A large portion of the Italian Renaissance was an obsession with finding order in everything in the universe. Its primary actors sought to show nature as orderly and fundamentally simple. Leonardo Da Vinci, the epitome of the Renaissance Man, was not the first to apply these ideas of geometric order and patterns to art, but he may be the most well known. Da Vinci used mathematical concepts like linear perspective, proportion and geometry in much of his artwork.

Leonardo did intensive studies on linear perspective. He applied this method to much of his work. According to the Thames and Hudson Dictionary of Art Terms, linear perspective is “the method of representing a 3-D object or a particular volume of space on a flat surface.” By making all of the lines in the painting converge on an single, invisible point on the horizon, a flat painting can appear to have depth. The Last Supper is a mural Da Vinci painted in the refectory of the church, Santa Maria delle Grazie. By using this method, Da Vinci made the painting appear to be an extension of the room itself (Brizio, 52). It should be noted that The Last Supper is his final piece showing evidence of linear perspective. It was completed in 1498. Of the 14 paintings attributed to Da Vinci before 1500, only four use linear perspective (Zwijnenberg, 130-5). So it is clear he was not bound by any one method, just as he was not bound by any one field of study. - Source

Leonardo Da Vinci, like other artists of his time, paid particular attention to proportion. In The Last Supper, he sought to create a perfect harmonic balance between the placement of the characters and the background. He did intensive studies on how the characters should be arranged at the table. Also, and it was not discovered until recently, he used a complex formula based on the relationship 12:6:4:3. According to Turner, the entire piece measures 6 by 12 units. The wall in the back is equal to 4 units. The windows are 3 units and the recession of the tapestries on the side walls is 12:6:4:3. These ratios are also very present in music. 3:4 is the interval of one fourth, 4:6 is a fifth, and 6:12 is an octave. It makes sense that Leonardo did this, he once noted on “the resonance between visual and aural harmonies.” He thought making use of this ratio would “offer praise to the harmonies of the universe” (Turner, 213). The image below is somewhat distorted and is not the complete mural, so it is difficult to fully appreciate the harmonic proportion. But this is an excellent example of linear perspective. - Source

Da Vinci elaborated on the relationship between painting and geometry in the first five sections of Paragone, a book written sometime between 1500 and 1505. He said, “the point is the first principle of geometry and no other thing can exist in nature or in the human mind from which the point can originate.” He said the other principles of geometry are the line, the surface and the “body clothed by these surfaces” (Zwijnenberg, 50-1). The Virgin of the Rocks, another very well known Da Vinci piece, incorporates geometry in a more concrete fashion. The arrangement of the four characters (the baby Jesus, Mary, an angel and the infant John the Baptist) is a triangle. The triangle can be interpreted in more than one-way, but once noticed, appears to be in stark contrast to the rich, organic background (Turner, 211). - Source

Leonardo contributed to the study of geometry in another way. He studied polyhedra with many other influential men of his time. Only five regular convex polyhedra can exist in a three dimensional space. This was known well before the Common Era, but Plato tried to use them as the basic building blocks for the cosmos, so today they are known as Plutonic solids. Leonardo contributed 60 drawings of the Plutonic solids to the De Divina Propotione, which was completed in 1509 (Emmer).

Leonardo Da Vinci’s use of mathematics in art was well ahead of his time. Some things he did were not fully understood until well after his death. He used linear perspective, proportion and geometry in many of his most famous pieces. This exaggerated attempt to achieve order, which was characteristic of the Italian Renaissance, is sometimes criticized. But he created harmony and balance in such a unique and beautiful way that his work is still studied 500 years later. - Source

Consideration for Ancientminds.com -

Leonardo Da Vinci is becoming one of my favorite ancient minds. In a lot of ways, I am like him. He is a artist, inventor, and mathematician. These are all aspects of my life that I love. Not only that, but he is a procrastinator. That is me in a nut shell. Like Da Vinci, I too start many artistic projects and leave them unresolved for one reason or another. Usually, it is a mental issue that blocks my ability to do good works.

Ancient Uniqueness -

There are not many people in the world that can match the likeness of Leonardo Da Vinci. He had the mind to invent, paint the most amazing pictures, and write about life and love. He also was way ahead when it came to anatomy and human understanding. He was a pioneer of the Renaissance era. Leonardo Da Vinci is still one of the most admired and famous people to have lived on the planet Earth. It is an honor to study him.

Please note that this site is strictly a hobby site. The authors of any pages do not have degree's nor wish to be accredited for any work. We are just stating that there is more out there than what you may realize. All information is food for thought.