randommarius:

“Phyllotactic Portrait of Fibonacci” by Robert Bosch

Mathematical artist Robert Bosch created this picture by adapting a well-known portrait of the Italian mathematician Leonardo Pisano Bigollo (c. 1170—1250), who was better known as Fibonacci.

Fibonacci described the sequence that bears his name in his 1202 book Liber Abaci, although the sequence was known to Indian mathematicians as early as the 6th century. The Fibonacci sequence begins 1, 1, 2, 3, 5, 8, 13, 21, the key property being that each of the terms from the third term onwards is the sum of the preceding two terms. 

Fibonacci used his sequence to study the growth of a population of rabbits, under idealising assumptions. The sequence can be used to model various biological phenomena, including the arrangement of leaves on a stem, which is known as phyllotaxis. Robert Bosch used a model of phyllotaxis to produce this picture. He explains:

Using a simple model of phyllotaxis (the process by which plant leaves or seeds are arranged on their stem), I positioned dots on a square canvas. By varying the radii of the dots, I made them resemble Fibonacci. Incidentally, the number of dots, 6765, is a Fibonacci number. So are the number of clockwise spirals (144) and counterclockwise spirals (233) formed by the dots. 

A framed version of this picture is currently being exhibited at the Bridges Exhibition at Gwacheon National Science Museum, Seoul. You can read more about the picture here: http://gallery.bridgesmathart.org/exhibitions/2014-bridges-conference/bobb. The same page discusses another version of the picture, also by Robert Bosch, but this time illustrating the Travelling Salesman problem. +Patrick Honner has posted about the other version of the picture here: https://plus.google.com/+PatrickHonner/posts/ALvhM8JK5kJ.

Relevant links

Robert Bosch’s website: http://www.dominoartwork.com 

Wikipedia on Leonardo Fibonacci: http://en.wikipedia.org/wiki/Fibonacci

The On-Line Encyclopedia of Integer Sequences on the Fibonacci numbers: http://oeis.org/A000045

Fibonacci numbers in nature: http://en.wikipedia.org/wiki/Fibonacci_number#In_nature

As well as featuring in this picture, the Fibonacci number 6765 is the name of an asteroid: http://en.wikipedia.org/wiki/6765_Fibonacci

“We’re also a band.” (http://en.wikipedia.org/wiki/The_Fibonaccis)

(Found via +Patrick Honner.)

#art #artist #mathematics #scienceeveryday

http://click-to-read-mo.re/p/8MYa/53e952d4

joerojasburke:

Mathematician Maryam Mirzakhani is the first woman to win a Fields Medal. It had been an all-boys club since the prizes were established in 1936.

Mirzakhani, a native of Iran, is a professor at Stanford University. She won for her work on “the dynamics and geometry of Riemann surfaces and their moduli spaces.”

Here’s how Nature summed up her contributions:

“Perhaps Maryam’s most important achievement is her work on dynamics,” says Curtis McMullen of Harvard University. Many natural problems in dynamics, such as the three-body problem of celestial mechanics (for example, interactions of the Sun, the Moon and Earth), have no exact mathematical solution. Mirzakhani found that in dynamical systems evolving in ways that twist and stretch their shape, the systems’ trajectories “are tightly constrained to follow algebraic laws”, says McMullen. He adds that Mirzakhani’s achievements “combine superb problem-solving ability, ambitious mathematical vision and fluency in many disciplines, which is unusual in the modern era, when considerable specialization is often required to reach the frontier”.

To Tumblr, Love Pixel Union