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Topic: Mathematics and architecture

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Vaastu Shastra

	Mathematics and Architecture references
		A Capanna, Conoids and hyperbolic paraboloids in Le Corbusier's Philips Pavilion, in Nexus III : architecture and mathematics, Ferrara, June 4-7, 2000 (Pisa, 2000), 35-44.
		L Pepe, Architecture and mathematics in Ferrara from the thirteenth to the eighteenth centuries, Nexus III : architecture and mathematics, Ferrara, 2000 (Pisa, 2000), 87-104.
		M Spigaroli, Pulchritudo sive proportio : Architecture and mathematics in the gothic of the mendicants, Nexus Netw.
	www-history.mcs.st-andrews.ac.uk /HistTopics/Printref/Architecture.html (557 words)

	Mathematics and architecture - Biocrawler (Site not responding. Last check: 2007-10-12)
		Mathematics and architecture have always enjoyed a close association with each other, not only in the sense that the latter is informed by the former, but also in that both share the search for order and beauty, the former in nature and the latter in buildings.
		In Islamic architecture, a proportion of 1: √2 was often used—the plan would be a square and the elevation would be obtained by projecting from the diagonal of the plan.
		Ancient architecture such as that of the Egyptians and Indians employed planning principles and proportions that rooted the buildings to the cosmos, considering the movements of sun, stars, and other heavenly bodies.
	www.biocrawler.com /encyclopedia/Mathematics_and_architecture (659 words)

	Mathematics and Architecture
		Although many readers of this archive might find an article on mathematics and architecture a little surprising, in fact architecture was in ancient times considered a mathematical topic and the disciplines have, up to the present time, retained close connections.
		Architecture was modelled on the teachings of Vitruvius and on the classical architecture which was still plentiful, particularly in Greece and Italy.
		This is not to say that the connections between mathematics and architecture vanished, just that the scientific and artistic aspects were seen as complementary skills not to be found in the same person.
	www-groups.dcs.st-and.ac.uk /~history/PrintHT/Architecture.html (3408 words)

	Mathematics and Architecture
		Architecture was another of his specialities and he learnt about it, in particular the mathematical principles behind it, from studying Alberti's texts.
		Another to combine his skills in both mathematics and architecture was Bramer who was employed directing constructions of fortifications and castles.
		It was clear that Wren saw mathematics as being a subject which had applications to a wide variety of scientific disciplines and his mathematical skills played an important role in his architectural achievements.
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Architecture.html (3448 words)

	Amazon.co.uk: Architecture and Mathematics in Ancient Egypt: Books: Corinna Rossi (Site not responding. Last check: 2007-10-12)
		In this fascinating study, architect and Egyptologist Corinna Rossi analyses the relationship between mathematics and architecture in ancient Egypt by exploring the use of numbers and geometrical figures in ancient architectural projects and buildings.
		While previous architectural studies have searched for abstract 'universal rules' to explain the history of Egyptian architecture, Rossi attempts to reconcile the different approaches of archaeologists, architects and historians of mathematics into a single coherent picture.
		Using a study of a specific group of monuments, the pyramids, and placing them in the context of their cultural and historical background, Rossi argues that theory and practice of construction must be considered as a continuum, not as two separated fields, in order to allow the original planning process of a building to re-emerge.
	www.amazon.co.uk /Architecture-Mathematics-Ancient-Egypt-Corinna/dp/0521829542 (493 words)

	"Architecture, Patterns, and Mathematics", by Nikos A. Salingaros
		Mathematics is a science of patterns, and the presence or absence of patterns in our surroundings influences how easily one is able to grasp concepts that rely on patterns.
		Mathematics teachers are bemoaning the fact that there is less and less interest in mathematics, which has resulted in a declining mathematical capacity among students.
		Classical and neoclassical architecture, which tries to imitate the spirit and style of the Greco-Roman tradition, is ordered in a simple, rectangular geometry (which originally included sophisticated Non-euclidean corrections due to "entasis", the subtle curvature on Greek temples [18]).
	www.math.utsa.edu /ftp/salingar.old/ArchMath.html (5061 words)

