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	Mizar
		Mizar B is also a type A main sequence star separated from A by 14 arc seconds, which corresponds to a projected separation of 340 AU or more than 8 times the diameter of the orbit of planet Pluto.
		Spectral analysis reveals Mizar A itself to be a binary star consisting of two main sequence A2V stars orbiting around each other with a period of 20.5 days in a rather elliptical orbit having a semimajor axis of about 27 million miles.
		Spectral analysis shows Mizar B itself to be a binary star, so that there are at least four stars in the Mizar system.
	domeofthesky.com /clicks/mizar.html (355 words)

	The Mizar Project
		Mizar, is the second magnitude star set in the middle of the Big Dippper's handle; Mizar is a quadruple star.
		Mizar Verification of Algorithms for Recognizing Chordal Graphs, Broderick Arneson, MSc Thesis, January 2007, (.ps,.pdf).
		Some remarks on translating Mizar texts into English are in Mizar and the Machine Translation of Mathematics Documents by G.
	web.cs.ualberta.ca /~piotr/Mizar (518 words)

	Big Dipper
		Mizar, at a distance of 78 light years from the Sun, and Alcor at 81 light years, while appearing to be a double star, are actually only an optical double.
		The components of the Mizar multiple star system are Mizar A (Zeta 1 Ursa Majoris at magnitude 2.27) and Mizar B (Zeta 2 Ursa Majoris at magnitude 3.95), located 14.42 arc seconds away.
		Between Mizar and Alcor is a fourth star, Sidus Ludoviciana, shining at magnitude 8, which is a field star that is not even part of the Ursa Major cluster.
	www.astropix.com /HTML/C_SPRING/BIGDIP.HTM (447 words)

	Mizar Home Page: Mizar System
		The Mizar System is the only implementation of the Mizar Language.
		The whole Mizar system (including verifier) is coded in Pascal using the Free Pascal compiler.
		The distribution of the Mizar system and the Mizar Mathematical Library is free of charge for non commercial purposes.
	mizar.org /system (358 words)

	Christoph Schwarzweller: Papers' Abstracts
		We propose the Mizar system as a theorem prover capable of verifying generic algebraic algorithms on an appropriate abstract level.
		Using Mizar we were able to give a rigorous machine assisted correctness proof of a generic version of the Brown/Henrici arithmetic in the field of fractions over arbitrary gcd domains.
		In this paper we report on the Mizar codification of formal concepts and concept lattices being part of the theory of formal concept analysis, a mathematical theory that formally describes the notion of concepts and concept hierarchies.
	delta.math.univ.gda.pl /~schwarzw/pub-abs.html (1715 words)

	A New View Of Mizar
		Compare the first reliable measurement of Mizar made by James Bradley and reduced to the epoch 1755 – position angle 143.1 degrees and angular distance 13.88 arcseconds, with the result of the Hipparcos satellite: 152 degrees and 14.43 arcseconds (epoch 1991.25).
		Her task was to devise a suitable system of spectral types and classify objective-prism spectra of bright northern stars taken with the 11-inch Clark refractor.
		Although Mizar A was not the first spectroscopic binary to be measured by this innovative technique – this priority belongs to bright Capella – it was observed by the first (and for many years also the last) functional astronomical interferometer, the 20-foot constructed by Michelson and Francis G. Pease at Mount Wilson.
	leo.astronomy.cz /mizar/article.htm (4651 words)

	Mizar
		Mizar is a language designed by A. Trybulec in the early seventies in order to represent mathematical proof in the computer.
		Mizar is currently the best approximation available to the QED dream of encoding real mathematics for digital proof checking.
		The Mizar project has its own website, which is the official source of Mizar files.
	www.cs.ru.nl /~freek/mizar (476 words)

	Welcome to the ETR (Site not responding. Last check: 2007-10-22)
		Mizar is a proof-checking system used to build the Mizar Mathematical Library (MML) - a long term project aiming at building a comprehensive library of formalized mathematical knowledge.
		The main goal for the design of Mizar (an effort led by Dr. Andrzej Trybulec) has been to create a formal system close to the mathematical vernacular used in main-stream mathematical publications with the requirement that the language be simple enough to enable computerized processing, in particular mechanical verification of correctness.
		The continual development of Mizar has resulted in a language, software for checking the correctness of texts written in it, numerous utility programs, a centrally maintained library of mathematics, and an electronic hyper-linked journal, all of which are available on the Internet (http://mizar.org).
	www.cs.uow.edu.au /etr/seminar_recent.htm (1548 words)

