When mathematics is used in art, it combines an exact science with the beauty of the human soul. Nearly everything in art, from pyramids around the world to the placement of f-holes on a Stradivarius violin, has a basis in mathematics. The Divine Proportion, also called Phi (pronounced “fee”), the Golden Mean and the Magic Ratio, is 1 to approximately 1. 618. While it is merely an irrational number like Pi, Phi has many unusual mathematical properties. Originally the basis of Pagan beliefs, the Divine Proportion is prevalent in nature, and as such used in art.
Even the pentagram used in Pagan worship is an embodiment of Phi. In Edward Burne Jones’s ”The Golden Stairs’, the Divine Proportion is used to painstakingly plan the smallest details, from the length of the women’s dresses to the width of the interior door. The ‘Vitruvian Man’ by Da Vinci is based solely on the proportions of the human body. Da Vinci believed, and correctly so, that the naval of the human body can be drawn as the center of a circle so that the fingers and toes will rest on the edge.
Everything about the human body has a proportion, from palms to height to ears to face. Even with all these proportions, Phi is still prevalent. From the top of your head to the floor is proportionate to Phi to the height of your bellybutton to the floor. An equation to find how many words Shakespeare used in his plays versus how many he knew but did not use was preformed by statisticians Bradley Efron and Ronald Thisted. They began by counting the words he used versus how many times he used them.
They discovered that 14,376 words were used once, 4343 words were used twice, and so on. Shakespeare used 31,534 different words and a whopping total of 884,647 words within his complete works. The two projected that, given enough new samples of the work of Shakespeare beyond what we know he wrote, there would be 35,000 new words that he did not use. They reached the conclusion that Shakespeare knew approximately 66, 534 words. Their projection has been used practically to identify other Shakespearean works. Music is completely dependant on math.
Pythagoras, most famous for the Pythagorean Theorem, was the first to study music in a mathematical since. He discovered that on the stringed harp, the note C is 4/5 of A, that the note D is 3/4 of A, that E is 2/3 of A, and so on. Pythagoras noticed that the notes of the strings, 1, 2, 3, 4, 5, lined up with the 5 planets known to exist and that they moved along their orbits in similar ratios. Later, of course, it was discovered that the universe is irrational, but it was an interesting bit of knowledge at the time.
Greek music only had 6 notes, (a minor scale, which sounds tragic and goes along with most Greek poetry), but soon these ratios were combined to create the 12 notes of the modern octave. Unfortunately, this led to problems, as musicians realized that the octave starting at A and the octave at A# is radically different. Around the time of Bach, 2 to the 1/12th power was used to create a “well tempered” scale. 21/2 is a constant in music and is used as the ratio between half tones (from A flat to A to A sharp. ) In the art of arranging flowers, Geometry is an asset.
The placement of the flowers must flow naturally, but it must also adhere to certain mathematical constants. The florist uses 3-Dimensional Spatial Geometry to express what is wanted for the space. Also, the size of the container used is directly proportional to the size of the finished arrangement. Phi is used here, so that an arrangement is either approximately 1. 618 times taller than its container, or it is inversely proportionate so that the height of the container is approximately 1. 618 times as tall as the arrangement.
