Discovering Math in Da Vinci’s Art

Introduction to Leonardo Da Vinci

Da Vinci’s Early Life o Leonardo Da Vinci was born April 15, 1452 in Vinci, Italy.o He was an illegitimate child of a notary and a peasant woman.o He lived with his grandparents and uncle for the first five years of his life.o At the age of 14 he was an apprentice to one of the most successful artists of the day, Verrocchio.

Early Professional Life o From 1466 – 1472 he worked in Verrocchio’s workshop. o He worked in his own workshop, which his father set up, from 1476- 1481. o In 1478, he was commissioned to paint an altar piece for the chapel of Saint Bernard.o Along with being a painter and sculptor, he was an mathematician, engineer, inventor, architect and musician.

Art of the Renaissance

• They took over the Greek idea that nature can be described best through mathematics.• Their way of describing nature was to paint it.• Lead to a new style of painting in which the main tool was geometry.• Created a whole new system which was the system of perspectives which is still taught in our school today.• They were impressed by depth and shading.

Da Vinci as a Mathematician o He thought that mathematics

was an essential tool for painting.o After meeting with Fazio Cardano, a mathematician from Univ of Pavia, his interests in mathematics skyrocketed.o When returning to Milan, he began two new notebooks, they were called Manuscripts A and C.o These dealt with problems involving weight, force and movement.o A few years later Luca Pacioli who helped him through the use of Euclid’s Elements. They wrote a book together called De Divina Proportione.o He studied polyhedra.

The Last Supper

The Last Supper was his most famous painting of the 1490’s.

He painted it while he was living in Milan. It was a painting for the chapel of Santa Maria delle Grazie. It was made to appear as an extension of the wall using focal points.

It shows specifically the moment when Jesus has said "one of you will betray me"

Math in

The Last Supper

Was fascinated with the Golden Ratio and used it in the last supper.

Jesus is the center of the painting, the line from the top of his head to the floor is the same ratio as the line from the top of his head to the top of the painting.

The whole painting is based on the ratio of 12:6:4:3.

Leonardo did extensive research on Linear Perspective and applied in this work.

The Vitruvian Man Uses the Golden

Ratio. Leonardo's Vitruvian man perfect mathematical proportions could be said to tap into the universal creation on an intimate level. Demonstrates the relationship between geometric shapes and human anatomy

Proportions in The Vitruvian Man

oThe top of your head to your eyes is proportional from the top of your eyes to your chin.oTop of your head to bellybutton is the same as your bellybutton to your feet.oThe drawing shows a square inscribed inside the circle, which touch both the circumference of the circle and the vertices of the square.oThe length of a man’s arm span is equal to his height.

Mona Lisa • His most famous painting.• Also uses the golden proportion in its creation.• From the top of her forehead to the bottom of her right fingers is 1.618 times the distance from the bottom of her neck to her right fingers.

Da Vinci in The Mona Lisa

Geometry Da Vinci elaborated on

the relationship between painting and geometry in the first five sections of his book called Paragone. He said that the point is the first principal of geometry and the other principles are the line, the surface and the body clothed by these surfaces.

Virgin of the Rocks incorporates geometry in a more concrete fashion, the arrangement of the four characters is a triangle.

In Jerome, His kneeling form takes on a trapezoid shape.

Flying

• Leonardo was obsessed with flight.• Leonardo designed a multitude of mechanical devices, including parachutes, and studied the flight of birds as well as their structure. About 1485 he drew detailed plans for a human-powered ornithopter (a wing-flapping device intended to fly).

Da Vinci’s Parachute

Da Vinci’s Later Lifeo Within Leonardo's own lifetime his fame was such that the King of France carried him away like a trophy, and was claimed to have supported him in his old age and held him in his arms as he died.

o His last words were “I have offended God and mankind because my work did not reach the quality it should have.

What Could Have Been…

Had his theories been published during his lifetime, they probably would have revolutionized the science of the 17th century.

Underwater diving suitHelicopterWatermillsDraglinesEscalators Weapons of war(crossbows and catapults)

Referenceshttp://www.ancientminds.com/GreatMinds/LeonardoDaVinci.html#

http://www.facstaff.bucknell.edu/udaepp/090/w2/magee.htm

http://mathematica.ludibunda.ch/mathematicians6.html

http://library.thinkquest.org/13681/data/links/math.htm

http://www.leonardo-da-vinci-biography.com/leonardo-da-vinci-mathematician.html

http://en.wikipedia.org/wiki/Leonardo_da_Vinci

http://www.youtube.com/watch?v=IQ9ar3X_u1k