Friday, April 24, 2009

Smoke gets in your eyes

One of the world's most recognized figures is the Vitruvian Man by Leonardo da Vinci. The accompanying notes to this particular drawing, written in mirror writing, was made as a study of the proportions of the human body was based on the works of the ancient Roman architect Marcus Vitruvius.

Leonardo da Vinci's artistic works are many, the most well known are the "Last Supper" and the "Portrait of Lisa Gherardini, wife of Francesco del Giocondo". The latter, drawn in sfumato, is also known as La Gioconda (Mona Lisa).

In collaboration with Luca Pacioli, a contemporary mathematician, da Vinci drew the illustrations of the regular solids in De divina proportione. The subject of this manuscript was mathematical and artistic proportion, especially the mathematics of the golden ratio and its application in architecture.

Friday, April 10, 2009

fe fi fo fum

Pi day is celebrated on March 14 of each year. Pi is an irrational number (its value cannot be expressed exactly as a fraction), represented by the Greek letter Π, is a mathematical constant whose value is the ratio of any circle's circumference to its diameter.

The Greek letter phi (φ) represents the golden ratio which is also is an irrational mathematical constant, with a value of approximately 1.6180339887. Unfortunately, the value of of the phi cannot be easily converted to a calendar date.

However, August 13th is a day that can be celebrated by a number of special people around the world.

Wednesday, April 1, 2009

A rose by any other name is just as sweet

Gertrude Stein wrote "Rose is a rose is a rose is a rose." The trick of this phrase is using the law of thricefold repetition, for emphasis of a particular point. However, a spiral is not a spiral is not a spiral.

One of the better known geometric forms is the Archimedean spiral, named after Archimedes, the famous ancient mathematician. This form is found in windup springs in mechanical toys and analog watches.
Another type of spiral, that is more frequent in Nature, is the logarithmic spiral. The best visual example of this type of spiral is the cut away section of the Nautilus Shell. A special type of logarithmic spiral is the Fibonacci spiral, which is based on the golden ratio. Many discussions have been made regarding artists having used in their works an approximation of the golden ratio in order to make it more aesthetically pleasing.

Philosophiæ Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica