Leonardo da Vinci was a great mathematician whose contributions to the discipline were immense, especially in the field of geometry. Besides being a mathematician, Leonardo da Vinci was a renowned painter, inventor, architect, and a student of scientific concepts (Cremante, Leonardo & Pedretti, 2005). Since Leonardo’s natural genius encompassed several disciplines, he personified the term “Renaissance man. ” At present, Leonardo is best acknowledged for his art masterpieces, particularly the “The Last Supper” and “Mona Lisa” that are still among the worlds most renowned and admired (Cremante et al. 2005).
In all his works, Leonardo believed that there is a significant connection between art, science and nature. Being mostly self-educated, Leonardo filled several secret notebooks with observations, theories, and inventions that ranged from aeronautics to anatomy. Even though he was praised in his time as a remarkable artist and scientist, his colleagues did not recognize his genius (Lucertini, Milla? n Gasca & Nicolo? , 2004).
He had a great combination of imagination and intellect that inspired him to design, at least on paper, inventions such as the bicycle, the airplane, and the helicopter from the physiology and flying ability of a bat (Lucertini at al. , 2004). In this paper, an incisive examination of the life and general contributions of Leonardo da Vinci is made. Place of Birth, Family Life and Upbringing In 1452, Leonardo was born in a farmhouse located in the middle of the rolling hills of Tuscany outside the Anchiano village in Italy.
He was born to Ser Piero, a respected Florentine notary, and Caterina, a young peasant woman (Bortolon, 1967). Having been born out of wedlock, Leonardo was raised by his father along with his stepmothers. At five, he relocated to his father’s family land that was close to Vinci, the Tuscan town from which Leonardo’s surname was derived, and stayed with his grandparents and uncle (Bortolon, 1967). Even though his artistic gifts were apparent from an early age, the young Leonardo got a little formal education outside the basic reading, writing, and mathematical instructions.
He later started a long apprenticeship with Andrea del Verrocchio, a noted artist in Florence. Under Andrea, he learned several technical skills such as metalworking, carpentry, leather arts, sculpting, drawing, and painting. In 1473, Leonardo sketched the scenery in the Arno valley, his first known dated work, using a pen and ink. At the age of 20, Leonardo qualified for master artist membership with Florence’s Guild of Saint Luke where he set up his workshop (Cremante et al. , 2005). However, he kept on working together with his teacher for an extra five years.
It is believed that Verrocchio’s work “Baptism of Christ” was completed around 1475 with Leonardo’s help. Leonardo painted a section of the background as well as the young angel clinging to Jesus’ robe. According to the Florentine court records, Leonardo was charged with sodomy, along with four other men. These charges were punishable by death or exile, but Leonardo was acquitted. Leonardo’s Career in Different Cities From Florence, Leonardo moved to Milan where he served the Duke of Milan. In the Duke’s staff list, he was described as a Dukes painter and engineer.
During his time with the Duke, he completed six paintings as he advised on architecture, military matters, and fortifications (Cremante et al. , 2005). During his service in Milan, he was also referred to as a mechanical and hydraulic engineer. It was here that his interest in geometry began, and he started reading Leon Battista’s book on architecture. He got so engrossed in geometry that he neglected his painting (Cremante et al. , 2005). After studying Euclid and Pacioli’s Suma, he started his geometry research, occasionally offering mechanical solutions.
At around this time he wrote a book on the basic theory of mechanics that materialized in Milan around 1498 (Bortolon, 1967). Leonardo also realized the likelihood of making a telescope. When the French armies’ invaded Milan and defeated the Duke, Leonardo left Milan for Mantua, Venice and returned to Florence afterward. Even though da Vinci was under continuous pressure to paint, mathematical studies kept him away painting much of the time. For a time, Leonardo worked for Cesare Borgia as a leading military architect and engineer (Cremante et al. 2005).
In Milan, he spent most of his time in scientific work than painting as he was occupied in anatomy, mechanics, hydrodynamics, mathematics and optics. When the French were evicted from Milan, Leonardo moved to Rome where he devoted most of his time to technical experiments and mathematical studies due to the lonely life in Rome. One year later, King Francis I invited Leonardo to join his service in France (Bortolon, 1967). In France, he was given the title “first painter, mechanic, and architect of the King” (Bortolon, 1967).
Leonardo passed on at age 67 at Cloux in 1519 and was buried adjacent to the Saint-Florentin palace church. Leonardo’s Contribution to Mathematics Besides having an interest in fine art, nature, mechanics, physics, anatomy, architecture, and weaponry and designing workable models for machines such as the bicycle, helicopter, military tank and submarine, Leonardo made an exceptional contribution to mathematics through geometry. Leonardo had an understanding of higher mathematics but never knew how to put it into the academic structure of numbers as in the contemporary mathematics (Cremante et al. 2005).
Even after learning the mathematical language, Leonardo preferred using geographical shapes to compute equations, and this enlisted his artist abilities. In mathematics, Leonardo’s major pursuit was in the exploration of the concept of spatial mechanics and proportionality (Lucertini et al. , 2004). The reason Leonardo preferred using drawings in mathematics is that pure mathematics excludes the incomprehensible characteristics of reality that are better described by drawing.
Since mathematics is a tool for producing outcomes, Leonardo chose to draw as his key tool in executing his proportionality and spatial awareness studies that were applied in his engineering designs. The ancient civilizations, as shown in the pyramids of Egypt, used drawings to perform precise mathematics for construction (Cremante et al. , 2005; Lucertini et al. , 2004). The diagrammatic type of mathematics applied requires a superior sense of spatial awareness than formal mathematics as shown by the Rhombicuboctahedron.
After studying traditional mathematics from Luca Pacioli, a renowned scholar, Leonardo collaborated with him to produce a book in the 1490’s (Lucertini et al. , 2004). He drew geometrical shapes that had a mathematical importance in engraved plate form that were later used in printing presses. The work of Leonardo and Pacioli, Divina Proportione, was published in 1509 (Cremante et al. , 2005). According to Leonardo, mathematics was an important painting tool, and he states in one of his books that those who had not studied mathematics should not even begin reading his work. Conclusion
Born from a humble background, Leonardo was the personification of a “Renaissance man. ” Being a possessor of keen intellect and a curious mind, Leonardo studied scientific and natural laws that significantly informed his work as an architect, painter, inventor, sculptor, military engineer and draftsman. His ideas and works such as “Mona Lisa,” The Last Supper” and “Virgin of the Rocks,” have had an immense influence on countless artists thereby making him a leading light during the Italian Renaissance. Importantly, his mathematical insights into geometry are no less substantial than those of notable philosophers in the field.