Proportion and the Golden Ratio: Fresh Take

  • Understand the concept of proportion and its significance in art, design, and architecture
  • Interpret and explain the golden ratio and the rule of thirds, including their applications in art, design, and architecture
  • Utilize the golden ratio and the rule of thirds to analyze and assess the composition of artworks, designs, and architectural structures

Understanding Proportions

The Main Idea 

Proportions refer to the relationship of size, quantity, or degree between different elements of a composition in art, design, and architecture. Proportions directly influence how a composition is perceived, affecting its aesthetics, functionality, and overall impact.

There are three types of proportions:

  • Symmetrical Proportion: This occurs when elements are mirrored on either side of an axis. It creates a sense of balance, harmony and stability.
  • Asymmetrical Proportion: This involves different elements that balance each other out, without being identical. It creates a more dynamic and visually interesting composition.
  • Hierarchical Proportion: This involves elements sized according to their importance or rank. For example, in graphic design, the most important information is often the largest and most noticeable.

Understanding proportion is a crucial aspect of design literacy and plays a significant role in the success of a design.

You can view the transcript for “PROPORTION in Art | The Principles of Design EXPLAINED!” here (opens in new window).

Proportional Systems

Golden Ratio

The Main Idea 

The golden ratio, approximately equal to [latex]1.618[/latex], is a mathematical concept found in many aspects of the natural world and used extensively in art, design, and architecture. It is thought to be aesthetically pleasing due to its balance and harmony.

If a person’s height is [latex]6[/latex] ft [latex]2[/latex] in, what is the approximate length from their belly button to the floor rounded to the nearest inch if the ratio is golden?

Golden Ratio and the Fibonacci Sequence Relationship

The Main Idea 

The Fibonacci Sequence is a series of numbers where each number is the sum of the two preceding ones, often starting with [latex]0[/latex] and [latex]1[/latex]. This sequence has a close relationship with the Golden Ratio; as the sequence progresses, the ratio of consecutive Fibonacci numbers converges to the Golden Ratio.

You can view the transcript for “What is the Fibonacci Sequence & the Golden Ratio? Simple Explanation and Examples in Everyday Life” here (opens in new window).

If a circular row on a pinecone contains [latex]21[/latex] scales and models the Fibonacci sequence, approximately how many scales would be found on the next circular row?

The [latex]23[/latex]rd Fibonacci number is [latex]28,657[/latex] and [latex]24[/latex]th is [latex]46,368[/latex]. Show that the ratio of the [latex]24[/latex]th and [latex]23[/latex]rd Fibonacci numbers is approximately [latex]\phi[/latex]. Round your answer to the nearest thousandth.

Golden Rectangles

The Main Idea 

A golden rectangle is a rectangle whose length to width ratio is the golden ratio. It possesses the unique property of remaining a golden rectangle even after removing a square. This shape, which is related to the Fibonacci sequence and the golden ratio, is often found in architectural and artistic designs due to its pleasing aesthetic qualities.

A frame has dimensions of [latex]10[/latex] in by [latex]8[/latex] in. Calculate the ratio of the sides rounded to the nearest thousandth and determine if the size approximates a golden rectangle.

Golden Ratio in Art

In art, the golden ratio has been used as a principle of aesthetic proportion. When a line is divided into two parts in such a way that the ratio of the whole line to the larger part is equal to the ratio of the larger part to the smaller part, this is said to exemplify the golden ratio. Many artists and designers use the golden ratio to create compositions that are visually balanced and harmonious.

It’s thought that Leonardo da Vinci’s “Mona Lisa” and “The Last Supper” and Salvador Dali’s “The Sacrament of the Last Supper” incorporate the golden ratio. However, its presence in art often invites debate, as interpretations can be subjective.

Golden Ratio in Design

In design, the golden ratio is employed to create pleasing, organic, and harmonious proportions. It is frequently applied in graphic design, logo design, product design, and even website design. Many designers create a golden rectangle, to guide the layout and placement of elements.

Golden Ratio in Architecture

The golden ratio is also observed in architecture. From the Parthenon in Athens to the Pyramids of Egypt, to more modern structures, the golden ratio has been used to create buildings that are pleasing to the eye due to their sense of balance and proportion. The architect Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion.

The Rule of Thirds

You can view the transcript for “Understanding the Rule of Thirds | Adobe Design Principles Course” here (opens in new window).