	Architecture and Mathematics in Ancient Egypt - Cambridge University Press
		Although it is undeniable that a link between architecture and geometry (and therefore mathematics in general) exists, in different periods the nature of this connection has been identified and judged in different ways.
		Even the connection between architecture and music was heavily criticised and dismissed in favour of a more individual point of view influenced by the limitations of human perception.
		In his Dictionnaire Historique d’Architecture, he wrote that in Egyptian architecture the large size of the construction, the vastness of the composition and the profuseness of signs and objects were due to a lack of science, a lack of creativity, and a lack of taste, respectively.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521829542&ss=exc (1965 words)

	"Query: Why is mathematics used in architecture?" in the Nexus Network Journal
		Anyway, mathematically based methods of design, to the extent they are likely to have been used, seem to have been part of the builders’ planning tools, and not something the clients were bothered with.
		Perhaps the simplest form of mathematical building is that which involves the use of prcise canons or measures - hence achitecture might also be defined as 'rational building' - especially when the use of a regular canon or measure enables the introduction of symmetry (or common measures) and hence, of modules.
		The role of mathematics in architecture wold make an excellent conference topic (I mean the general theory or philosophy of mathematics and architecture, as opposed to particular examples of their interrelations).
	www.univie.ac.at /EMIS/journals/NNJ/Query04-WhyVsHow1.html (2777 words)

	93.01.07: Mathematics and Architecture Designs
		The introduction phase of Architectural understanding is excluded from most, if not all modern educational programs at both the elementary and high school levels, despite the overwhelming presence of buildings in the everyday life, of cities and suburbs and despite the unique role of architecture in orienting people to personal and public space and history.
		Because Mathematics and Architecture have traditionally been treated by the curriculum as an either/or polarity, students are denied the opportunity to see the unique inter-relationship between the two disciplines.
		Briefly stated, Classical Architecture is a combination of the temple architecture of the Greek and the religious, military and civil architecture of the Romans.
	www.yale.edu /ynhti/curriculum/units/1993/1/93.01.07.x.html (4064 words)

	Architecture and Mathematics in Roman Amphitheaters by S. Duvernoy for the Nexus Network Journal vol.4 no.3 (Summer ... (Site not responding. Last check: 2007-10-12)
		Architecture has such qualitative and quantitative demands that it not only brings theoretical geometry into practical application, but also leads it to the establishment of new theories.
		Architecture history shows that geometry and its related aesthetic symbolism were always present, hidden in architectural and urban design from antiquity to modern times.
		After having worked for a few years in the Parisian office of an international Swiss architecture firm, she is now partner of an associate office in Florence, the design projects of which cover a wide range of design problems, from remodeling and restoration to new constructions, in Italy and abroad.
	www.maths.tcd.ie /EMIS/journals/NNJ/N2002-Duvernoy.html (752 words)

	Science in India: History of mathematics: Indian Mathematicians and Astronomers,
		Mathematics was thus brought into the service of both the secular and the ritual domains.
		Mathematics and Architecture: Interest in arithmetic and geometric series may have also been stimulated by (and influenced) Indian architectural designs - (as in temple shikaras, gopurams and corbelled temple ceilings).
		Of course, the relationship between geometry and architectural decoration was developed to it's greatest heights by Central Asian, Persian, Turkish, Arab and Indian architects in a variety of monuments commissioned by the Islamic rulers.
	india_resource.tripod.com /mathematics.htm (4603 words)

	Architecture and Mathematics in Ancient Egypt - Cambridge University Press
		In this fascinating new study, architect and Egyptologist Corinna Rossi analyses the relationship between mathematics and architecture in ancient Egypt by exploring the use of numbers and geometrical figures in ancient architectural projects and buildings.
		While previous architectural studies have searched for abstract ‘universal rules’ to explain the history of Egyptian architecture, Rossi attempts to reconcile the different approaches of archaeologists, architects and historians of mathematics into a single coherent picture.
		Using a study of a specific group of monuments, the pyramids, and placing them in the context of their cultural and historical background, Rossi argues that theory and practice of construction must be considered as a continuum, not as two separated fields, in order to allow the original planning process of a building to re-emerge.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521829542 (281 words)

	Indian mathematics. Know more about Indian architecture, astronomy, mathematics, medicine, science.
		To a typical historian of mathematics today, if there is one certainty, it is that Isaac Newton (1642—1727) and Gottfried Leibniz (1646—1716) were the first to ‘invent’ a generalised system of infinitesimal calculus, an essential prelude to modern mathematics.
		Indian scholars made vast contributions to the field of mathematical astronomy and as a result contributed mightily to the developments of arithmetic, algebra, trigonometry and secondarily geometry (although this topic was well developed by the Greeks) and combinatorics.
		As Indian mathematics is (generally) devoid of proof it is not considered 'true' mathematics in its purest sense.
	www.nriol.com /content/columns/ashok/indian-mathematics1.asp (1321 words)

	Mathematics in Architecture
		I had the opportunity to explore the architecture of this vibrant city and found it to be replete with extraordinary examples of geometry, proportion, and symmetry.
		This thorough "exploration of the mathematics of beauty," with topics including myth, music, architecture, art, and mathematics, shows that, whether the bridge is natural or man-made, the connections between art and science are plentiful and inspiring.
		By far the best indication of the validity of the interdisciplinary study of math in architecture, however, was the arrival of the conference Nexus '96: The Relationship Between Architecture and Mathematics, held in Florence, Italy in the Summer of 1996.
	www.dean.sbc.edu /wassell.html (923 words)

	Architecture - Mathematics and the Liberal Arts
		The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses.
		A mathematically precise treatment of the problem (and of a problem using a conical mirror) was given by Jean-Louis Vaulezard in the 1600s, but even Niceron gave only an approximate method.
		It follows that mathematical chaos can be highly symmetric." He closes with a discussion of modern architecture, where he finds that symmetry concerns are important as well: "But the variety of historical reminiscences and asymmetrical elements in architecture does not mean a movement back to historicism or eclecticism.
	math.truman.edu /~thammond/history/Architecture.html (1783 words)

	Courses of architecture (Site not responding. Last check: 2007-10-12)
		An introductory course about architecture and architectural education.
		- The course is a prerequisite for entry to the Bachelor of Architecture, which fulfils the academic requirements for membership of...
		Architecture and ICT courses, understand how to focus and develop architecture towards your organisation's strategic goals.
	architecture.arqhys.com /courses.html (129 words)

	Architecture, Engineering and Mathematics
		These guidelines must be strictly followed and the designers must understand the mathematical terms that are used, such as the maximum slope of a ramp.
		A series of mathematical conversions are necessary to ensure the printed drawing is not too large, or too small, for the size paper being used.
		With the wide variety of professional services that are offered by ARMCG, and the extensive mathematics that are involved for ARMCG to fulfill their obligations, we feel that this class trip will be very enlightening to us as future teachers of secondary mathematics.
	jwilson.coe.uga.edu /EMAT6680/Parsons/MVP6690/Essay3/general.html (1889 words)

	architecture with math
		We have computer, which helps us applying mathematical principles of recent developement into basic concept of architecural form.
		Methodology of how mathematics can be used or applied into forming or designing architecture (computer-tech)
		The mathematical form in the architecture doesn't always represent a structural system.
	www.iit.edu /~tamahir/track01/mat.html (451 words)

