
	Where results make sense

Topic: Flexagon

In the News (Thu 16 Oct 08)

Tamil Nadu

American Airlines

Bob Schieffer

Steven Gerrard

Stephen Harper

Richard Garriott

Janet Jackson

Iron Man

Steve Jobs

Atletico Madrid

	Flexagon - Wikipedia, the free encyclopedia
		The discovery of the first flexagon, a trihexaflexagon, is credited to the British student Arthur H. Stone who was studying at Princeton University in the USA in 1939, allegedly while he was playing with the strips he had cut off his A4 paper to convert it to letter size.
		Flexagons were introduced to the general public by the recreational mathematician Martin Gardner writing in Scientific American magazine.
		The construction of the tritetraflexagon is similar to the mechanism used in the traditional Jacob's Ladder children's toy, in Rubik's Magic and in the magic wallet trick.
	en.wikipedia.org /wiki/Flexagon (826 words)

	Kathryn Huxtable's Flexagon Page
		Flexagons were discovered in 1939 by Arthur H. Stone, then a graduate student at Princeton University.
		There are many kinds of flexagons, with varying numbers of faces and edges, but I find the symmetric hexaflexagons the most interesting.
		Not rotating the flexagon between flexes, or rotating an extra 60 degrees allows escape from the original cycle into another, which includes the face just flexed from, plus the face which would have been flexed into, with its triangles permuted, plus a new face not part of the original cycle.
	www.kathrynhuxtable.org /flexagon (716 words)

	Flexagon: Encyclopedia topic (Site not responding. Last check: 2007-10-13)
		In geometry (geometry: The pure mathematics of points and lines and curves and surfaces), flexagons are flat models made from folded strips of paper that can be folded, or flexed, to reveal a number of hidden faces.
		Flexagons were introduced to the general public by the recreational mathematician (recreational mathematician: recreational mathematics includes many mathematical games, and can be extended to cover...
		To reveal it, fold the flexagon flat and then unfold it, like this: The construction of the tritetraflexagon is similar to the mechanism used in the traditional Jacob's Ladder (Jacob's Ladder: the original jacobs ladder was the biblical jacobs ladder_(bible)ladder to heaven...
	www.absoluteastronomy.com /reference/flexagon (542 words)

	LavaCUBED \Science\Math\Recreations\Flexagons (Site not responding. Last check: 2007-10-13)
		Flexagons - Includes a definition of the word, instructions on how to make a Trihexaflexagon, how to flex it and information about it and another flexagon.
		Flexagons - Contains instructions on how to fold a flexagon, history of flexagons and printable models of some.
		Flexagons - 1962 technical report which includes an introduction to the history of Flexagons.
	www.lavacubed.com /new.cats.php?path=/Science/Math/Recreations/Flexagons (125 words)

	Building and Operating the Flexagon
		In order to flex the flexagon, one must first find a hinge between two pats at which the thumb of finger can be passed between the two leaves of the larger pat.
		As the flexagon is now flexed and turned over, and the various sides are approached via various other sides, the marking devices, or ``dots", indicate that different angles of the leaves are brought to the center of the flexagon at different times.
		This is the distortion of the heretofore constant order of the sides in the flexagon structure, which is usually accomplished accidentally, and wich often results in a disassembly and consequent reassembly of the flexagon involved.
	theory.lcs.mit.edu /~edemaine/flexagons/Conrad-Hartline-1962/node3.html (2392 words)

	Magnus Enarsson
		A flexagon is a polygon folded from paper with a very remarkable quality; you can turn it inside out to make it reveal hidden surfaces.
		The B corners will now be at the edge and the A corners will be at the center on the back of the flexagon.
		If the flexagon doesn't open like a flower, you have to flatten it again and try with the other three alternating corners (unmarked).
	www.enarsson.nu /Flexagon (484 words)

	My Flexagon Experiences
		Flexagons were always something to play with, and one kept one hearing them mentioned, or finding them recognized in one way or another.
		A flexagon is really defined by one third of the visible hexagon, so three identical sectors have to be prepared; of course that can be done from the outset by making the figure three times as long, by repeating one sector three times.
		Once the normal flexagons have been established, any number of variants come to mind, beginning with relaxing the building rules of the primitive stack to include other polygons besides the regular ones, oe even foregoing the assumption that they are all equal.
	delta.cs.cinvestav.mx /~mcintosh/comun/fxgonw/fxgon.html (5544 words)

	flexagon
		Flexagons are amusing toys but they have also caught the interest of mathematicians.
		The discovery of the first flexagon, a trihexaflexagon, is credited to the British student Arthur H. Stone who was studying at Princeton University in 1939.
		Flexagons were introduced to the general public by Martin Gardner writing in Scientific American.
	www.daviddarling.info /encyclopedia/F/flexagon.html (257 words)

