Throughout history, thinkers from mathematicians to artists have pondered the mysterious relationship between number and form. This relationship is captured in many ancient works of art such as the Parthenon of Greece, the Pyramids, and also in more recent works like Leonardo Da Vinci's Mona Lisa. Mathematical proportions have been conveyed in many forms of art, architecture, music, and nature that bring beauty, order and mystery to people and cultures everywhere.
Looking into the past, through the millennia, we can see the use of these proportions and ratios emerge. The use of mathematical tools from the straightedge, to the more sophisticated computer technology, has given us the beautiful perspective, symmetry, and patterns seen in art. These proportions have been shown to us through the use of these tools from the paintings in the time of Greek culture, to the fractal geometry of modern technology in the present. We can also see that many of these ideas and mathematical uses have, and are being used in architectural design. Ratios such as the Golden Mean have been seen everywhere in architecture of the past, and even in the design of modern buildings. This Golden Mean proportion is a ratio of numbers, which has fascinated generation after generation, and brought mystery to cultures all over the world in the past. This wondrous ratio can also be seen, heard, and felt in music. One of the first people to attempt to mathematically understand the essence of musical harmonic proportions was Pythagoras. Also, Mozart and Beethoven have been believed to use mathematics such as the Golden Mean ratio in the composure of their musical pieces. The many interconnections between mathematics, music, art, and architecture are such that it would take years of research and study to fully understand all of the relationships between them. .
The book Exploring the Invisible, by Lynn Gamwell, explores how Pythagoras discovered a mathematical basis to music, and how mathematics is used in the creation of abstract art.