Semiautomaton - Revision history

109.31.168.97: /* Transformation semigroups and monoid acts */ typo

2014-10-09T08:25:01Z

Transformation semigroups and monoid acts: typo

← Older revision		Revision as of 10:25, 9 October 2014
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en>Mark viking: Removing 5 1/2 year old cleanup tag with no specified complaint

2014-02-24T23:41:40Z

Removing 5 1/2 year old cleanup tag with no specified complaint

← Older revision		Revision as of 01:41, 25 February 2014
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	[[File:Orthic triangle.png\|thumb\|380px\|orthic triangle: <math>\triangle DEF </math> <br/> inscribed triangles: <math>\triangle DEF\,,\triangle GHI </math> <br/> <math>\|DE\|+\|EF\|+\|FD\|\leq \|GH\|+\|HI\|+\|IG\| </math>]]		I would like to introduce myself to you, I am Andrew and my wife doesn't like it at all. Distributing production has been his profession for some time. Ohio is where his home is and his family loves it. To play lacross is the thing I adore most of all.<br><br>Review my page: email psychic readings ([http://breenq.com/index.php?do=/profile-1144/info/ breenq.com])
	~~In [[geometry]]~~, '~~''Fagnano's problem''' is an [[Optimization (mathematics)\|optimization]] problem that was first stated by [[Giovanni Fagnano]] in 1775:~~

	~~:''For a given [[acute triangle]] determine the inscribed triangle of minimal [[perimeter]]''~~.

	~~The [[orthic triangle]]~~ has ~~the smallest perimeter of all triangles inscribed into an acute triangle, hence it~~ is ~~the solution of Fagnano's problem. Fagnano's original proof used [[calculus]] methods~~ and ~~an intermediate result given by~~ his ~~father [[Giulio Carlo de' Toschi di Fagnano]]~~. ~~Later however several geometric proofs were discovered as well, amongst others by [[Hermann Schwarz]] and [[Lipót Fejér]]. These proofs use~~ the ~~geometrical properties~~ of ~~reflections to determine some minimal path representing the perimeter~~.

	~~==References==~~
	*Heinrich Dörrie: ~~''100 Great Problems of Elementary Mathematics: Their History and Solution''. Dover Publications 1965, ISBN 0-486-61348-8, problem 90~~ ([http://~~books~~.~~google~~.~~de/books~~?~~id=i4SJwNrYuAUC&pg=PA359&vq=fagnano&source=gbs_search_r&cad=1_1 restricted online version (Google Books)])~~
	*Paul J. Nahin: ''When Least is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible''. Princeton University Press 2004, ISBN 0-691-07078-4, p. 67
	*[[Harold Scott MacDonald Coxeter\|Coxeter, H. S. M.]]; Greitzer, S. L.:''Geometry Revisited''. Washington, DC: Math. Assoc. Amer. 1967, pp. 88–89.

	==~~External links==~~
	*[http://~~www.cut~~-~~the-knot.org/Curriculum~~/~~Geometry~~/~~Fagnano~~.~~shtml Fagnano's problem at cut-the-knot~~]
	*[http://eom.springer.de/f/f038140.htm Fagnano's problem] in the [[Encyclopaedia of Mathematics]]
	*[http://www.pballew.net/orthocen.html Fagnano's problem at a website for triangle geometry]
	*{{MathWorld\|urlname=FagnanosProblem\|title=Fagnano's problem}}

	~~{{DEFAULTSORT:Fagnano'S Problem}}~~
	~~[[Category:Triangle geometry]]~~
	~~[[Category:Mathematical problems]]~~


	~~{{elementary-geometry-stub}}~~

en>UKoch: math formulas

2013-07-23T15:39:55Z

math formulas

← Older revision		Revision as of 17:39, 23 July 2013
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	~~I would like~~ to ~~introduce myself to you, I am Andrew~~ and ~~my spouse doesn~~'~~t like it at all~~. ~~To play lacross~~ is ~~something I truly appreciate performing~~. ~~Ohio is exactly where her home is~~. ~~Credit authorising is where my main income comes from~~.~~<br><br>Review my weblog~~ :: ~~phone psychic (~~[http://~~help~~.~~ksu~~.~~edu~~.sa/~~node~~/~~65129 Read Full Report~~])		[[File:Orthic triangle.png\|thumb\|380px\|orthic triangle: <math>\triangle DEF </math> <br/> inscribed triangles: <math>\triangle DEF\,,\triangle GHI </math> <br/> <math>\|DE\|+\|EF\|+\|FD\|\leq \|GH\|+\|HI\|+\|IG\| </math>]]
			In [[geometry]], '''Fagnano's problem''' is an [[Optimization (mathematics)\|optimization]] problem that was first stated by [[Giovanni Fagnano]] in 1775:

			:''For a given [[acute triangle]] determine the inscribed triangle of minimal [[perimeter]]''.

			The [[orthic triangle]] has the smallest perimeter of all triangles inscribed into an acute triangle, hence it is the solution of Fagnano's problem. Fagnano's original proof used [[calculus]] methods and an intermediate result given by his father [[Giulio Carlo de' Toschi di Fagnano]]. Later however several geometric proofs were discovered as well, amongst others by [[Hermann Schwarz]] and [[Lipót Fejér]]. These proofs use the geometrical properties of reflections to determine some minimal path representing the perimeter.

			==References==
			*Heinrich Dörrie: ''100 Great Problems of Elementary Mathematics: Their History and Solution''. Dover Publications 1965, ISBN 0-486-61348-8, problem 90 ([http://books.google.de/books?id=i4SJwNrYuAUC&pg=PA359&vq=fagnano&source=gbs_search_r&cad=1_1 restricted online version (Google Books)])
			*Paul J. Nahin: ''When Least is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible''. Princeton University Press 2004, ISBN 0-691-07078-4, p. 67
			*[[Harold Scott MacDonald Coxeter\|Coxeter, H. S. M.]]; Greitzer, S. L.:''Geometry Revisited''. Washington, DC: Math. Assoc. Amer. 1967, pp. 88–89.

			==External links==
			*[http://www.cut-the-knot.org/Curriculum/Geometry/Fagnano.shtml Fagnano's problem at cut-the-knot]
			*[http://eom.springer.de/f/f038140.htm Fagnano's problem] in the [[Encyclopaedia of Mathematics]]
			*[http://www.pballew.net/orthocen.html Fagnano's problem at a website for triangle geometry]
			*{{MathWorld\|urlname=FagnanosProblem\|title=Fagnano's problem}}

			{{DEFAULTSORT:Fagnano'S Problem}}
			[[Category:Triangle geometry]]
			[[Category:Mathematical problems]]


			{{elementary-geometry-stub}}

en>Mansour.cs at 11:56, 4 July 2012

2012-07-04T11:56:22Z

New page

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