	Flexagons (Site not responding. Last check: 2007-10-13)
		A flexagon is a polygon, usually made from paper, that can be folded in certain ways to produce a series of faces.
		The specific name of each flexagon has two prefixes, the first stating how many faces can be made to appear, and the second giving the shape of the flexagon.
		Triangles that are the same color end up on the same face when the flexagon has been constructed (with the exception of the gray faces, which are the two ends glued or taped together in the last step of each construction).
	www.geocities.com /CapeCanaveral/Hangar/7773/flexagon.html (466 words)

	Flexagon Fever
		As the flexagon is flexed, sections shift position to create an almost kaleidoscopic effect, and different faces come into view, in cyclic order.
		It would have been lost on me at the time how coincidental it was that I was fascinated with both Alice and flexagons because the man who introduced flexagons to my sisters and the world at large, Martin Gardner in his mathematics columns for Scientific American, is also the author of The Annotated Alice.
		These are the second flexagons to be discovered (after the trihexaflexagon, which has six sides and three alternating faces) and the ones that have been anlayzed in the most detail.
	www.eighthsquare.com /flexagon.html (1649 words)

	Flexagon Discovery: The Shape-Shifting 12-Gon
		During this time I rediscovered the Flexagon Committee's 12- and 24-faced flexagons, made a flexing triangle, and folded what I thought was a tri-tetra-flexagon, a square composed of 8 right triangles.
		And the flexagon has what I call "rogue" triangles, a pair of triangles that swing along 1 hinge; the triangles are not attached to the flexagon on all 3 sides.
		After assembly, the flexagon’s triangles are radially arranged in alternating groups of thicknesses, the layers of paper heaped up in the individual piles of triangles.
	www.eighthsquare.com /12-gon.html (2470 words)

	Abebooks Search Results - Flexagon
		Flexagons bring maths to life and will appeal to anyone interested in puzzles or recreational maths.Flexagons are hinged polygons that have the intriguing property of displaying different pairs of faces when they are flexed.
		Flexagons have a surprisingly complex mathematical structure and just how a flexagon works is not obvious on casual examination of a paper model.
		Flexagons are described as "paper polygons, folded from straight or crooked strips of paper, which have the fascinating property of changing their faces when they are flexed." Plans of houses, studios, Manila City plans, a magnet master, a "string lamp", a keel chair" etc. are included.Printed in 1960.
	www.abebooks.co.uk /search/sortby/3/kn/Flexagon (3007 words)

	Construction of a -Flexagon of General Order .
		If we now rotate the flexagon and attempt to flex, the flexagon instead opens up using a set of hinges other than the 1-hinges and becomes a closed strip of four polygons in which the hinges do not meet in the center.
		Any flexagon made so that it always flexes left (or right if it is wound the other way) will be called a proper flexagon.
		If we add a new side by slitting the single left hand leaf in a tubulating flexagon and hinging the new leaf in a number one position, we find that we have not destroyed the tubulation but rather we have hidden it by making it easier for the flexagon to flex using a 1-hinge.
	www.pbrc.hawaii.edu /~danh/flexagon/node9.html (1203 words)

	Introduction: The story of the Flexagon
		The story has it that Arthur Stone, an English graduate student, was in the practice of doodling with the strips of paper that he cut from around the edges of his notebook paper.
		It is, however, chiefly due to three influences that flexagons are as well known as they are today.
		Although flexagons have on several occasions been used as cards or announcements, the commercial possibilities they seem to present apparently have never been exploited.
	www.pbrc.hawaii.edu /~danh/flexagon/node2.html (486 words)

	Tetra-tetra-flexagon (Site not responding. Last check: 2007-10-13)
		Flexagons are folded paper polygons that have the fascinating property of changing their faces when they are flexed.
		Flexagons can be made from a pattern of squares or equilateral triangles.
		Turn the flexagon over so that the 2-squares are face up.
	britton.disted.camosun.bc.ca /tetraflex/jbtetraflex.htm (231 words)

	Better than Sex? \| MetaFilter
		Within days copies of these "flexagons" - or, as this subspecies came to be more precisely known, "hexahexaflexagons" (six sides, six internal faces) - were circulating across the [Princeton] dining hall at lunch and dinner.
		Rotate the flexagon so that one of those triangles is at 12 o'clock.
		I bought one from a science museum, it was covered with pictures of outer space, and looked a bit like a cross between a flexagon, a Hoberman sphere, and a doughnut.
	www.metafilter.com /mefi/33521 (1091 words)

	Flexagon theory
		A flexagon is effectively invariant when rotated by a third of a turn (we just get another two pats to look at which are the same as the two we just had).
		Flex your flexagon accordingly to the state diagram you have chosen; whenever the flexagon reaches a corner on the state diagram, make sure that there is only one thickness of paper in the middle top pat.
		But turn the flexagon over, and the sequence is reversed (it looks exactly the same except that R is now the top, and P the bottom).
	www.drking.plus.com /hexagons/flexagons/theory1.html (5298 words)

	Flexagon: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-13)
		Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons), Exception Handler: No article summary found.
		a flexagon with a total of six faces is called a hexahexaflexagon.
		Flexagons were introduced to the general public by the recreational mathematician (Recreational mathematics includes many mathematical games, and can be extended to cover such areas as logic...)
	www.absoluteastronomy.com /ref/flexagon (1329 words)

