THE FORM OF THE ARGUMENT van der Rohe's House with Three Courts and Giuseppe Terragni's Danteum both utilize two-dimensional geometries central to their architectural logic.How- ever,while Mies'project(13)remains uniform in section,the Danteum embod- ies a helix of spatial movement and serves as a complement for analysis of three-dimensional form through two-dimensional means. The two precedents in CHAPTER 9-not surprisingly-continue to develop the investigation of three-dimensional design thinking,adding analysis of material tectonics and volumetric strategies.Louis Kahn's Exeter Library and Frank Lloyd Wright's Unity Temple serve as companionable subjects,each embodying a manifestation of resolutely volumetric architecture(14-15). Certain ideas weave their way through this chapter sequence.Relational measure plays against the universal grid.Two-dimensional analysis and dia- grams contrast with three-dimensional counterparts,extending a growing vocabulary to introduce and then develop fundamental architectural terminol- ogy and organizational principles. Figure 14:Kahn's Exeter Library-shown in isometric section-receives a The illustrations throughout the majority of the text-as in this introduc- full three-dimensional analysis in CHAPTER 9. tory chapter-render examples as LINE and tone,the dominant form of tra- ditional architectural representation.In the first year design studio at our institution,we use physical media to accomplish the exercises for both draw- ing and making models.In contrast,our examples make full use of digital con- struction and processing to create a consistent palette for reproduction. Our final essay,CHAPTER 10,takes full advantage of digital flexibility to present color variations of the project images as a basis for discussing the effective use of color and material palettes to enhance presentation.The intent is to use simple variations to suggest alternatives in media and presen- tation for the analysis detailed throughout the book. The form of the argument This book holds three parallel narratives,intertwined and juxtaposed:chap- ters,illustrations and supplements.Chapter texts-like the one you are read- ing now-present an ongoing account of learning about design through dia- grams.The images and captions that accompany the text also stand on their own as a sequence of illustrations with commentary.Continuing the pattern Figure 15:Wright's Unity Temple-shown in section-provides the basis for of words and pictures,following the chapters the reader will find the third a comparable three-dimensional investigation also in CHAPTER9. episodic narrative also in three parts:glossary,thematic essay and visual sup- plement.The glossary of terms accrues key vocabulary found in each chapter. The'Descriptions'-mentioned earlier-present fundamental architectural precedents relevant to CHAPTERS 1-6.In addition,'Demonstrations'augment the examples and procedures encountered within the primary narrative.These appear following the chapters where the need exists more profoundly.This reflects our experience teaching this material. A quick glance at the table of contents will help guide the reader through this structure
van der Rohe’s House with ree Courts and Giuseppe Terragni’s Danteum both utilize two-dimensional geometries central to their architectural logic. However, while Mies’ project () remains uniform in section, the Danteum embodies a helix of spatial movement and serves as a complement for analysis of three-dimensional form through two-dimensional means. e two precedents in – not surprisingly – continue to develop the investigation of three-dimensional design thinking, adding analysis of material tectonics and volumetric strategies. Louis Kahn’s Exeter Library and Frank Lloyd Wright’s Unity Temple serve as companionable subjects, each embodying a manifestation of resolutely volumetric architecture (–). Certain ideas weave their way through this chapter sequence. Relational measure plays against the universal grid. Two-dimensional analysis and diagrams contrast with three-dimensional counterparts, extending a growing vocabulary to introduce and then develop fundamental architectural terminology and organizational principles. e illustrations throughout the majority of the text – as in this introductory chapter – render examples as and tone, the dominant form of traditional architectural representation. In the first year design studio at our institution, we use physical media to accomplish the exercises for both drawing and making models. In contrast, our examples make full use of digital construction and processing to create a consistent palette for reproduction. Our final essay, , takes full advantage of digital flexibility to present color variations of the project images as a basis for discussing the effective use of color and material palettes to enhance presentation. e intent is to use simple variations to suggest alternatives in media and presentation for the analysis detailed throughout the book. The form of the argument is book holds three parallel narratives, intertwined and juxtaposed: chapters, illustrations and supplements. Chapter texts – like the one you are reading now – present an ongoing account of learning about design through diagrams. e images and captions that accompany the text also stand on their own as a sequence of illustrations with commentary. Continuing the pattern of words and pictures, following the chapters the reader will find the third episodic narrative also in three parts: glossary, thematic essay and visual supplement. e glossary of terms accrues key vocabulary found in each chapter. e ‘Descriptions’ – mentioned earlier – present fundamental architectural precedents relevant to –. In addition, ‘Demonstrations’ augment the examples and procedures encountered within the primary narrative. ese appear following the chapters where the need exists more profoundly. is reflects our experience teaching this material. A quick glance at the table of contents will help guide the reader through this structure. Figure 14: Kahn’s Exeter Library – shown in isometric section – receives a full three-dimensional analysis in CHAPTER 9. Figure 15: Wright’s Unity Temple – shown in section – provides the basis for a comparable three-dimensional investigation also in CHAPTER 9.
