History of Perspective Drawing and Projective Geometry Margaux Burnham, Carlos Flores, Siddharth Parasnis

Art before Perspective

The Calling of Apostles Peter and Andrew, Duccio di Buoninsegna 1308-1311

“Fowling Scene” from the Tomb of Nebamun Thebes, Egypt

Illusion in Art

Vertical Perspective Often depicted in Ancient Egyptian art, this type of perspective puts more of a focus higher up of the image that emphasizes a hierarchy scale such as the use of religious beings.

Pre-Renaissance

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From the 1st-2nd century, Chinese artists combined “oblique perspective” and naturally sizing down objects and figures to develop a sense of distance, although no consistent technique was worked on.

Pre-Renaissance: Europe ●

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Sceneography in Greek theatres are often thought to be the first attempts in developing perspective art. During the Late Antique period, techniques for perspective art had dropped, and it wasn’t until the early medieval times were perspective art saw forms of revival, such as in Carolingian Art.

St. Matthew from the Coronation Gospels, 795-819 A.D.

Pre-Renaissance: Europe (cont.)

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The Annunciation by Duccio 1307-11

Duccio di Buoninsegna’s used shadows to add depth to his art(as shown on the left). One of Giotto’s first attempts on perspective drawing using an algebraic method was on Christ Before Caiaphas (to the right). Christ Before Caiaphas by Giotto (1305)

Pappus of Alexandria (c. 290 - c. 350 AD) ● ● ●

A greek Mathematician born in Alexandria of Egypt Well known for his works in the “Synogoge” or the Mathematics Collection. Some of his work has been lost in translation from Greek and Arabic.

Pappus’s Theorem ●

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Start off with a set of collinear points A, B, C and a second set of collinear points A’, B’, C’ that are not parallel to each other. Form three pairs of lines for AB’|A’B, B’C|BC’, and A’C|AC’. The intersecting points made from the pairs, denoted as X, Y, Z are incident to a third straight line. The configuration of this theorem is self-dual. ○

http://tinyurl.com/h84384h

Blaise Pascal (1623-1662) ● ●

A French Mathematician, physicist, writer, inventor and philosophist. Made important contributions to the study of fluids, invented the “pascal calculator”, as well as help create the topic of projective geometry and probability theory.

Pascal’s Theorem ● ● ●

Start by arbitrarily inserting six points on a conic (ellipse, parabola, or hyperbola). Connect the points via the points they are across from. The intersecting points on these set of lines are collinear. This is known as the Pascal line of a hexagon.

Medieval and Renaissance-Introduction ●

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Berlingheiro, 13th century

Humanism: increased interest in human subjects, their needs and abilities Realism: the depiction of an accurate and realistic image of the world around you Italy, 15th-17th centuries

Raphael, 1505

Artists began to try to create perfect form and symmetry

Dramatic use of light, Balance and proportion, Sfumato

Perspective Trying to create a three dimensional space on a two dimensional surface

Leonardo da Vinci, Annunciation, 1472

Filippo Brunelleschi (1387-1446)

Linear Perspective

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Vanishing point Horizon Line Orthogonals Transversals

https://www.khanacademy.org/humanities/renaissance-reformation/early-renaissance1/beginnersrenaissance-florence/a/linear-perspective-interactive

Albrecht Dürer (1471-1528) “... the new art must be based upon science - in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.”

Leonardo da Vinci 1452-1519

Da Vinci ● ● ●

Born out of wedlock to a respected notary and a young peasant class woman Received little formal education but at the age of 14 began an apprenticeship with Andrea del Verrocchio in Florence, Italy At age 20 becomes a master artist in the Guild of Saint Luke in Florence

The Renaissance ● ● ●

Artists of the renaissance wanted to represent the natural word as it was rather than how it appeared Art and Science developed in parallel “Those who fall in love with practice without science are like pilots who board a ship without rudder or compass”

Da Vinci on Perspective Perspective, with respect to painting, is divided into three parts… the first is the diminution of size of bodies at various distances; the second part is that which deals with the diminishing in color of these bodies; the third is the diminution in distinctiveness of the shape and boundaries which the bodies exhibit at various distances. -Leonardo da Vinci

Rayleigh Scattering ● ● ●

Why is the sky blue? Rayleigh scattering is a phenomenon in which light is scattered at a rate related inversely to the length of the wavelength of the particle of light Specifically:

Leonardo da Vinci Mona Lisa, 1503-06 Oil 77 cm × 53 cm (30 in × 21 in)

Leonardo da Vinci Mona Lisa (Detail), 1503-06 Oil 77 cm × 53 cm (30 in × 21 in)

Leonardo da Vinci Madonna of the Rocks, 1483–1486 Oil on panel 199 cm × 122 cm (78.3 in × 48.0 in)

Leonardo da Vinci Madonna of the Rocks, 1495-1508 Oil on panel 189.5 cm × 120 cm (74.6 in × 47.25 in)

Leonardo da Vinci Adoration of the Magi, 1481 Oil on Wood 246 cm × 243 cm (97 in × 96 in)

Leonardo da Vinci The Last Supper, 1495-98 tempera on gesso, pitch, and mastic 460 cm × 880 cm (181 in × 346 in)

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Girard Desargues 1591–1661

Filippo Brunelleschi elevation of Santo Spirito 1434-83

https://www.flickr.com/photos/randyconnolly/9504451722

Desargues Theorem ●

Two triangles are perspective from a point if and only if they are perspective from a line

One Point Perspective

Two Point Perspective

Three Point Perspective

Works Cited "Albrecht Dürer." Durer Biography. N.p., n.d. Web. 08 Apr. 2016. Atalay, Bülent. Math and the Mona Lisa: The Art and Science of Leonardo Da Vinci. New York: Smithsonian, 2006. Print. Crannell, Annalisa, and Stephanie Douglas. "Drawing on Desargues." Springer Science+Business Medi 34.2 (2012): 7-14. Worldcat. Web. 5 Apr. 2016. "Filippo Brunelleschi." Bio.com. A&E Networks Television, n.d. Web. 07 Apr. 2016. "How One-point Linear Perspective Works." Khan Academy. Khan Academy, n.d. Web. 07 Apr. 2016. "Khan Academy." Khan Academy. Khan Academy, n.d. Web. 07 Apr. 2016. "Linear Perspective: Brunelleschi's Experiment." Khan Academy. Khan Academy, n.d. Web. 07 Apr. 2016. "Perspective in Mathematics and Art." Perspective in Mathematics and Art. N.p., n.d. Web. 07 Apr. 2016. "Simulating the Colors of the Sky." Scratchapixel. N.p., n.d. Web. 05 Apr. 2016. Wallace, Robert. The World of Leonardo: 1452-1519. New York: Time-life, 1966. Print.