tag:blogger.com,1999:blog-362699732014-04-15T14:46:25.341-05:00The Mathematical TouristMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.comBlogger172125tag:blogger.com,1999:blog-36269973.post-17936644130037678262013-12-10T17:07:00.002-05:002013-12-10T17:07:46.862-05:00Pinball Chaos
Sending a steel ball speeding across a tilted board studded with
bumpers can be an addictive pastime—a tantalizing blend of skill to keep the
ball in play and unpredictability in the ball's erratic path, rebound by rebound.
The pinball
machine can serve as a model of deterministic chaos—a system that embodies a sensitive
dependence on initial conditions. Balls with slightly different Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-16340772936641915352013-11-26T21:14:00.000-05:002013-11-26T21:14:40.959-05:00Restroom Illusions
There's something to tickle the eye just about anywhere you
go at San Francisco's Exploratorium—even
the restrooms.
The entryway to the main pair of restrooms features a
dramatic array of black and white ceramic tiles, carefully arranged to recreate
an optical effect known as the Café Wall Illusion.
Described and popularized by psychologist Richard Gregory, the illusion makes the
parallel Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-10546907373029318952013-11-24T21:01:00.001-05:002013-11-24T21:01:03.352-05:00Counting on Success
The setup looks simple, but people attracted to the long row
of nine-sided, wooden rings at the Exploratorium
in San Francisco can't resist trying it—again and again.
Each ring bears the numbers from 1 to 9. You "shuffle" the
rings, rotating them so that you can read a scrambled string of digits along
the top of the row.
Starting at one end, you think of a number from 1 to 9, and
Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com1tag:blogger.com,1999:blog-36269973.post-22036761555225696892013-10-18T10:09:00.000-05:002013-10-19T20:14:40.933-05:00Martin Gardner and Mathematics, Magic, and Mystery
One of my fonder memories of growing up in an isolated
town in northwestern Ontario in the 1950s was my delight when the mail
brought fresh issues of Humpty Dumpty's
Magazine and Children's Digest.
What I didn't appreciate until long afterward was that Martin Gardner was a key
contributor to the early success of these magazines.
For Humpty Dumpty,
Gardner was responsible for writing stories Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-83497088252408052442013-08-19T19:47:00.001-05:002013-08-19T19:48:31.410-05:00Cross-Stitch Symmetry
The craft of counted
cross-stitch lends itself to the creation of elegant patterns on fabric,
and mathematician Mary D. Shepherd
has taken advantage of this form of needlework to vividly illustrate a wide
variety of symmetry patterns.
Mary Shepherd with her cross-stitch symmetries sampler.
Photo by I. Peterson
The fabric that Shepherd uses is a grid of squares, and the
basic stitch Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com1tag:blogger.com,1999:blog-36269973.post-86018566022992885542013-08-15T20:51:00.001-05:002013-08-19T19:18:00.401-05:00Möbius Mentions I
References to Möbius strips can pop
up unexpectedly in all sorts of settings, including novels. I'm especially
intrigued by examples in which the term is used without further explanation.
The reader is expected to understand the reference and know all about the peculiar
one-sided, one-edged character of this mathematical object.
One example that I recently encountered is in an amusing,
quirkyMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-24741761292735882872013-06-25T20:20:00.000-05:002013-06-25T20:20:04.284-05:00Pentagons and Game BallsThe game of sepak takraw, a popular form of kick volleyball in Southeast Asia, uses a woven ball that, in its simplest form, has 12 pentagonal holes and shows a weaving pattern with 20 intersections. The twelve pentagons remind me of a regular dodecahedron, one of the Platonic solids.
Traditionally made from rattan, such a ball may be constructed from six long strips (instructions), with five Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-84666368833929135112013-06-24T19:48:00.000-05:002013-06-24T19:48:38.053-05:00Elevator Buttons and Stone StepsHuman activity can leave telltale marks on its surroundings. These marks, in turn, can provide clues about the nature of the activity that created them or about the setting itself. See, for example, "Statistical Wear" and "An Irresistible Edge."
