Introduction to the Golden Ratio

The Golden Ratio, often denoted by the Greek letter phi (φ), is an irrational number approximately equal to 1.618. It has fascinated mathematicians, artists, and architects for centuries due to its unique properties and aesthetic appeal. The ratio can be found in various natural phenomena, and it has been employed in art and architecture to create visually pleasing compositions. This project examines three diverse examples of the Golden Ratio in art and architecture, showcasing its application and significance.

Example 1: The Parthenon

The Parthenon, an ancient temple dedicated to the goddess Athena, is a prime example of the Golden Ratio in architecture. Located on the Acropolis of Athens, this structure is renowned for its perfect proportions and harmony.

In the Parthenon, the ratio of the width to the height of the facade approximates the Golden Ratio. The longer sides of the building correspond to a length that is approximately 1.618 times the shorter sides, creating a visually balanced appearance. Additionally, the placement of columns and other architectural features follows this ratio, enhancing the temple’s aesthetic appeal.

For a science fair project, students can explore how the Golden Ratio influences modern architecture by comparing the Parthenon with contemporary buildings that utilize similar proportions.

Notes/Variations:

• Compare the Parthenon to other ancient structures, such as the Temple of Hephaestus, to analyze the use of the Golden Ratio in different contexts.
• Create scale drawings to illustrate the ratio on paper and visualize the proportions.

Example 2: The Mona Lisa

Leonardo da Vinci’s famous painting, the Mona Lisa, is not only celebrated for its artistic mastery but also for its use of the Golden Ratio. The dimensions of the painting itself and the positioning of key elements align closely with this mathematical concept.

In the Mona Lisa, the ratio of the width of the canvas to its height is approximately 1.618. Furthermore, the placement of the subject’s face and the horizon line follows the Golden Ratio, creating a sense of balance and focus that draws the viewer’s eye. This meticulous attention to proportion contributes to the painting’s enduring appeal.

For a science fair project, one could analyze other works by da Vinci to see how the Golden Ratio appears in his paintings and explore the impact of this ratio on visual perception.

Notes/Variations:

• Create a grid overlay on a printed image of the Mona Lisa to visually demonstrate the Golden Ratio in the composition.
• Research additional artists who have utilized the Golden Ratio, such as Salvador Dalí or Piet Mondrian.

Example 3: The Great Pyramid of Giza

The Great Pyramid of Giza, one of the Seven Wonders of the Ancient World, is another striking example of the Golden Ratio in architecture. Built as a tomb for the Pharaoh Khufu, this monumental structure exhibits remarkable geometric precision.

If we analyze the pyramid’s dimensions, the ratio of its height to the length of one of its sides closely approximates the Golden Ratio. This intentional use of proportion not only reflects mathematical sophistication but also contributes to the pyramid’s visual grandeur. The alignment of the pyramid with cardinal points further enhances its architectural significance.

For a science fair project, students can create models of the Great Pyramid and calculate the ratios involved, comparing them to the Golden Ratio to understand its application in ancient engineering.

Notes/Variations:

• Explore the significance of the Golden Ratio in other ancient structures like Stonehenge or the Colosseum.
• Develop a presentation that includes 3D models or digital simulations to illustrate the proportions involved.