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Topic: Ham sandwich theorem

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Sandwich

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	Ham sandwich theorem - Wikipedia, the free encyclopedia
		The ham sandwich theorem, also known as the Stone-Tukey theorem in measure theory in mathematics, states that given n "objects" in n-dimensional space, it is possible to divide each one in half (according to volume) with a single (n − 1)-dimensional hyperplane.
		The ham sandwich theorem takes its name from the case when n = 3 and the three objects of any shape are a chunk of ham and two chunks of bread — notionally, a sandwich — which can then each be bisected with a single cut (i.e., a plane).
		In discrete geometry and computational geometry, the ham sandwich theorem usually refers to the special case in which each of the sets being divided is a finite set of points.
	en.wikipedia.org /wiki/Ham_sandwich_theorem (1086 words)

	Sandwich - Wikipedia, the free encyclopedia
		Sandwiches are commonly carried to work or school in lunchboxes or brown paper bags (sandwich bags) to be eaten as the midday meal, taken on picnics, hiking trips, or other outings.
		As part of a full meal sandwiches are traditionally accompanied with such side dishes as a serving of soup (soup-and-sandwich), a salad (salad-and-sandwich), or potato chips and a pickle or coleslaw.
		The sandwich theorem, frequently used in calculus and real analysis, states that if a real-valued function (the filling) lies everywhere between two other real-valued functions (the bread) which both converge to the same limit, then the "middle function" also converges to that limit.
	en.wikipedia.org /wiki/Sandwich (824 words)

	Squeeze theorem - Wikipedia, the free encyclopedia
		In calculus, the squeeze theorem (also known as the pinching theorem or the sandwich theorem) is a theorem regarding the limit of a function.
		The theorem asserts that if two functions approach the same limit at a point, and if a third function is "squeezed" ("pinched", "sandwiched") between those functions, then the third function also approaches that limit at that point.
		The squeeze theorem is a technical result which is very important in proofs in calculus and mathematical analysis.
	en.wikipedia.org /wiki/Squeeze_theorem (713 words)

	sandwich (Site not responding. Last check: 2007-10-20)
		The sandwich is a food item consisting of bread and other fillings such as one or more layers of meat (often a type of cold cut), cheese, vegetables, condiments, sauces or other filling.
		The dish was named after John Montagu, 4th Earl of Sandwich, an English aristocrat, in the 18th century, although it is unlikely to have been invented by him.
		Sandwiches are common foods to be taken on picnics or for hiking, and to bring to work, school, or outings for lunch in lunchboxes.
	www.yourencyclopedia.net /Sandwich.html (415 words)

	Sandwich - Unipedia (Site not responding. Last check: 2007-10-20)
		The sandwich is a food item typically consisting of two slices of bread between which are laid one or more layers of meat, cheese, or other filling, together with optional condiments, sauces, and other accompaniments.
		Many sandwich producers are known for their criminal obsession of putting condiments and other, less than solid, ingredients in their sandwiches, like mayonnaise, ketchup or mustard.
		Sandwiches are commonly carried to work or school in lunchboxes to serve as the midday meal, taken on picnics, hiking trips, etc.
	www.unipedia.info /Sandwich.html (767 words)

	Sandwich -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-20)
		It is said that Lord Sandwich was fond of this form of food because it allowed him to continue (The act of playing for stakes in the hope of winning (including the payment of a price for a chance to win a prize)) gambling while eating.
		Nowadays some types of sandwich are too unwieldy to be held in one hand, thus defeating Montagu's original purpose, and must be eaten with a (Click link for more info and facts about knife and fork) knife and fork, or at least with both hands.
		A sandwich filled with (Electronic equipment consisting of a small crystal of a silicon semiconductor fabricated to carry out a number of electronic functions in an integrated circuit) chips (US: french fries) is known as a 'chip buttie' (also butty).
	www.absoluteastronomy.com /encyclopedia/s/sa/sandwich.htm (1404 words)

	Sandwich
		In many countries, a sandwich traditionally takes the form of two or more slices of bread enclosing the sandwich fillings.
		In Scandinavia a sandwich traditionally takes the form of one slice of bread topped by the sandwich "fillings".
		Nowadays some types of sandwich are too unwieldy to be held in the hand, thus defeating Montagu's original purpose, and must thus be eaten with utensils.
	encyclopedia.codeboy.net /wikipedia/s/sa/sandwich.html (398 words)

	PlanetMath: Borsuk-Ulam theorem
		For example, this theorem implies that at any time there exists antipodal points on the surface of the earth which have exactly the same barometric pressure and temperature.
		It is also interesting to note a corollary to this theorem which states that no subset of
		This is version 3 of Borsuk-Ulam theorem, born on 2001-11-17, modified 2002-02-12.
	planetmath.org /encyclopedia/BorsukUlamTheorem.html (99 words)

	Ham hock - Encyclopedia Glossary Meaning Explanation Ham hock (Site not responding. Last check: 2007-10-20)
		Ham hocks are essential ingredients in soul food and other forms of Southern country cooking.
		A ham "hock" in the sense contemplated here is the end of a smoked ham where the foot was attached to the hog's leg.
		It is the portion of the leg that is neither part of the ham proper nor the foot or ankle, but rather the extreme shank end of the leg bone and the associated skin, fat, tendons, and muscle.
	www.encyclopedia-glossary.com /en/Ham-hock.html (153 words)

	PlanetMath: ham sandwich theorem
		According to this theorem it is possible to make one cut to simultaneously cut all three objects exactly in half.
		This is version 3 of ham sandwich theorem, born on 2003-10-13, modified 2003-11-24.
		The only (m-1)-dim hyperplane that would satisfy the theorem is the hyperplane that the subsets lie within.
	planetmath.org /encyclopedia/HamSandwichTheorem.html (117 words)

	Sandwich - Open Encyclopedia (Site not responding. Last check: 2007-10-20)
		It is said that Montagu was fond of this form of food because it allowed him to continue gambling while eating.
		Nowadays some types of sandwich are too unwieldy to be held in the hand, thus defeating Montagu's original purpose, and must thus be eaten with utensils, or at least both hands.
		British Sandwich Week, organised by the British Sandwich Association which represents the UK sandwich industry, occurs on the week beginning on the second Sunday of May.
	open-encyclopedia.com /Sandwich (433 words)

	Shop Fresh : Article 'Universal coefficient theorem' (Site not responding. Last check: 2007-10-20)
		In mathematics, the universal coefficient theorem in algebraic topology establishes the relationship in homology theory between the integral homology of a topological space X, and its homology with coefficients in any abelian group A. It shows that the integral homology groups Hi(X,Z) do in a certain, definite sense determine the groups Hi(X,A).
		The universal coefficient theorem explains that homology with integer coefficients determines all other homology theories, by use of the tensor product; it is not anodyne, in that (as we would now put it) the tensor product has derived functors that enter into a general formulation.
		This is an unsolved problem, as of 2004; it is known that being a Hodge cycle is a necessary condition to be an algebraic cycle that is rational, and numerous particular cases of the conjecture are known.
	www.shop-fresh.net /DisplayArticle428121.html (745 words)

	ham sandwich theorem
		Given a sandwich in which bread, ham, and cheese (three finite volumes) are mixed up, in any way at all, there is always a flat slice of a knife (a plane) that bisects each of the ham, bread, and cheese.
		In other words, however messed up the sandwich — even if it's been in a blender — you can always slice through it in such a way that the two halves have exactly equal amounts, by volume, of the three ingredients.
		This theorem generalizes to higher-dimensional ham sandwiches, when it essentially becomes the Borsuk-Ulam theorem: in n-dimensional space in which there are n globs of positive volume, there is always a hyperplane that cuts all the globs exactly in half.
	www.daviddarling.info /encyclopedia/H/ham_sandwich_theorem.html (196 words)

	Chickscope: Explore: EggMath: The White/Yolk Theorem
		This is a two-dimensional analog of the intermediate-value theorem; it is the two-dimensional case of the Borsuk-Ulam theorem.
		The Borsuk-Ulam theorem in general dimensions can be stated in a number of ways but always deals with a map d from sphere to sphere or from sphere to euclidean space which is odd, meaning that d(-s)=-d(s).
		The usual proof of the theorem is by induction.
	chickscope.beckman.uiuc.edu /explore/eggmath/wy/borsuk.html (967 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		It stated >something like: >Given two pieces of bread and a slice of ham, I can 'assemble' a >sandwich of these 3 items (by placing the 3 items anywhere in 3-space!!) >and there always exists a single swip of a knife (who's trace is a >hyperplane) such that all 3 pieces will be equally divided.
		State it carefully so that it's clear that "...for every assembly of the sandwich there exists..." rather than this possible interpretation of your statement "...for some assembly of the sandwich there exists..." The pieces of your sandwich need only be bounded and measurable.
		I learned this as the Borsuk-Ulam theorem, but in Fulton's algebraic topology text he lists this as a corollary to the B-U theorem which he attributes to Stone and Tukey (presumably the article in Duke Math Jour 9 (1942) 356--359).
	www.math.niu.edu /~rusin/known-math/98/ham_sandwich (209 words)

	Braingle: Newsgroups
		Consider a ham sandwich, consisting of two pieces of bread and one of ham.
		Is it still possible to divide the ham sandwich with a straight knife cut such that both the ham and each slice of bread are divided in two parts of equal volume?
		There is a theorem in topology called the Ham Sandwich Theorem, which says: Given 3 (finite) volumes (each may be of any shape, and in several pieces), there is a plane that cuts each volume in half.
	www.braingle.com /news/hallfame.php?path=geometry/ham.sandwich.p&sol=1 (188 words)

	Eggs and Ham Sandwiches (Site not responding. Last check: 2007-10-20)
		Fundamentally speaking, eggs and ham sandwiches are on the same plane as mathematics.
		I learned about ham sandwiches from one of my teachers, Ashley Reiter, who studied these topics when she was in college.
		The Ham Sandwich Theorem is much like the Egg White and Yolk Theorem, but expands the idea to three objects: bread, ham and cheese.
	www.mssm.org /math/vol4/issue1/eggs.htm (316 words)

	Ham-sandwich cut -- from InfoWorld (Site not responding. Last check: 2007-10-20)
		Suppose you and your brother (sister, or whoever) were given a ham sandwich, and you each wanted half.
		But by the ham sandwich cut theorem there is always a way to cut the sandwich so that each person gets exactly half of the ham and half of the bread.
		ham-sandwich theorem guarantees the existence of such a cut.
	www.eleves.ens.fr /home/trung/ham-sandwich_cut.html (161 words)

	Ham sandwich theorem (Site not responding. Last check: 2007-10-20)
		=3 and the three objects of any shape are a chunk of ham and two chunks of bread - notionally a sandwich - which can then each be bisected with a single cut.
		In two dimensions, it is known as thepancake theorem of having to cut two (infinitesimally thin) pancakes on a plate each in half with a singlecut.
		It has no relationship to the " squeeze theorem " (sometimes calledthe "sandwich theorem").
	www.therfcc.org /ham-sandwich-theorem-35913.html (130 words)

	Ham sandwich (Site not responding. Last check: 2007-10-20)
		Sandwich Ham is the perfect 4x4cm sandwich sized ham.
		An alternative ham and cheese sandwich that uses miso and wasabi instead of the traditional mustard and mayonnaise to give it a zesty flavor.
		Ham in the sandwich, annecdote by Australian Vet from the Korean War.
	www.bassinet.org /ham-sandwich.html (882 words)