	Kim Williams Books
		This includes studies dealing with of the relationships between art, architecture and the sciences, the history of science and mathematics and the history of the arts.
		Kim Williams is the director of the successful, ongoing conference series, "Nexus: Relationships Between Architecture and Mathematics." When she first began writing about architecture and mathematics in 1988, there was no specific venue for the publication of scholarly studies regarding the relationships of architecture to geometry, theories of proportion, number symbolism and the like.
		The response to the biennial conferences was so great that in 1999 Kim Williams founded the Nexus Network Journal, a peer-reviewed journal for mathematics and mathematics.
	www.kimwilliamsbooks.com /about.htm (335 words)

	Term Paper on Mathematics and Architecture 1700's
		The effect of the new mathematical ideas were on architecture was a gradual transformation of space from pure, static and isolated to composite, dynamic and interpenetrating.
		Now, it has been shown throughout history that the sciences drift apart and then return to each other a later time to re- orient the way a building should be designed.
		Be it as a symmetrical form or as an abstract piece of art, the bottom line is that this geometrical or mathematical essence must exist- especially in today's buildings not only visually, to support the eye's need for balance, but also structurally, to serve a better use in housing our needs.
	www.swiftpapers.com /essay/Mathematics_and_Architecture_1-6313.html (177 words)

	Mathematical Imagery Presented by the American Mathematical Society - Home
		Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings.
		An aspect of my art work that I particularly enjoy is that I write the software for all the programs I use and build the computers that run the software.
		In this sense, I like to feel that theory (mathematics), art (outcome), software (algorithms) and engineering (hardware) are integrated and interdependent and that no part survives without the others.
	www.ams.org /mathimagery (309 words)

	Mathematics and architecture
		The term Cartesian planning given to the planning of cities in a grid-iron fashion shows the close association between architecture and geometry.
		Modern town planning used the grid-iron pattern extensively, and according to some, resulting in monotony and traffic problems.
		The Schroeder House by Gerrit Rietveld is a good example of this approach.
	www.fact-index.com /m/ma/mathematics_and_architecture.html (647 words)

	Mathematics and architecture - WebArticles.com
		Golden rectangleIn Greek architecture, the Golden mean or the Golden rectangle served as a canon for planning.
		The Parthenon, Athens, GreeceThe optical illusions of the Parthenon at the Acropolis, Athens, could not have been done without a thorough knowledge of geometry.
		Peter's Square in Rome, fronting the St. Peter's Basilica, is an approximately key-hole shaped (albeit with non-parallel sides) exterior space bounded by columns giving a very dynamic visual experience.
	www.webarticles.com /print.php?id=418 (659 words)

	"THEORY OF ARCHITECTURE", by Nikos A. Salingaros.
		The search has led me to apply science and mathematics to architecture, which has proved remarkably fruitful in establishing new and useful results.
		Most architects know of the historical application of ancient mathematics such as proportional ratios -- yet it is not this type of mathematics that actually governs general architectural form.
		Their main message is that architecture should be based on principles that stand scientific scrutiny and experimental test.
	www.math.utsa.edu /sphere/salingar/architecture.html (386 words)

	The Math Forum - Math Library - Architecture
		AIE uses architecture as the basis for hands-on, interactive projects that connect, integrate and deepen K-12 student learning across the curriculum.
		A unit about architecture and its unique relation to mathematics, incorporating the study of such mathematical concepts as ratio, proportion, scales, symmetry, and similarity, and providing definitions and explanations of the mathematical concepts of...more>>
		To produce structures that are functional as well as models of architectural beauty, designers must apply principles of mathematics in their work.
	mathforum.org /library/topics/architecture (2203 words)

	Mathematics in Art and Architecture - References
		George L. Hersey, Architecture and Geometry in the Age of the Baroque, The University of Chicago Press, 2000.
		Kim Williams (ed.), NEXUS: Architecture and Mathematics, Edizioni dell'Erba, 1996.
		Kim Williams (ed.), NEXUS II: Architecture and Mathematics, Edizioni dell'Erba, 1998.
	www.math.nus.edu.sg /aslaksen/teaching/maa/refs.html (1527 words)

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