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Topic: Heesch

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Noord Brabant

Bernheze

	Heesch number
		The Heesch number of a triangle, quadrilateral, regular hexagon, or any other single shape that can completely tile the plane (see tiling), is infinity.
		The Heesch number of a shape is the maximum value of k for which all tiles in the k-th corona of any tiling are congruent to that shape.
		This was thought to have a Heesch number of three; however, in 2000, Alex Day argued that the Ammann hexagon actually has a Heesch number of four, though there is a dispute about whether the difference has to do with a definition of tiling.
	www.daviddarling.info /encyclopedia/H/Heesch_number.html (492 words)

	Heesch's Problem
		The Heesch number of a shape is the maximum value of k for which all tiles in the kth corona of any tiling are congruent to that shape.
		Heesch's problem is to determine the largest possible finite Heesch number, or more generally what values other than zero and infinity can occur as the Heesch numbers.
		It was believed that this shape had Heesch number three, until in April 2000 Alex Day pointed out that the actual number is four (perhaps this simply reflects a disagreement on the definition of a tiling, since his tiling is not simply connected -- the common boundary of certain pairs of tiles is disconnected).
	www.ics.uci.edu /~eppstein/junkyard/heesch (753 words)

	Heesch
		Heesch number 3 examples (The first one was discovered by Robert Ammann, and it was the record holder for a long time):
		The proof that Amman's tile has Heesch number 3 is quite nice, and this proof stimulated some research on my part.
		Of course, a prototile that can be used to tile the entire plane has infinite Heesch number, but I am interested in those prototiles that cannot be used to tile the plane.
	math.uttyl.edu /cmann/math/heesch/heesch.htm (628 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Heesch stated, ``Physicians Search is a 30 year old legend in the world of physician recruiting, having placed thousands of physicians throughout the United States and around the world.
		Heesch stated, ``Athlete's foot is an age-old problem that most people experience at one time or another in their life.
		Heesch stated, ``In contrast to our announcements concerning treatments for wound healing and scar prevention, we feel confident, with the patients we have treated, that the numbers are sufficient to prepare a marketing plan for sale of this medication sometime in early 2002.
	www.acor.org /drugs/pipeline/companies/news/3269.news (802 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		The authors of [2] define a Heesch tile with Heesch number r to be a tile T which can be surrounded r times but not r+1 times by tiles congruent to T. Let us define the surround number of a tile T to be the minimum number of such tiles needed to surround T once.
		It is clear that this tile is a Heesch tile with Heesch number 1.
		To show that this is indeed a Heesch tile with Heesch number 1, we start with the following observation: semicircular bumps in a straight line can only be completely covered by a single tile.
	www.stetson.edu /~efriedma/papers/heesch/heesch.html (346 words)

	SGVTribune.com - Heesch guilty of shooting Realtor (Site not responding. Last check: 2007-10-22)
		A Pomona Superior Court jury found John Steven Heesch, 29, guilty of assault with a firearm in the Nov. 1 shooting of Ontario resident Eric Hinks, 30.
		Heesch is scheduled to be sentenced in August.
		John Heesch, who lives near his younger brother's home on Hipass Drive in Diamond Bar, claimed he thought Hinks was someone he'd had an altercation with in Orange County when he saw him walking to James Heesch's door, Cabral said.
	www.sgvtribune.com /news/ci_4077686 (356 words)

	Brothers Charged in Alleged Shooting of Real Estate Agent
		John Steven Heesch, (dob 7-28-76), is charged with one count of assault with a firearm, with the special allegation of causing great bodily injury and personal use of a firearm in case No. KA072907, said Deputy District Attorney Abram Weisbrot.
		Heesch’s brother, James Howard Heesch Jr., (dob 9-23-78), is charged with one count of possession of marijuana for sale and one count of cultivating marijuana.
		John Heesch, who is being held on $150,000 bail, is scheduled to be arraigned after 1:30 p.m.
	da.co.la.ca.us /mr/archive/2005/110305a.htm (202 words)

