What is a Golden Rectangle?
A rectangle whose sides are in the Golden Ratio. A rectangle is a Golden Rectangle when the ratio of the length plus the width to the length equals the ratio of the length to the width.
A golden rectangle is a special kind of rectangle where the sides follow the golden ratio. That means the relationship between the length and the width is the same as the golden ratio, about 1.618.
In a golden rectangle:
- The ratio of the length plus width to the length is the same as
- The ratio of the length to the width
We can write this as:
\(\Large\frac{l + w}{l}\) = \(\Large\frac{l}{w}\)
Golden rectangles are considered very pleasing to the eye, which is why artists, architects, and designers have used them for thousands of years. You can find examples of golden rectangles in:
- Ancient buildings like the Parthenon
- Famous art like the Mona Lisa
- Everyday objects like books, credit cards, and screens
When Do Students Learn About Golden Rectangles?
Golden rectangles are often introduced as an enrichment topic when students explore geometry, proportions, or the golden ratio, usually in middle school or high school.
Grades 6–8 – Discovering Shapes and Ratios
Students may explore golden rectangles when learning about ratios, patterns, and the golden ratio in geometry or art-based math projects.
Grades 9+ – Applying Golden Rectangles in Math and Art
Students connect golden rectangles to algebraic ratios, Fibonacci numbers, and real-world design.