Recently, I started paying attention to wear caused by finger contact in the vicinity of elevator buttons. Shown below is a set of buttons for a hotel Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com2tag:blogger.com,1999:blog-36269973.post-30172209644696178832013-06-23T09:17:00.000-05:002013-06-23T09:17:11.516-05:00Roots of a Base Tiling
Like a strangely ordered root system, a fragment of an Archimedean tiling serves as the supporting structure for a metal pillar in an odd artwork in downtown Toronto. The sculpture, which consists of a pair of quirkily incomplete pedestrian bridges, stretches across paving bricks amid the restored, industrial-style buildings of the city's Distillery Historic District.
Titled Passerelle et Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-89652220432960860362013-03-17T11:44:00.000-05:002013-03-17T11:44:17.713-05:00Wild Beasts around the Corner
Some mathematical problems are easy to describe but turn out to be
notoriously difficult to solve. In some instances, these difficulties may stem
from fundamental issues of provability, especially for mathematical problems apparently poised
between order and chaos.
In a provocative article titled "On
Unsettleable Arithmetical Problems," John H.
Conway (Princeton University) offers some Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com1tag:blogger.com,1999:blog-36269973.post-33824483636367227192012-12-15T14:20:00.000-05:002012-12-15T14:20:42.568-05:00Umbilic Torus, Writ Large
Stony Brook University
has a new landmark—a gracefully contoured, intricately patterned ring that
rises 24 feet above its granite base. Installed
and dedicated
in October, this bronze sculpture is a visual testament to the beauty of mathematics.
Created by noted sculptor and mathematician Helaman Ferguson, the sculpture was
constructed from 144 bronze plates, each one unique and formed in a Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-41802892523990886912012-12-03T20:05:00.000-05:002012-12-03T20:22:09.449-05:00A Normal Haystack
This gracefully contoured haystack at the Ikalto Monastery in the
country of Georgia has a symmetric shape that resembles the characteristic "bell" curve of a normal distribution—with
a readily visible y-axis poking
through the top.
Photo by I. PetersonMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-27786921100925655882012-11-22T10:32:00.000-05:002012-11-22T10:32:03.236-05:00Crafting a Penrose Tiling
An array of wooden tiles assembled into an intriguing
pattern flecked with stars forms a striking contrast to the regular arrangement of bricks making up the
wall on which it hangs on the third floor of Avery Hall, home of the mathematics department at the University of
Nebraska-Lincoln.
Constructed by Nebraska mathematician Earl S. Kramer from diamond-shaped
cherry and maple tiles andMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com1tag:blogger.com,1999:blog-36269973.post-32502056252219181742012-11-17T12:47:00.000-05:002012-11-17T12:52:06.495-05:00Plaster Models of Mathematical Surfaces
The shapes of surfaces captured the imagination and attention
of many mathematicians during the nineteenth century. To unfold the visual
secrets compressed and hidden within the shorthand of algebraic expressions, geometers
drew pictures, fashioned models, and even wrote manuals on how to visualize or
construct geometric forms.
These models and drawings were not only a source of pleasureMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-66782260197111432812012-08-19T15:33:00.001-05:002013-10-23T09:46:07.905-05:00Ocean Park"The 'Ocean Park' paintings of contemporary artist Richard Diebenkorn glow with
a soft, hazy light. Translucent, luminous colors wash over barely
visible skeletons of horizontal, vertical and diagonal lines. Each canvas
stands as a window onto an abstract landscape—a serene sea or a stretch of open
land."
I wrote those words in 1986 to start off an article
for Science News magazine about an
Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-38313954881808239862012-08-19T09:34:00.000-05:002012-08-19T09:54:02.875-05:00Geometreks in Madison I: Van Vleck Hall
Van Vleck Hall houses the mathematics
department at the University of Wisconsin-Madison. Standing atop Bascom
Hill, it consists of an austere tower of offices and meeting rooms and a
classroom block burrowed into the hillside.
Designed by the architecture firm John J. Flad &
Associates, the complex was dedicated in 1963. It is named in honor of prominent
Wisconsin mathematics professor Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-21229558317089102072012-02-27T21:41:00.001-05:002012-02-27T21:50:29.528-05:00Endless Ribbon
Endless Ribbon by Max Bill (1953, original 1935), granite, Baltimore Museum of Art.
Swiss artist Max Bill (1908-1994) was a pioneer in sculpting Möbius strips. Starting in the 1930s, he created a variety of "endless ribbons" out of paper, metal, granite, and other materials.