	Unified Judicial System (Site not responding. Last check: 2007-10-22)
		As Heesch and Ewer entered section five, Schouten removed his pillow from the pillow case and threw the pillow case against the door of his cell.
		Heesch observed the spit leave Schouten’s mouth and fly toward him through the mesh of the cell door.
		Heesch moved his head back and to the left, but the spit struck him on the right cheek in two places.
	www.sdjudicial.com /index.asp?category=opinions&nav=53&year=2005&month=12&record=1486 (2496 words)

	Meridian Magazine :: Music : Music for Missionaries
		Other than an occasional private concert or a brief performance in sacrament meeting, Heesch's singing was put on hold while he made a living to support his wife Varna and six children (who’ve so far provided 12 grandchildren).
		Heesch's CD, released on the Eagle Records label, is the kind of romantic album that takes you back to the days when high school dances featured dance bands (and real dancing with actual dance steps), velvet-voiced singers, and musical instruments besides guitars and drum sets.
		Cuts from Heesch’s album are being played on local radio stations in that state, and he hopes they’ll soon be heard nationwide.
	www.meridianmagazine.com /music/040206sweet.html (664 words)

	The Gazette-Enterprise
		Public Affairs Officer Jack Heesch said out of 25,000 to 30,000 evacuees in the greater San Antonio area, only 273 were still living in temporary housing.
		As for those who have been considered ineligible, Heesch said the situation is usually a matter of lack of paperwork or miscommunication.
		However, Heesch said the number of hurricane evacuees is likely much higher because only the head of household is required to sign up with the agency.
	www.seguingazette.com /story.lasso?ewcd=0ec5f475403b6c65 (571 words)

	CD Baby: CRAIG HEESCH: From Out of the Wings
		Craig Heesch a dreamy melt on your ear singer and former recording artist returns with this new album.
		In 1961 a young vocalist named Craig Heesch was singing and recording as Craig Adams for Overland Records in Hollywood, California.
		CVA Entertainment and CVA Records are very pleased to present the return of the wonderful musical talent of this great crooner Craig Heesch with his new album, "From Out of the Wings" as well as his exciting live performances.
	www.cdbaby.com /cd/heesch (698 words)

	Complaint: SEC v. Frank J. Custable, Jr., et al.
		The officer defendants are: 1) Gary Heesch ("Heesch"), and David Giles ("Giles") of Wasatch, 2) David Calkins ("Calkins") of Pacel, and 3) Richard Bailey ("Bailey") of Gateway.
		As part of the requested temporary restraining order, the Commission seeks to have the Court require Wasatch, Heesch and Giles to provide an accounting of their assets and for the transactions that are the subject of this action and to be prohibited from destroying or concealing documents relevant to this action.
		Gary Heesch ("Heesch") is the Chief Executive Officer and a director of Wasatch and a resident of Utah.
	www.sec.gov /litigation/complaints/comp18057.htm (7021 words)

	Apple Computer - Education (Site not responding. Last check: 2007-10-22)
		Carmel College Heesch is the secondary school for Heesch, a town with a population of about 15,000 and situated in an agricultural area of the Netherlands.
		The school belongs to a religious foundation called the Carmel Foundation (http://www.carmel.nl) and is the smallest of the secondary schools in this group.
		Carmel College Heesch has become one of the 100 ICT pilot schools established by the Netherlands education ministry and one of its responsibilities is to exchange with other schools the discoveries it has made in the use of ICT with students.
	www.apple.com /es/education/ads/netherlands.html (898 words)

	M103 Notes 3-22-05
		A given set S of configurations can be proved unavoidable if for a triangulation T which does not contain a configuration in S we can redistribute the charges (without changing the total charge) so that no vertex ends up with a positive charge.
		Heesch thought that the Four Colour Conjecture could be solved by considering a set of around 8900 configurations.
		There were difficulties with his approach since some of his configurations had a boundary of up to 18 edges and could not be tested for reducibility.
	www.humboldt.edu /~mef2/Courses/m103n3_22_05.html (1068 words)

	Archives: Story (Site not responding. Last check: 2007-10-22)
		Sparta finally began to find the bottom of the bucket midway through the second period, but by then the Golden Eagles had built a lead that would prove to be insurmountable.
		Mauston coach Joel Heesch was happy to see his young squad get out of the gates with a win.
		Heesch said one of the key things he liked about Tuesday's win was the fact that he was able to rotate 10 players into the game and keep continuity.
	star-times.scwn.com /articles/2004/12/04/news/sports/sports2.txt (624 words)

