Atmospheric vs mathematical_perspectives-_schwappach

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Running head: Atmospheric and Mathematical Perspectives
Atmospheric and Mathematical Perspectives of the Italian Renaissance
Phase #3, Assignment #6, Individual Project #3
TSgt Loren Karl-Robinson Schwappach
Colorado Technical University
Prepared for Tammy Starzyk
HUM140-0804A-08 Art Appreciation
28 October, 2008

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Abstract
The Italian Renaissance or “rebirth” in French was one of the most influential and fruitful
periods in art history, especially in the creation of techniques used to create illusions of depth
and realism in art. This essay will discuss the origins and differences between two techniques
that were born in this era of rebirth and their ability to morph a two dimensional surface into a
three dimensional dreamscape. The two techniques you will read about are the atmospheric and
mathematical perspectives. This paper will also explain how the later forever changed the
approach to creating realistic art through science.

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Until the early fourteenth century the use of perspective, or point of view in painting was
represented in an intuitive or instinctive manner. Three intuitive techniques were used to imply a
sense of depth and reality in artwork. These three techniques were overlapping (things in front
appeared closer), vertical (things in the distance appeared closer), and diminution (smaller
elements are assumed to be farther away).
Atmospheric perspective was popularized in the early fourteenth century and is also
known commonly as aerial perspective. The birth of atmospheric perspective is credited to
Filippo Brunelleschi, although elements of the style have been observed by scholars prior to the
Italian Renaissance, even as far back as Roman times. It is said that atmospheric perspective was
made famous by Leonardo da Vinci through paintings such as Mona Lisa, which has brought
confusion on who really deserves credit for the style. (ArtLex on Aerial Perspective)
Atmospheric perspective accomplishes the illusion of dimension though imitating the
atmosphere and building upon a law of natural observation. When you naturally observe objects
in nature the dust in the atmosphere causes a scattering of light, which increases the further an
object, is from the observer. In other words, as the distance between an object and the viewer
increases, the contrast between the object and its background decreases. This decrease in
contrast makes the object appear blurred and hazy. The object not only looses clarity to the
viewer but takes on the color and luminosity of the background. The aerial perspective creates
this illusion of depth for the audience by making distant objects appear lighter, less detailed and
normally much cooler in hue than any nearby objects. (ArtLex on Aerial Perspective)

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As mentioned earlier the creation of atmospheric perspective in art is recognized by
Filippo Brunelleschi, yet most say it was Leonardo da Vinci that made the style famous. Thus,
in homage to Leonardo, the famous Mona Lisa (see image 1, below) is a grand example of the
atmospheric perspective technique in painting.
Image 1: Mona Lisa, by Leonardo da Vinci: Image obtained on 28 Oct 2008 from worldart.com at http://www.worldart.com.au/classic-female-
portraits/
Leonardo was a master at creating illusions of reality and perception of depth in his
artwork. The Mona Lisa while not only one of the most famous paintings in history is also a
perfect example of the atmospheric perspective in artwork. For example, first take a look at the
size of Mona Lisa compared to the background scenery behind her. In the scene Mona Lisa
appears much larger than the background. This is an example of diminution described above.
Second, notice how the image of Mona Lisa is much sharper than the corresponding background.
Although the painting is essentially a flat object, the curving mountains, oceans, and scenery in

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the exemplified in the background seem miles upon miles away. In actuality as your eyes fall
farther and farther into the background, the background slowly blurs together, becoming lighter,
and becomes significantly cooler in hue. This blurring of detail and cooling of color is the
atmospheric perspective in action, and allows Leonardo to create a sweet three definitional sense
of depth through a purely intuitive means. (Stokstad, 2007)
As mentioned in the abstract, the Italian Renaissance was one of the most influential and
fruitful periods in art history. One of the greatest fruits born during this period was the
convergence between art and science, specifically mathematics. The convergence between art
and mathematics lead to several of man kinds great and more rewarding discoveries. One of
these amazing discoveries was a method that could use the growing knowledge obtained from
mathematics to grant the illusion of dimension in a much more realistic way. This method is
known as the mathematical perspective also known as linear perspective, and its' creation is also
credited to Filippo Brunelleschi. (ArtLex on Li)
Filippo Brunelleschi was a renowned architect, painter, sculptor, engineer, and
mathematician. Brunelleschi was one of the first persons to experiment on mathematical theories
of perspective in painting. Though these experiments and the foundations on rays laid out by
Euclid, new rules of proportions and symmetry were developed and eventually lead to the
creation of mathematical perspective in art.

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Mathematical or linear perspective is a rough depiction of an image as it is perceived by
the eye on a flat surface. Mathematical perspective works by representing the lines of light that
pass from an object in a scene through an imaginary rectangle or in the case of a painting the
painting itself. It is a lot like looking through glass and painting the scene your eyes create onto
the glass plane. This essential mimics the eyes ability of depth perception an tricks the observer
into thinking the object is three dimensional. Mathematical perspective uses foreshortening (a
distortion effect where objects seem shorter because they are angled towards the observer), a
horizon line (the line opposite of an observers eye represents objects infinitely far away), and
vanishing points (the point or points where parallel lines converge). (ArtLex on Li)
The painting by Pietro Perugino of Jesus Handing the Keys to St. Peter (see image 2,
below) is a great example of mathematical perspective. Notice how the buildings on the left and
right of the cathedral are slightly distorted, this is foreshortening. Light brownish grey, lines of
perspective are drawn from the vanishing point in the middle of the center buildings door and
stretch out perpendicular to each other. Using mathematical perspective the image creates a
great sense of depth and distance to the observer. Notice also the size of the background
audience is much smaller than the audience in the front, using the lines of perspective as guides
the artist is able to ensure incredibly realist ratios of size in order to simulate their respective
distances, this is the use of diminution once again. This painting also illustrates an aspect of the
atmospheric perspective. Notice how the background landscape becomes hazy and blurred.

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Image 2: Jesus Handing the Keys to St. Peter, by Pietro Perugino: Image obtained on 28 Oct 2008 from upload.wikimedia.org at
http://upload.wikimedia.org/wikipedia/commons/e/ec/Pietro_Perugino_034.jpg
Leonardo da Vinci believed there was more to perspective than Brunelleschi's works on
linear perspective could offer. He felt that linear perspective failed to take into account the
appearance of objects held close to the eyes. Thus, Leonardo's use of perspective utilized not
only beams of light but his direct observations. (Stokstad, 2007)
The painting of The Last Supper by Leonardo da Vinci (see image 3, below) is another
great example of linear perspective in art. This wall painting again uses the tools of
foreshortening, notice the strange distortions of the wall rugs on the left and right. You should
also notice there is a vanishing point this time vanishing within the head of Christ. Again the use
of mathematical perspective in the perpendicular lines on the ceiling tricks the observer into
realizing an accurate three dimensional space. Leonardo also utilizes the atmospheric
perspective in this painting. Notice how the background landscape is cooler than the foreground.

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Image 3: The Last Supper, by Leonardo da Vinci: Image obtained on 28 Oct 2008 from southernledger.com at
http://southernledger.com/blogs/artdrawingconclusions/
In summary the Italian Renaissance birthed new methods for enhancing the illusions of
dimension in art. The atmospheric or aerial method used the ideas found in nature where objects
in the distance appear cooler and less sharp than objects in the foreground. The mathematical or
linear perspective used concrete laws of science and mathematics, such as the angles created by
rays of light, to create a near perfect dimensional space. These two techniques forever changed
the role of science, and mathematics in art and gave the artist an amazing tool to create dreamy
landscapes of depth.

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References
Stokstad, M. (2007). Art: a brief history (3rd ed.).
Upper Saddle River, New Jersey: Pearson Education, Inc.
ArtLex on Aerial Perspective from ArtLex.com retrieved on 28 October 2008 from
http://www.artlex.com/ArtLex/a/aerialperspective.html
ArtLex on Aerial Perspective from ArtLex.com retrieved on 28 October 2008 from
http://www.artlex.com/ArtLex/a/aerialperspective.html
ArtLex on Li from ArtLex.com retrieved on 28 October 2008 from
http://www.artlex.com/ArtLex/Li.html