When Bill first made a Möbius strip, in 1935 in Zurich, he thought he had invented a completely new shape.
The artist had Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-264883812566903902012-02-21T22:00:00.000-05:002012-02-21T22:00:58.809-05:00A Flight of Tetrahedra
Standing near the shore of a large pond, the sculpture looks poised for flight. Consisting of an overlapping array of eight tetrahedra, half painted black and half white, it slants steeply into the sky.
The alternating colors and triangular surfaces remind me of the Canada geese that strut nearby, unfolding their wings before they take flight and gather into their ragged V-formations.
Titled Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-1174255968821088262012-01-09T20:42:00.000-05:002012-01-09T20:42:08.850-05:00Twitter Math Journal
Courtesy of Frank Farris, Santa Clara University.
Published in Mathematics Magazine, Vol. 84, No. 4 (October 2009), p. 254.
We need more articles! Suggest titles and/or authors.Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com1tag:blogger.com,1999:blog-36269973.post-43604281860869372322012-01-08T21:18:00.000-05:002012-01-08T21:18:19.559-05:00Pleated Cone
This year's display of mathematical art at the Joint Mathematics Meetings in Boston featured an eye-popping array of three-dimensional structures. One of my favorites was a crinkled surface—an intricately pleated cone—crafted from a single sheet of blue paper.
Titled Pleated Multi-sliced Cone, this beautiful example of geometric origami was the product of a collaboration. Origami artist Robert JMath Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-61954828750311553572011-12-06T11:40:00.000-05:002011-12-06T11:40:48.764-05:00Geometreks in Boston
Boston skyline as seen from Cambridge, Mass., across the Charles River. The tallest building in the photo is the Prudential Tower at 800 Boylston Street. The skyscraper to its left is 111 Huntington Avenue, sometimes called the "R2-D2" building.
Boston will host the Joint Mathematics Meetings (JMM) on January 4-7, 2012, bringing more than 5,000 mathematicians to the city.
One of the more Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-21217557985183909082011-12-05T16:24:00.000-05:002011-12-05T16:24:45.508-05:00Beautiful Mathematics and Imaginative WordsSome years ago, David Wells surveyed readers of the Mathematical Intelligencer about what they consider to be beautiful in mathematics. The respondents ranked Euler's identity linking e, π, and i as the most beautiful expression in mathematics. See "Euler's Beauties."
In the intriguing new book Beautiful Mathematics (MAA, 2011), Martin Erickson expands on this theme, contemplating the esthetic Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com2tag:blogger.com,1999:blog-36269973.post-19632745808053208662011-10-27T20:56:00.000-05:002011-10-27T20:56:26.109-05:00Oval Track PuzzlesThe puzzle known as TopSpin consists of 20 circular pieces, numbered 1 to 20, filling and sliding along an oval track. TopSpin was introduced by ThinkFun (formerly Binary Arts) in 1988.
Pieces can be moved around the track in either direction, keeping their order. Or any four consecutive pieces can be maneuvered into reverse order. For example, consecutive pieces labeled 1, 2, 3, and 4, can be Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-47430438323150396892011-10-11T20:50:00.000-05:002011-10-11T20:50:20.821-05:00Split Strips"Möbius bands (or strips) are beautiful as objects of art, and their mysterious qualities fascinate those who discover or encounter them," sculptor Larry Frazier wrote in an article titled "Möbius strips of wood and alabaster," published in the Journal of Mathematics and the Arts.
"I'm not a mathematician, but as a sculptor, I have been fascinated by the myriad forms that a Möbius band can take, Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0tag:blogger.com,1999:blog-36269973.post-44655847272769248402011-10-07T21:04:00.000-05:002011-10-07T21:04:46.756-05:00LeWitt's Complex Form
To bring a trace of irregularity to his pristine geometric structures, conceptual and minimalist artist Sol LeWitt (1928-2007) started with a polygon sketched on a flat surface. He placed dots at various positions within the polygon. These points were then elevated to different heights, dictating the edges of the resulting three-dimensional, faceted object that eschewed the right angles typical Math Touristhttp://www.blogger.com/profile/00014397210725962876noreply@blogger.com0