	The Moon (Site not responding. Last check: 2007-10-22)
		The two stars form an optical pair in the night sky and are not truly a binary system.
		Mizar shines at magnitude 2.3 while Alcor shines at fourth magnitude, and the two are separated by 11.5 arc minutes in the sky, with a separation in space of 10 light years.
		As seen in the picture however, Mizar does have a true fourth magnitude companion and both Mizar and it's companion have been shown spectroscopically to have a companion star.
	users.sunbeach.net /shine/stars.htm (275 words)

	Ursa Major - The Constellation Home Page
		Several other "firsts" are associated with this constellation; the star Mizar was the first double star to be discovered through a telescope (1662), the first star to be photographed (1857), and the first star to be identified as a spectroscopic binary (1889).
		Mizar and its visual companion, however, are a true double star system.
		Mizar is again a spectroscopic binary, but its closer companion cannot be seen with an optical telescope.
	www.astromax.com /con-page/spring/uma-01.htm (856 words)

	DOUBLE AND MULTIPLE STARS (Site not responding. Last check: 2007-10-22)
		Mizar and Alcor form an optical pair; in other words, they appear in the same line of sight from Earth but are actually far away from each other.
		This companion is actually a member of the same star system as Mizar.
		This system is even more complicated than it seems to the eye: both Mizar and its companion are double, although this has been determined only through spectroscopy.
	skytour.homestead.com /files/ds.html (588 words)

	Alpha Ursae Majoris (Site not responding. Last check: 2007-10-22)
		Zeta is the second star on the handle and is one of the most famous binary systems in the heavens: binoculars.
		Mizar has another fourth-magnitude companion fixed at PA 152º and separation 14.4".
		If Mizar is at the left-hand side of your glasses (it being winter and the constellation being upside down) then M101 will be just off the edge toward the right.
	www.dibonsmith.com /uma_z.htm (198 words)

	APOD: February 19, 1997 - Mizar Binary Star (Site not responding. Last check: 2007-10-22)
		Mizar (sounds like "My Czar") is a binary star.
		Mizar is the middle star in the handle of the Big Dipper and at a distance of 88 light years, was the first binary star system
		able to detect the companion star to Mizar A. This composite image of their observations shows the daily and monthly relative orbital motion in the binary system.
	antwrp.gsfc.nasa.gov /apod/ap970219.html (214 words)

	An Overview of the Mizar Project (Site not responding. Last check: 2007-10-22)
		Mizar is a system for the computer formalization of mathematics.
		The system has been used to formalize a large body of mathematics (including set theory, algebra, analysis and topology among others), far more than in any comparable system.
		Using a real example of a Mizar article, I will show how proofs are presented to the system in quite a similar style to ordinary mathematical textbooks, using the idea of `proof skeletons'.
	www.cl.cam.ac.uk /Research/HVG/ARG_Talks/abstracts/abstract_950803.html (197 words)

	[No title]
		Mizar A is spectral class A2 V mag = 2.4, while Mizar B is a main sequence spectral class A7 p mag.
		Mizar A and Mizar B are held together by the force of gravity.
		Mizar A (brilliant white, A2 V star) has a magnitude of 2.4 and Mizar B (pale emerald, A7 p)has a magnitude of 4.0.
	rigel.csuchico.edu /roth/presentation/roth_bak.html (6133 words)

	Why use an interferometer?
		One such pair could be the binary star system Mizar, visible to the naked eye and found in the handle of the Big Dipper.
		Mizar lies very close to Alcor, another naked eye star, and both may be seen as distinct stars by the unaided eye.
		Mizar itself is a pair of stars, Mizar A and Mizar B, that are separated by about 14 seconds of arc, too close to be seen by the naked eye as a distinct pair.
	www.nofs.navy.mil /projects/npoi/whynpoi.htm (994 words)

	Formal Methods Virtual Library
		Circal (CIRcuit CALculus) System supporting a process algebra which may be used to rigorously describe, verify and simulate concurrent systems.
		Mizar System, a long-term effort aimed at developing software to support a working mathematician in preparing papers.
		VIS (Verification Interacting with Synthesis), a system for formal verification, synthesis, and simulation of finite state systems, especially logic circuits.
	www.afm.sbu.ac.uk (1654 words)

	MBase Related Efforts
		The proposal for a general system-independent knowledge base for mathematics is not new: Around 1995, an anonymous group of authors put forward the QED Manifesto, which advocates building up a mathematical knowledge base (and supporting software systems) as a kind of "Human Genome Project" for the deduction community (QED activities).
		The Mizar Mathematical Library is a large collection of formalized mathematics, that has been verified by the Mizar system.
		The Maya is a system that manages the Development Graph.
	www.mathweb.org /mbase/related.html (445 words)

