September 2006 - mathfun@mailman.xmission.com

[math-fun] LATimes: Jeannine Mosely: Hole new take on a sponge
by Henry Baker 02 Sep '06

02 Sep '06

http://www.calendarlive.com/galleriesandmuseums/cl-et-galleries1sep01,0,137… September 1, 2006 AROUND THE GALLERIES Hole new take on a sponge *Artist makes a mathematical figure come to life, with folded business cards and lots of time. By David Pagel, Special to The Times On first glance, the exhibition at Machine Project looks like a standard recap of Minimalism. Three tidy white cubes rest on pedestals in the otherwise empty storefront gallery. But a closer look reveals something wondrous another brain-stretching, comprehension-defying, do-it-yourself exercise with many of the ingredients with which Echo Park's small, weekends-only gallery has been making a name for itself for the last couple of years. There is low-tech labor-intensity, hands-on dexterity, profound curiosity about the ordinary world and an unflagging passion for the complexity of the seemingly simplest of things. Each cube is an intricate mathematical figure known as a Menger sponge, made of folded business cards. These "origami fractals" were fashioned by software engineer Jeannine Mosely, with hundreds of volunteers assisting on the biggest. The smallest measures 6 inches on a side. It's built from 168 folded business cards and takes a novice about 90 minutes to make. It's easy if you follow the precisely illustrated instructions in a field guide that accompanies the exhibition. The $8 booklet, co-written by Mosely and curator Margaret Wertheim of the Institute for Figuring, includes a brief history of the Menger sponge, its place in physics and a biographic sketch of its inventor, Austrian mathematician Karl Menger (1902-85). The medium-size piece, known as a Level Two sponge, is an 18-inch cube made of 3,456 business cards. It took Mosely 30 hours to construct. The centerpiece, a Level Three sponge, is a 54-inch cube made of 66,048 cards. It weighs 150 pounds and exceeded Mosley's 600-hour fabrication estimate exponentially. She began in 1995 and finished in 2004, with more than a little help from her friends. Actually building something turns out to be a lot more complicated and time consuming than conceptualizing it in the abstract or designing it on paper. Describing a Menger's sponge is no mean feat. Here is how Mosely begins her contribution to the field guide: "Take a cube, divide it into 27 (3 x 3 x 3) smaller cubes of the same size; now remove the cube in the center of each face plus the cube at the center of the whole. You are left with a structure consisting of the eight small corner cubes plus twelve small edge cubes holding them together. Now, imagine repeating this process on each of these remaining twenty cubes. Repeat again, and again, ad infinitum ...." This accounts for the lacy appearance of the business card cube, which increases as the size of the cube does. Seeing three together invites the mind's eye to picture a fourth. And a fifth, if your imagination is up to it. And so on, with no end in sight. Eventually you are left with a cube that occupies space but no longer fills it. Menger sponges hover in the ambiguous space been two and three dimensions. The beauty of fractals is that they describe the world far more accurately than such simple geometric shapes as cubes, spheres and cones. Grasping their formal structure, however, requires a bit of mental agility. The beauty of Mosely's sculpture is that it makes this easier for everyone, inspiring awe in the everyday stuff all around us and doing its little bit to keep minds open, engaged and in action. Machine Project, 1200-D N. Alvarado St., (213) 483-8761, through Sept. 24. Open Saturdays and Sundays only.

1 0

RE: Re: Re: [math-fun] Choreography of large complete graphs
by Andy Latto 01 Sep '06

01 Sep '06

> -----Original Message----- > From: math-fun-bounces+andy.latto=pobox.com(a)mailman.xmission.com > [mailto:math-fun-bounces+andy.latto=pobox.com@mailman.xmission.com]On > Behalf Of Michael Kleber > Sent: Friday, September 01, 2006 12:22 PM > To: math-fun > Subject: Re: Re: Re: [math-fun] Choreography of large complete graphs > > > In my rephrasing of Otto's solution, I should have mentioned that > this method of having everyone meet everyone else is commonly > used in English Country line dances, those described by the > original source (John Playford, from 1651 on) as "longways for as > many as will". It's also what change-ringers refer to as "plain hunt on an odd number of bells", and may be even older in this context than in dancing. Andy Latto andy.latto(a)pobox.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun >

1 0

[math-fun] William Shanks, historical computation of pi available on google books.
by Simon Plouffe 31 Aug '06

31 Aug '06

Hello, there are a number of significant documents that are available with Google Book service, they apparently added quite a collection of full and complete documents. One of them is of interest : The historical computation of Pi using Machin formula by William Shanks. http://books.google.com/books?vid=0A2yyrfAXNsNSwg9B-&id=axjockOKyikC&pg=PA2… and the following pages describe the digits, the formulas and results, quite interesting! and the result is : http://books.google.com/books?vid=0A2yyrfAXNsNSwg9B-&id=axjockOKyikC&pg=PA2… which contains the known error. Another document is the Differential Calculus by De Morgan: http://books.google.com/books?vid=08Wx_wKklYK4hOCS&id=95x4IrIcHrgC&printsec… These documents are normaly quite difficult to get and see for real even in a big city with lots of libraries around... Simon Plouffe

1 0