Essay 2 | Page 1
Dr. Shanyu Ji | Math 4388, Section 18577
ART USES MATHEMATICS AS ITS ULTIMATE TOOL:
The Golden Ratio and Linear Perspective
Have you ever wondered how painters are able to paint three dimensions onto a flat surface making it look almost like a photograph? How are they able to paint the subjects of their piece proportional in size to one another to make it more realistic? Before the Renaissance period, which was between 1400 and 1600, artists did not use certain mathematical tactics in their work. Perspective was considered but applied using inaccurate methods and proportions were not always apparent. During the Renaissance, individuals like Leonardo da Vinci and
Filippo Brunelleschi contributed to society and mathematics by rediscovering and reintroducing ideas such as proportion and perspective. Not everyone sees art as a science, but it truly is because many works are made inconsideration with mathematical calculations and tactics.
Before the Renaissance period, many countries in Europe were experiencing poverty and disease. Religion played a vital role in society and culture in European countries. Due to religious constraints, individuals during this time were not able to explore and discover new techniques in mathematics.1 The birthplace of the Renaissance era was in Italy, where Italian cities were able to grow, flourish, and establish trading networks, which gave citizens room to discover and practice academics and other trades. It was a movement towards humanism, where humans strived to become the best they can be rather than be limited to study theology and medieval practices. This allowed individuals to rediscover the work of previous mathematicians and scientists, which is why this era was known as the ‘rebirth’ of society.2
1 "What Was Life like before the Renaissance?" Birthplace of the Renaissance. 2013. Accessed September 29, 2016. 2 Shuttleworth, Martyn. "Renaissance Science - The Path to Enlightenment." Explorable. Accessed September 29, 2016. Essay 2 | Page 2
Individuals reexamined and added onto intellectual ideology from works previously written by Greeks, Egyptians, and others before the conquest of the Roman Empire. Revisiting previous works led Leonardo da Vinci, who was an artist, mathematician, and inventor during this era, to rediscover Euclid’s formula for the ‘Golden Ratio’ (Figure 1). Euclid was the first to
record the definition of the Golden
Ratio in his work, “Elements” around
300 B.C.3 The ‘Golden Ratio’ is
represent as the Greek uppercase letter
Φ or � for lower case modern Greek,
Figure 1: The ‘Golden Ratio’ by Euclid which is known as Phi and its unique (Used by Artists Like Leonardo da Vinci) Taken from http://www.livescience.com/37704-phi-golden-ratio.html value is rounded off to 1.618. It is also known as the Golden Number, Golden Proportion, Golden Mean, and many others because it has been rediscovered numerous times.
The formula for the Golden Ratio is described as