	Cheryl Heesch (Site not responding. Last check: 2007-10-22)
		Dr. Heesch's research is focused on central nervous system regulation of blood pressure and efferent sympathetic nerve activity in both physiological and pathophysiological states, such as hypertension.
		One major project in the laboratory is directed towards elucidating the central nervous system sites, and transmitters involved, in both inhibitory and excitatory influences on efferent sympathetic outflow.
		Neurosteroid modulation of arterial baroreflex sensitive neurons in the rostral ventrolateral medulla of the rat.
	www.cvm.missouri.edu /vbms/faculty/heesch.html (328 words)

	The Four Color Theorem (Site not responding. Last check: 2007-10-22)
		While the concept of reducibility was studied by other researchers as well, it appears that the idea of discharging, crucial for the unavoidability part of the proof, is due to Heesch, and that it was he who conjectured that a suitable development of this method would solve the Four Color Problem.
		We confirm a conjecture of Heesch that in proving unavoidability, a reducible configuration can be found in the second neighborhood of an "overcharged" vertex; this is how we avoid "immersion" problems that were a major source of complication for Appel and Haken.
		K has ring-size at least 2, where the ring-size of K is defined to be the sum of g(v)-deg(v)-1, summed over all vertices v incident with the infinite region such that G\v is connected.
	www.math.gatech.edu /~thomas/FC/fourcolor.html (1878 words)

	AMERICAN MATHEMATICAL MONTHLY -April 2004
		Surprising consequences of these new results are: several families of incongruent solids having both equal volume and equal total surface area; the quadrature of the sine curve; and the centroid of any slice of a spherical surface.
		Heesch’s tiling problem concerns the number of layers that can be formed from copies of a tile T around a centrally placed copy of T (this number is the Heesch number of T).
		We go on to discuss the connections of Heesch’s tiling problem to other famous unsolved tiling problems, including the Einstein problem that concerns aperiodic monotiles.
	www.maa.org /pubs/monthly_jun_jul04_toc.html (416 words)

	The Heesch Tile: An Interesting Non-Tiler (Site not responding. Last check: 2007-10-22)
		The Heesch Tile consists of a square joined to an equilateral triangle and a 30-60-90 half triangle as shown by the yellow tile at lower right.
		Here a ring of tiles in red and purple is completely enclosed by other Heesch Tiles.
		In fact the Heesch number of a tile is the number of times a single tile can be surrounded before the tiling breaks down.
	www.uwgb.edu /dutchs/symmetry/heesch.htm (183 words)

	Heesch's problem - Wikipedia, the free encyclopedia
		In geometry, the determination of the maximum number of times that any closed plane figure could be completely surrounded by congruent copies of itself is Heesch's problem.
		The number for a given figure is known as the Heesch number of that figure.
		This page was last modified 15:47, 16 November 2005.
	en.wikipedia.org /wiki/Heesch's_problem (74 words)

	Tess 1.63 - Make and explore symmetric illustrations. - tessellations, symmetry, drawing, illustrating, patterns, ...
		While you draw, Tess will maintain the symmetry group you have chosen; 11 rosette (circular), all 7 frieze (strip), and all 17 wallpaper groups are included.
		Tess also supports all 28 / 29 types of Heesch tilings.
		Tess, tessellations, symmetry, drawing, illustrating, patterns, Heesch, tiling, manifold
	www.freetrialsoft.com /Tess-review-15045.html (91 words)