	Dagstuhl 97: A Mizar demo
		This is a short summary of a Mizar demo performed at the Schloss Dagstuhl Seminar "Deduction" on February 27, 1997.
		Mizar does not permit recursive definitions of functors, therefore we first define (recursively) a set theoretic function using one of the available schemes for recursive definitions of functions.
		At the evening part of the Mizar demo, we were joined, for most of the time, by M. Kohlhase, T. Nipkow, and H. de Nivelle.
	www.cs.ualberta.ca /~piotr/Mizar/Dagstuhl97 (1426 words)

	The NSDL Scout Report for Mathematics, Engineering, & Technology -- Volume 1, Number 2
		There are several categories of robotic systems to browse, including autonomous land robots; unmanned ground, air, and undersea vehicles; and telepresence and virtual reality.
		Mizar is a system used to represent mathematical vernacular so that it can be read and manipulated by humans and verified by computers.
		The Mizar Project began in 1973 and continues at the University of Bialystok in Poland.
	scout.wisc.edu /Reports/NSDL/MET/2002/met-020301-research.html (909 words)

	Some Features of the Mizar Language - Trybulec (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		The italic is used for names of Mizar grammatical constructions.
		If I have used them in a skeletal Mizar text I rather use boldface for reserved words of Mizar and roman otherwise.
		0.7: Commutative Algebra in the Mizar System - Rudnicki, Schwarzweller, Trybulec (2001)
	citeseer.ist.psu.edu /trybulec93some.html (455 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		One prerequisite for making such systems practical is to develop a formal mathematics library on a large scale.
		He discussed the Mizar system developed in Poland, noting that the declarative style it employs is very easy to use.
		Mizar will tell you that the structure of a proof is valid, even if it cannot justify single steps in it, and Mizar relies on its existing library.
	4c.ucc.ie /~tw/ar/radm.txt (954 words)

	Mizar system -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		Mizar system -- Facts, Info, and Encyclopedia article
		Mizar articles are written in ordinary ((computer science) a code for information exchange between computers made by different companies; a string of 7 binary digits represents each character; used in most microcomputers) ASCII.
		The proof checker uses classical logic, is written in (French mathematician and philosopher and Jansenist; invented an adding machine; contributed (with Fermat) to the theory of probability (1623-1662)) Pascal, and can be downloaded and used for free for non-commercial purposes.
	www.absoluteastronomy.com /encyclopedia/m/mi/mizar_system.htm (408 words)

	Natural History: Seeing Doubles - Brief Article
		They're systems of multiple stars so far from Earth that to the naked eye, each system appears to be a single entity.
		Most standard sources credit Italian astronomer Giovanni Battista Riccioli with being, in 1650, the first to resolve Mizar (through a telescope) into Mizar A and Mizar B, though recent research indicates that the honor might belong to Benedetto Castelli and date back to 1617--less than a decade after the invention of the telescope.
		Then in 1889, Harvard astronomer Edward C. Pickering examined the lines in the stars' spectra and found that one of the two, Mizar A, was itself a binary, thereby bestowing on it the distinction of being the first spectroscopic binary.
	www.findarticles.com /p/articles/mi_m1134/is_8_110/ai_79051537 (748 words)

	Desert Exposure Starry Dome May 2005
		Alcor and Mizar are only a fifth of a degree apart, but Alcor is over six times fainter than Mizar.
		Mizar itself is actually part of a triple star with Mizar A and Mizar B only 14.4 seconds of arc apart, while the third member of the family, Mizar C, is over 700 seconds away.
		In turn, Mizar A and B are each a double star, but the stars are so close together that they cannot be separated with even a powerful telescope.
	desertexposure.com /200505/200505_starry_dome.html (1197 words)

	Mizar system - Wikipedia, the free encyclopedia
		The source code is only available to members of the Association of Mizar Users.
		Browsable abstracts of MML articles are available as the Journal of Formalized Mathematics, and MML Query implements a search engine for MML.
		Main Mizar site, contains links to the MML, to the Journal of Formalized Mathematics, and a bibliography section linking to several introductions to the system
	en.wikipedia.org /wiki/Mizar_system (443 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		The Mizar system from Poland is mentioned often, but not many people know it from first hand experience.
		It is special in the sense that it uses declarative proofs, in contrast to the procedural proofs of most other proof tools.
		A short overview of the history proof checking will be followed by an introduction to the Mizar system, and an assessment of its strengths and weaknesses.
	cage.rug.ac.be /prooftool/wiedijk.html (74 words)

	30 Years of Mizar
		The goal of this workshop is to celebrate 30 years of Mizar.
		Andrzej Trybulec started the Mizar project in 1973 and has been leading the project since then.
		We look for original papers on all aspects of theory and practice related to the automation of deductive systems and to mechanized proof assistants in particular.
	merak.pb.bialystok.pl /mkm2004 (401 words)

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