	Talk:Ham sandwich theorem - Wikpedia (Site not responding. Last check: 2007-10-20)
		I'd always assumed that the 'ham' was the bisecting line/plane itself.
		The idea being that you cut each piece of bread into two equal slices, and then insert the ham.
		Well, I suppose there is a planet somewhere with sandwiches made of three slices of bread...
	bostoncoop.net /~tpryor/wiki/index.php?title=Talk:Ham_sandwich_theorem (55 words)

	Ham sandwich theorem - Encyclopedia Glossary Meaning Explanation Ham sandwich theorem (Site not responding. Last check: 2007-10-20)
		Ham sandwich theorem - Encyclopedia Glossary Meaning Explanation Ham sandwich theorem.
		Here you will find more informations about Ham sandwich theorem.
		The orginal Ham sandwich theorem article can be editet
	www.encyclopedia-glossary.com /en/Ham-sandwich-theorem.html (208 words)

	Universal Book of Mathematics: list of entries
		Brouwer's theorem says that there must be at least one point on the top sheet that is in exactly the same position relative the bottom sheet as it was originally.
		Brower's theorem insists that there must be some point in the coffee that is in exactly the same spot as it was before you started stirring (though it might have moved around in between).
		This theorem also means that somewhere on the Earth's surface there has to be a point where the horizontal wind speed is zero, even if it's windy everywhere else.
	www.daviddarling.info /works/Mathematics/mathematics_samples.html (5705 words)

	Sandwich (Site not responding. Last check: 2007-10-20)
		For other uses see: sandwich (disambiguation).'' ------- Deli Sandwiches The sandwich is a food item consisting of bread and other fillings such as one or more layers of meat (often a type of cold cut), cheese, vegetables, condiments, sauces or other filling.
		According to Washingtonpost, USA sandwich business was worth $105 billion US in sales in 2003, with a 6% annual growth.
		British Sandwich Week, organised by the British Sandwich Association which represents the UK sandwich industry, occurs on the week beginning on the second Sunday of May. The ham sandwich theorem can be used to prove mathematically that a single cut can divide two pieces of bread and the filling each exactly in half.
	www.findterm.net /sa/sandwich.html (628 words)

	Graduate Seminar Abstract 9/7/01 (Site not responding. Last check: 2007-10-20)
		Suppose we have a piece of ham on a plate and we would like to cut it in half.
		The intermediate value theorem tells you that there is a place to cut so that each side will be half.
		Now suppose that you have a piece of ham and a hunk of cheese and a bit of bread all arranged in some arbitrary way in front of you.
	www.math.uic.edu /~marker/gss/ABS090701.html (159 words)

	CSAIL Event Calendar
		The Ham-Sandwich theorem is a well known theorem in n-dimensional geometry.
		Proving the theorem for n = 2 (where it is known as the "pancake theorem") is simple and can be found in Courant and Robbins (1978).
		For n=3, the theorem is a consequence of the wonderfully versatile Borsuk-Ulam theorem.
	www.csail.mit.edu /events/eventcalendar/calendar.php?show=event&id=420 (249 words)

	Killing My Lobster
		In a 1944 strip, Dagwood, Blondie’s husband, creates a sandwich that is as big as his head and has to be doweled together with frankfurter.
		This theorem has such a colorful name because in the case m = 3 it can be viewed as cutting a ham sandwich in half.
		This theorem sounds great but we think all hell breaks loose if you cut the sandwich diagonally or if you prefer to have the crusts cut off.
	www.killingmylobster.com /content/view/539/87 (1165 words)

	Squeeze theorem (Site not responding. Last check: 2007-10-20)
		This theorem argues that if two functions approach the same limit at a point, and a third function "lies" between those functions; then, the third function also approaches that limit at that point.
		It was first used geometrically by the mathematicians Archimedes and Eudoxus in an effort to calculate pi.
		The sandwich theorem has no relation to the ham sandwich theorem.
	www.worldhistory.com /wiki/S/Squeeze-theorem.htm (361 words)

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