	Self-surrounding tiles
		The tile is a square joined to an equilateral triangle and a 30-60-90 triangle, as shown, and you can surround it with copies of itself, so that each point on the central tile’s perimeter is a positive distance (> 0) from any point exterior to the area covered by the tiles.
		But tiles that surround themselves once seem to be not too hard to find, at least if you don’t require convexity.
		He has also discovered an infinite family of Heesch tiles based on odd-order regular polygons; like mine, his are concave, but his are bilaterally symmetrical and resemble heart-shapes.
	home.flash.net /~markthom/html/self-surrounding_tiles.html (1097 words)

	cannabisnews.com: Raid Turns Deadly
		Twenty of them went to the split-level house on Overlook Drive that Rasanen was renting.According to Heesch, the events transpired this way: Eight officers from State Police's Mobile Response Team walked up to the front door, announced they were coming in, and used a battering ram to enter.
		Rasanen sprang up, Heesch said, and the shooting occurred."It's very quick," Heesch said.Heesch said all four raids were linked as part of the ongoing investigation of East End drug sales.
		All four of the state cops in the room during the shooting are being questioned about the incident.
	www.cannabisnews.com /news/thread12879.shtml (1650 words)

	Pascal van Heesch
		Pascal van Heesch is a Dutch photographer who specialises in social documentary photography.
		He usually produces work in series, so that the viewer can follow the story of ordinary people, often within their daily or work environment.
		All work is available, with permission, for publication on high quality scans as well a limited number on archival quality baryt prints.
	www.photoboxgallery.com /pascalvanheesch (267 words)

	A Tile with Heesch Number 1 and Surround Number 2 (Site not responding. Last check: 2007-10-22)
		A Tile with Heesch Number 1 and Surround Number 2
		The surround number of a tile is the minimum number of congruent copies of that tile that can be used to completely surround the tile.
		It was conjectured by Erich Friedman that a tile with surround number 2 does not exist (see ref. (1)).
	www.math.unl.edu /~cmann/math/surround/surround2.htm (64 words)

	A tiling by Heesch answering a question of Hilbert (Site not responding. Last check: 2007-10-22)
		A tiling by Heesch answering a question of Hilbert
		The tiling by Heesch, published in 1935, answers the question in the positive.
		Moreover, any tiling of the plane with this tile has at least 2 transitivity classes.
	www.spsu.edu /math/tiling/17.html (63 words)

	Koders Search: dimitri (Site not responding. Last check: 2007-10-22)
		Results 1-25 of about 143 results found for 'dimitri' in 0.14 seconds
		/* * Copyright (C) 1997-2000 by Dimitri van Heesch and Sven Meyer.
		(C) 1997-2000 by Dimitri van Heesch & Sven Meyer.
	www.koders.com /?s=dimitri (1054 words)

	CNS Effects of Ovarian Hormones and Metabolites on Neural Control of Circulation -- HEESCH and FOLEY 940 (1): 348 -- ...
		CNS Effects of Ovarian Hormones and Metabolites on Neural Control of Circulation -- HEESCH and FOLEY 940 (1): 348 -- Annals of the New York Academy of Sciences
		Articles by HEESCH, C. Articles by FOLEY, C. Articles citing this Article
		Address for correspondence: Dr. Cheryl M. Heesch, University of Missouri Dalton Cardiovascular Research Center, Research Park, Columbia, MO 65211-3300.
	www.annalsnyas.org /cgi/content/abstract/940/1/348 (365 words)

	Education :: Tess 1.52 by Pedagoguery Software Inc. tessellations, symmetry, drawing, ...
		Education :: Tess 1.52 by Pedagoguery Software Inc. tessellations, symmetry, drawing, illustrating, patterns, Heesch, tiling, manifold
		Tess also supports all 28 types of Heesch tilings.
		Using cracks, key generators, illegal serial numbers & registration codes prevents developing new software.
	mysoftwear.com /go/0405/10992512383e89cd28a66b9.html (90 words)

	Math Illustrator Update From Pedagoguery \|\| The Mac Observer
		You can now create a Heesch tiling by selecting "New Heesch Tiling" under "File".
		Information on Heesch tilings can be viewed by selecting "Heesch Tilings" from the help menu
		All 28 Heesch tilings are supported; Heesch tilings are symmetric illustrations that use a single type of tile to fill the plane without gaps
	www.macobserver.com /article/2001/12/14.4.shtml (605 words)

	Heesch Software: Tess
		Make and explore symmetric illustrations, tilings, and tessellations.
		tessellations, symmetry, drawing, illustrating, patterns, Heesch, tiling, manifold
		It works great for me, I ended up putting it on all the PCS in the office (a total of 22) and centralized the restriction list.
	www.windfile.com /find/heesch (107 words)

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