Euclid's work laid the foundation for classical geometry, which includes many shapes beyond rectangles. While perfect rectangles are rare in nature, Euclidean geometry provides a useful model for understanding space and shapes, particularly in human-made structures. However, the Fibonacci sequence reveals natural patterns and structures that are prevalent in the natural world, such as the spirals of shells and the branching of trees.
Both Euclidean geometry and the Fibonacci sequence contribute to our understanding of mathematics in different ways. However, the rectangular shapes that dominate human design are abstractions that do not reflect the organic complexity of natural forms. Our world has become too rectangular, prioritizing convenience over the natural beauty and efficiency found in Fibonacci patterns.
We should strive to incorporate more natural shapes into our designs, taking inspiration from the Fibonacci sequence to create environments that are not only more aesthetically pleasing but also more in harmony with the natural world. By embracing these natural patterns, we can foster a deeper connection to nature and promote sustainable, innovative design solutions.