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Hypothesis/Conjecture

Most famous paintings will show the Golden Ratio, with Van Gogh having more instances of the Golden Ratio than Monet or Picasso. I think that Van Gogh will have the most because his paintings are popular with a lot of people.

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What is the Golden Ratio?

The Golden Ratio is said to result in the most pleasing shape, and is found by using the formula a/b = a+b/a. The formula is equal to about 1.618, also known as Phi (𝛗). Like Pi, it never repeats or terminates, making it an irrational number. It is not a shape, but a comparison to the length and width. Phi is connected with the Fibonacci Sequence, which is also found in nature.

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Materials

Dimensions of most famous paintings according to websites (Starry Night, Cafe Terrace at Night, Painter of Sunflowers, Impression, Sunrise, Woman With a Parsol - Madame Monet and Her Son, The Artist’s Garden At Giverny, The Weeping Woman, The Old Guitarist, Girl Before a Mirror)

Calculator

Scissors

Paper to cut and to record data

Yellow-Van Gogh

Blue-Monet

Green-Picasso

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Procedure

Use dimensions of paintings
Split the long side by a square the based on the short side(lay the square over),and divide the square’s length by the remaining side that is not covered up’s length.
Then see if it is 1.61803399….
Also check for other appearances of the golden ratio; trails, positions of people, etc.
Record the data

Black square width ÷ blue rectangle width

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Data Table

Starry Night	No Golden Ratio, but the star/swirls have (or are based off) the Golden Spiral (the spiral on the background on page 4 that can be made by making more golden rectangles in a already golden rectangle)
Cafe Terrace at Night	No Golden Ratio
Painter of Sunflowers	No Golden Ratio
Impression, Sunrise	No Golden Ratio
Woman With a Parasol-Madame Monet and Her Son	No, but the people in the painting reside in a Golden Section (an area of the painting that is golden, but the whole painting is not golden)
The Artist’s Garden at Giverny	No Golden Ratio
The Weeping Woman	No Golden Ratio
The Old Guitarist	No Golden Ratio
Girl Before a Mirror	No Golden Ratio

Van Gogh=Orange

Monet=Blue

Picasso=Green

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Conclusion and Proofs

My hypothesis was rejected.

Phi showed up 0 out of 9 times that I calculated, but Monet and Van Gogh had paintings with the Golden Ratio, however it was not in the dimensions of the painting.

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Real World Connection

This project relates to the real world because we see the golden ratio everyday and you are not completely aware of it. Your brain subconsciously notices it and thinks, hmmm, this looks nice, and you then enjoy looking at it, but you never consciously know. A lot of visually pleasing things follow the Golden Ratio.*

*Hurricanes follow the Golden Ratio,

we hear a lot about them! So do

tornadoes, whirlpools, and tsunamis.

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