Wednesday, February 10, 2010
The connection between music and mathematics has fascinated scholars for centuries. More than 200 years ago Pythagoras reportedly discovered that pleasing musical intervals could be described using simple ratios.
And the so-called musica universalis or "music of the spheres" emerged in the Middle Ages as the philosophical idea that the proportions in the movements of the celestial bodies -- the sun, moon and planets -- could be viewed as a form of music, inaudible but perfectly harmonious.
Now, three music professors – Clifton Callender at Florida State University, Ian Quinn at Yale University and Dmitri Tymoczko at Princeton University -- have devised a new way of analyzing and categorizing music that takes advantage of the deep, complex mathematics they see enmeshed in its very fabric.
Writing in the April 18 issue of Science, the trio has outlined a method called "geometrical music theory" that translates the language of musical theory into that of contemporary geometry. They take sequences of notes, like chords, rhythms and scales, and categorize them so they can be grouped into "families."
Creativity in mathematics
Mathematicians have always felt a strong creative aspect in their subject, but only in recent years has the flowering of connections between mathematics and the arts made this aspect apparent to the general public. This collection of three articles explores some of the various ways in which art and beauty appear in mathematics.
Mathematics and MimeIn "Envisioning the Invisible", Tim Chartier describes how the performing arts can be used to capture mathematical concepts...In one of Chartier's mime sketches, he gets the audience to visualize the one-dimensional number line as a rope of infinite length.....
Mathematics and Music
How does the brain sometimes fool us when we listen to music, and how have composers used such illusions?....How can math help create new music?...
Mathematics and Visual Art
...The forms emerging from this iterated function system are fractals. By serendipity, the article on music by Don et al employs some of Barnsely's work on fractal images to produce new music. Using Barnsley's Iterated Function Systems formulas, the authors created fractal images of a fern and of Sierpinski's triangle and used these images to create notes for musical compositions...
Sunday, February 7, 2010
The Egyptians supposedly used it to guide the construction the Pyramids. The architecture of ancient Athens is thought to have been based on it. Fictional Harvard symbologist Robert Langdon tried to unravel its mysteries in the novel The Da Vinci Code.
"It" is the golden ratio, a geometric proportion that has been theorized to be the most aesthetically pleasing to the eye and has been the root of countless mysteries over the centuries. Now, a Duke University engineer has found it to be a compelling springboard to unify vision, thought and movement under a single law of nature's design.
Also know the divine proportion, the golden ratio describes a rectangle with a length roughly one and a half times its width. Many artists and architects have fashioned their works around this proportion. For example, the Parthenon in Athens and Leonardo da Vinci's painting Mona Lisa are commonly cited examples of the ratio.(Image credit: yorgos.ca)
Wednesday, February 3, 2010
Thanks to medical imaging techniques such as X-ray CT, ultrasound imaging and MRI, doctors have long been able to see to varying degrees what's going on inside a patient's body, and now a Texas A&M University mathematician is trying to find new and better ways to do so.
The professor, Peter Kuchment, a leading researcher in mathematical techniques for medical imaging, says the research may enhance the process for detecting cancer and many other diseases.
When talking about medical imaging, most people know that physics and computer sciences are involved, but few may be aware that mathematics is indispensable. Indeed, many imaging methods are based on mathematical analysis.
(Image credit: tutorvista.com)