The Mathematics of Drawing in Perspective

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The Mathematics of Drawing in Perspective
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Pre-Renaissance

• Era was characterized by
• unrealistic proportions
• size indicating importance
• unnatural appearance of objects

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Joachim and Anna Meet at the Golden Gate
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Renaissance Period

• Period between mid 1400s and 1800s
• Came about because of the Scientific Revolution
  which increased the interest in the human body
  and a realistic viewing of surroundings
• Majority of works in art as well as other fields
  were controlled by the church. They were the
  largest commissioner of art during this period.

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Painting Methods

• Subject matter was determined by the person
  paying for the work.
• Fresco Painting Artists painted on wet plaster
  applied directly to the wall.
• Oil and Water Color Painting Not as widely
  used.

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Changes in Mathematics

• There was a growing need for everyone to learn
  mathematics because of increased trade.
• Common Currency and Central Bank
• Changes in University Studies
• Trivium grammar, logic, rhetoric
• Quadrivium arithmetic, geometry, music, astronomy

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Filippo Brunelleschi

• First to paint in perspective
• The Baptistery and Town Square
• Unusual viewing practices
• The Baptistery was to be seen through a pin hole
• The Town Square cut at the tops of the buildings

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Leon Battista Alberti

• First to publish written account of how to
  correctly construct a perspective painting nearly
  twenty years after Brunelleschi
• Was not written for the artist, but for the
  patron
• Description of how to create a pavimento

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Paviamento Constructions

• Basic Construction
• Extravagant Construction
• Ultra-Extravagant Construction

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Ambrogio Lorenzetti's Presentation of Christ in
the Temple
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Pierro Della Francesca

• Major Contributor to Perspective Drawing
• Known as an artist as well as a mathematician
• Wrote three treatise The Abacus Treatise, Short
  Book on the Five Regular Solids, On Perspective
  of Painting

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On Perspective of Painting

• Was written for drawing in perspective, and not
  other aspects of painting
• The treatise was divided into three separate
  books.
• Piero uses Euclids Elements to justify his work
  as well as prove an original theorem

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Piero's PavimentoOn Perspective of Painting Book
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On Perspective of PaintingBook 2

• This book explains how to draw shapes based upon
  the pavimento
• Objects such as columns, platforms, and other
  polygons can be built based upon the pavimento

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The Flagellation of Christ
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On Perspective of PaintingBook 3

• The final book deals with objects that are harder
  to draw such as molded bases of columns and human
  heads.
• He introduces a new method of drawing in this
  book which is introduced by using a square as an
  example.

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Perspective Square
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Domenico Ghirlandaio

• Know for meticulously mapping out his paintings
  before starting.
• One of the best perspective painters of the
  Renaissance

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Michelangelo Buonarroti
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Other Methods

• Calculating the mathematics was not the only way
  for an artist to draw in perspective
• Instruments were created to make this process
  easier for the artist