts associated with magnitude: a figure, generally thought to be Euclid, drawing a circular figure on another slate, represents Geometry, whilst above a figure with a celestial globe represents Astronomy. The two slates specifically link Arithmetic and Geometry.

Nick Kollerstrom says

Well maybe, but let’s bear in mind that no numerical value of the Golden Ratio is given in the Pacioli text. That does not appear until the next century around the time of Kepler … does it?

The frame of the Botticelli Birth of Venus gives phi to the amazing 1.614 but he would have done that by a construction with a compass, not by having units of measure..

Is that not the first ever exact expression of phi? In 1483. Or alternately, Leonardo’s ‘Annunciation’ a bit earlier with his Annunciation as Gary Meisner has indicated., but its not quite so definite. There is a phi-horizon line in this picture which looks intentional

Venus’ synodic cycle is to the Year as phi to half a percent, that would have been known to the ‘Platonic’ Florentine academy with which Botticelli was connected,