Week2_by Heeseok Lee_Interlinking between Art and Mathematics in Pyramid

As an engineer, I have taken so many mathematics classes from Algebra to Calculus in college, and I have realized that math brings numerous artistic characteristics. Especially, for problem-solving, Mathematics always requires to bring up some imagination or creative thought to reach the answer. In addition, Mathematician also has creativity as much as Artist does. Personally, I think that Both Art and Mathematic are oriented in the same motivation, in terms of seeking and trying to explain how the nature works. Only differences are that Art takes more advantages of not having limit on appealing their thought or idea while mathematic is outlined and has boundaries under some rules and principles.
From historical piece of art or architecture, It is easily seen how math and art are interlinked and enables each other to be more expressive and completed. Most of all, pyramids shows a good example of how ancient Egyptian used mathematical concept on designing of it and constructing process. Pyramids shows golden ration as pantheon shows, as mentioned in lecture. If you take a cross-section through a pyramid, you would get a triangle. If the pyramid is the Great Pyramid, we get the so-called Egyptian Triangle. It is also called the Triangle of Price, and the Kepler triangle. The ratio of the slant height(S) to half the base(B) is said to be the golden ratio. From my high school’s trigonometry class , I was supposed to verify this golden ratio in pyramids by computation of Slant Height.

*Here is my computation to verify existence of Golden ratio in pyramid.
height = 146.515 m,   and    base = 230.363 m
(These values are determined by various expeditions.)
Half the base is      230.363   ÷   2 = 115.182 m
So,  S^2 = 146.515 + 115.182 2 = 34,733 m2
S = 18636.9 mm
Dividing slant height s by half base gives
186.369   ÷   115.182 = 1.61804
The Egyptian triangle thus has a base of 1 and it equals to hypothetical value. Its height h,
h^ 2=  Φ^2 – 1^2  as solving for h, value of Φ^1/2 is determined.
By Computing the value for the height of the Egyptian triangle to verify the ratio .
1: Φ^1/2: Φ
Therefore, the sides of the Egyptian triangle are in the golden ratio
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In addition, pyramids contains not only mathematical concept used but also full of symbolism.
“If flooding of the Nile symbolized the annual return of watery chaos, then geometry, used to reestablish the boundaries, was perhaps seen as restoring law and order on earth. We’ll see this notion again of geometry being sacred because it represents order, especially in the Middle Ages. The rope stretchers triangle when opened out gives a zodiac circle, with the number of knots the most important of the astrological numbers. The square, with its four corners like the corners of a house, represents earthly things, while the circle, perfect, endless, infinite, has often been taken to represent the divine or godly. So squaring the circle is a universal symbol of bringing the earthly and mundane into a proper relationship with the divine, and the Golden Ratio reverberates with the idea of the Golden Mean, the principle of moderation, defined by Aristotle as the mean between the two extremes of excess and insufficiency, as generosity is the mean between prodigality and stinginess, and by Horace, called the philosopher of the golden mean, advocated moderation even in the pursuit of virtue.” (Heroditus Book II, Paragraphs 124, 135)
I was very impressed that Egyptian artists used mathematical concept and ratio to reflect their values and thoughts. Although it is modern scholars’ interpretation and assumption, but it is really amazing to see how ancient people put art and math/science in one masterpiece. It is very unpleasant to see how Art and Science fields are divided and generally do not put effort to interlink and collaborate with each other to seek more accurate way to express and explain our thoughts, values, and the principles of world where we are living.

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844 Responses to “Week2_by Heeseok Lee_Interlinking between Art and Mathematics in Pyramid”

  1. Heeseok Lee says:

    I posted this on Week1 by mistake, I just re-posted here Week2, that’s why it appears as Jan19.

  2. afingrut says:

    cool.

  3. [...] apply the golden ratio theory to pyramid by calculating whether it was constructed in golden ratio. http://classes.design.ucla.edu/Winter09/9-1/blog/a/?p=578 In every single structure in pyramid, there exists ancient Egyptian culture, their value, and even [...]