Transcription
Mathematics and music. You're by mathematics in the kindest places. Watch.
First, we'll need a straight stretch. It good and tight. Pocket. Now divide in half. Plunk. Again. You see it's the same tone, one octave higher. Now divide the next section and the next.
The flag was discovered. The octave had a ratio of 2 to 1 with simple fractions. He got this, and from this, harmony in numbers developed the musical scale of today. The mathematical discoveries. Only members were allowed to attend. They had a secret temple.
Pentagram. It was our old friend Pythagoras who discovered that the pentagram was full of mathematics. The two shorter lines combined exactly equal the third, and this line shows the magic proportions of the famous golden section. The second and third lines exactly equal the fourth. Once again, we have the golden section.
But this is only the beginning. Hidden within the pentagram is a secret for creating a golden rectangle, which the Greeks admired for its beautiful proportions and magic qualities. The star contains the golden rectangle many times over.
[Music]
It's a most remarkable shape. It can mathematically reproduce itself indefinitely. All these rectangles have exactly the same proportions. This figure also contains a magic spiral that repeats the proportions of the golden section into infinity.
To the Greeks, the golden rectangle represented a mathematical law of beauty. We find it in classical architecture. The Parthenon, perhaps one of the most famous of early Greek buildings, contains many golden rectangles.
[Music]
These same golden proportions are also found in their sculpture. In the centuries that followed, the golden rectangle dominated the idea of beauty and architecture throughout the Western world. The Cathedral of Notre Dame is an outstanding example. The Renaissance painters knew this secret.
World today. The golden rectangle is very much a part of our modern world. Modern painters have rediscovered the magic of these proportions. Indeed, this ideal proportion is to be found in life itself. Can't all be mathematically.
Now that you're all paired up in a pentagon, let's see how nature uses this same mathematical form. Petunia, the star jasmine, the wax. Whoa. Literally thousands of members in good standing in nature's Pythagorean Society of the star. All nature's works have a mathematical logic, and their patterns are limitless.
Magic proportions of the golden section are often found in the spirals of nature's designs. Confusion of mathematical forms brings to mind the words of the vagueness. Everything is arranged according to number and mathematical shape. Yes, there is mathematics and music and art and just about everything. And as the Greeks had guessed, the rules are always the same.