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Mathematics and Art – III


The Golden Ratio, or Golden Number, has been well known for centuries as a pleasing balance of length to height and is seen in nature. Therefore, it is commonly used in Architecture and Art. For mathematicians, this ratio is called Phi:

Phi (Φ and φ, pronounced [fī]) is a Greek letter. In mathematics it is used to represent the number 1.6180339887…,  the key number in the Golden Ratio. Many living organisms grow according to the golden ratio; the bones in a human  finger are proportioned in a ratio of approximately 1:1.6; the branching of veins and nerves in animals and humans  follow similar proportions. (click here for source and other examples) Click here for more info!
This “Golden Ratio” is based on the Fibonacci Series and is thought by many to be a foundational code in our universe. Click on this youtube video (3min 42sec) for more info:

Another great example of Golden Ratios can be found in the famous painting of the Mona Lisa, by Leonardo da Vinci:

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The graph on the left (Coronavirus) is for a time period of 30 days, while the one on the right (SARS) is for 8 months! Very poor graphical comparison and hardly relevant, unless it is attempting to downplay the seriousness of the coronavirus?

10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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