	Flexagon - TheBestLinks.com - Mathematician, Martin Gardner, Princeton University, Richard Feynman, ... (Site not responding. Last check: 2007-10-13)
		Flexagon - TheBestLinks.com - Mathematician, Martin Gardner, Princeton University, Richard Feynman,...
		Flexagon, Mathematician, Martin Gardner, Princeton University, Richard Feynman...
		Flexagons are flat models made from folded strips of paper that can be folded, or flexed, to reveal a number of hidden faces.
	www.thebestlinks.com /Flexagon.html (416 words)

	The Flexagon Funhouse (Site not responding. Last check: 2007-10-13)
		Tetra-tetra flexagon, offset printed, presents a photographic record of milestones in an artist's life.
		Revolving flexagon, offset printed in two colors, records quotes by famous Mexicans on art, education, life, death and politics.
		Tri-hexa flexagon, printed with carved erasers, used as a teaching tool for a workshop on artist books at the papermaking cooperative near Oaxaca, Mexico.
	www.artistbooks.com /editions/flexagons.html (139 words)

	Creative Ideas
		A Flexagon is a hexagon that rotates and flexes.
		Fold the left three triangles of the Flexagon upward and across (Figure B).
		The Flexagon will be stiff and difficult to bend at first.
	www.ellison.com /creativeideas?p=detail&idea=4326 (293 words)

	Blogger: Email Post to a Friend (Site not responding. Last check: 2007-10-13)
		When you fold or pinch corners together, the flexagon 'flexes,' meaning a formerly hidden layer will come to light as the top layer folds underneath." In a subsequent sister, Ela's sister, Ann Schwartz, writes about her discovery of the HEXA-DODECA-FLEXAGON, which, she explains, "...flexes into totally new shapes in its flattened positions.
		The hexa-dodeca flexagon also naturally combines triangles from its basic faces to produce a number of hybrid faces, all this with proper flexing, no twisting or pulling.
		Oddly enough, even when these triangles are not lying in what one would consider the right position, the hexa-dodeca still flexes smoothly."For those of us who share fascination in the ever unfolding mysteries of fun, Ela and Ann's delight is infectiously validating, no matter how many sides or shapes their toys of wonder embrace.
	www.blogger.com /email-post.g?blogID=3510012&postID=112343639426182469 (311 words)

	Flexagons
		Basically they are a sheet of paper folded and cut in a special way so that as well as having a front and a back you can fold them to reveal hidden sides.
		The most simplest flexagon is the tetra-flexagon meaning with 4 sides, this is the one we are going to make.
		You have to print the flexagon on two sides of the same paper so make sure they are aligned.
	www.mathemagic.org /MathsAndArt/flexagon.htm (276 words)

	Flexagons - discussions at ClueIn (Site not responding. Last check: 2007-10-13)
		A flexagon is a hexagon, which you can make from a strip of triangles.
		The objective is to open the flexagon in the middle and have a previously hidden face appear.
		Arthur Stone, an English graduate student, was in the practice of doodling with the strips of paper that he cut from around the edges of his notebook paper.
	www.cluein.com /clufrm_154416.aspx (194 words)

	Flexagon
		The flexagon was invented in 1939 by A. Stone, a graduate student at Princeton University.
		Most of what is known about the flexagon was laid out by this group during their Flexagon Committee meetings.
		The flexagon is usually made from a strip of paper divided into triangles and folded into an arrangment similar to a Mobius strip only with more twists.
	www.dcgeorge.com /gpage12.html (682 words)

	Make Your Own Flexagon
		Turn the flexagon over you are back you started.
		Technically, this structure is called a "tetra-tetra flexagon" (it has four faces and four sides).
		Some go in one direction to a dead end, some return to their starting point and some branch off into different directions.
	www.artistbooks.com /flexagons/flexmake.html (281 words)

	David Mitchell's Origami Heaven - Flexagons - A Flexagon Bibliography
		The last six pages are devoted to templates from which the flexagons discussed in the earlier pages can easily be constructed.
		The bulk of the book consists of vividly decorated templates for eleven different flexagons, which are structured to present a series of increasingly difficult manipulative challenges.
		The booklet also includes details of Robert E Neale's remarkable Cross Flexagon and what may well be the first ever publication of a silverflexagon design (though the potential inherent in the design is not explored).
	www.mizushobai.freeserve.co.uk /flexbibliography.htm (471 words)

	Murderous Maths: The Fabulous Flexagons
		A flexagon looks like a piece of card folded into a hexagon shape, but you can turn it inside out.
		The first one is a simple "triflexagon" which is just for a bit of practise, and then we'll make the amazing "hexaflexagon".
		We found a nice site with much tidier pictures than ours (but they forgot to include a bloke with rolling eyes.) It's: FLEXAGONS and it even has a brilliant moving demo of a hexaflexagon which we are very jealous of.
	www.murderousmaths.co.uk /games/flex/flexmake.htm (1186 words)

Try your search on: Qwika (all wikis)