1-INTRODUCTION GLOSSARY OF TERMS ANALYSIS:A detailed examination of the parts or structure of something,the pro- cess of separating something into its constituent elements.Derived from the Greek for'unbundling,it is often contrasted with synthesis. ARCHETYPE:An ideal form that existing things approach but never duplicate BIG IDEA:The primary idea or conceit governing the development of a particular design.Architects often call this the PARTI or main concept of a project. COMPOSITION:The elements that comprise any intentional arrangement,form or shape.The formal configuration of parts within a whole. DESIGN THINKING:A practice for discerning,analyzing and composing systems of order,wherein critical assessment is balanced with generative and iterative creation. ECOLE DES BEAUX-ARTS:Generally considered the first 'school'of architecture,it developed many of the formal rituals and terminology of architectural edu- cation.Responsible for a corresponding'style'of public works of architec- ture,which held sway in Northern Europe and America throughout much of the nineteenth and early twentieth centuries. FORMAL:Of and relating to form and composition. MATTER:The'stuff'of the physical world,material. MEASURE:Comprises the dimensional attributes of form and space. ORDER:The organizational principle of any composition. PURPOSE:The identification of ends reflecting a sense of final state or goals. STRATEGY:A plan of action designed to achieve a major or overall end. TACTIC:An action or strategy carefully planned to achieve a specific end,a compo- nent of an overall STRATEGY. 9
– GLOSSARY OF TERMS : A detailed examination of the parts or structure of something, the process of separating something into its constituent elements. Derived from the Greek for ‘unbundling’, it is often contrasted with synthesis. : An ideal form that existing things approach but never duplicate. : e primary idea or conceit governing the development of a particular design. Architects often call this the or main concept of a project. : e elements that comprise any intentional arrangement, form or shape. e formal configuration of parts within a whole. : A practice for discerning, analyzing and composing systems of order, wherein critical assessment is balanced with generative and iterative creation. -: Generally considered the first ‘school’ of architecture, it developed many of the formal rituals and terminology of architectural education. Responsible for a corresponding ‘style’ of public works of architecture, which held sway in Northern Europe and America throughout much of the nineteenth and early twentieth centuries. : Of and relating to form and composition. : e ‘stuff’ of the physical world, material. : Comprises the dimensional attributes of form and space. : e organizational principle of any composition. : e identification of ends reflecting a sense of final state or goals. : A plan of action designed to achieve a major or overall end. : An action or strategy carefully planned to achieve a specific end, a component of an overall
1-INTRODUCTION DESCRIPTION 1 Order measure From the divine to the secular As we initially describe it,order may seem an abstract notion,disconnected from the earthy reality of the built environment.Nothing could be further from the truth.The deceptively simple,physical act of measurement binds architecture to the concepts of order that we discuss at length in this book. This is true not only of contemporary building practices;order and measure are intrinsic to the earliest traces of human occupation throughout the world Ancient Egyptian mythology credited the goddess Seshat,'she who scribe', with the invention of surveying.They also identified her as the goddess of architecture,astronomy,mathematics,record keeping and writing.The com- mingling of these forms of knowledge in one divinity is instructive.For the Egyptians,two pressing necessities prompted the invention of surveying: water,and religious observance.The development of intensive agriculture along the Nile valley relied upon an irrigation network of channels and chases. Figure1:Egyptian surveyors formed ropes of 1 equally-spaced knots into In turn,this intricate system required accurate measurement of distance and triangles with sides3,4 ands knots long to ensure accurate right angles. area,as well as minute changes in elevation.These practices also aided in re- establishing,or scribing.property lines following the annual floods. Equally significant,surveying enabled the Egyptians to transcribe the divine order of the universe onto,and into,the natural world.Instruments designed to map the movement of the heavens also found use in chart- ing the surface of the earth.Sacred texts contained mathematical formulae and their resultant proportional systems,their secrets guarded closely by a caste of architect-priests and their attendant surveyors-harpedonaptae,or rope-stretchers'.Scholars believe that the Pharaohs themselves symbolically assumed this role:Egyptian mythology describes Seshat assisting pharaohs in 'stretching the rope',the ritual related to laying out the foundations of tem- ples and other sacred structures in order to establish dimensional precision, thereby assuring celestial alignments.Murals and reliefs throughout Egypt depict various pharaohs wielding ropes associated with the literal act of ruling: Kings chamber knotted cords one-hundred royal cubits in length measured distance,while Grand gallery shorter cords twelve knots long form a right angle when arrayed as a triangle with sides three,four and five knots in length respectively (1). Stonehenge provides another vivid example of measure in the service of order.Inhabitants repeatedly altered the site over the course of more than fifteen hundred years,and theories about its use and significance vary widely in past decades'scholarship.Nevertheless,several self-evident attributes Unfnished subterrancn chaber of the archeological evidence suggest one pre-eminent role:that of celestial observatory.From the center of its iterative rings of post-holes,trenching and trilithons,the so-called Heel Stone-a monolith to the northeast-marks the Figure 2:Egyptian builders achieved great precision.The square footprint of the Great Pyramid at Giza is accurate to within two inches on each side. 11
– Figure 2: Egyptian builders achieved great precision. The square footprint of the Great Pyramid at Giza is accurate to within two inches on each side. Figure 1: Egyptian surveyors formed ropes of 12 equally-spaced knots into triangles with sides 3, 4 and 5 knots long to ensure accurate right angles. DESCRIPTION Order & measure From the divine to the secular As we initially describe it, order may seem an abstract notion, disconnected from the earthy reality of the built environment. Nothing could be further from the truth. e deceptively simple, physical act of measurement binds architecture to the concepts of order that we discuss at length in this book. is is true not only of contemporary building practices; order and measure are intrinsic to the earliest traces of human occupation throughout the world. Ancient Egyptian mythology credited the goddess Seshat, ‘she who scribe’, with the invention of surveying. ey also identified her as the goddess of architecture, astronomy, mathematics, record keeping and writing. e commingling of these forms of knowledge in one divinity is instructive. For the Egyptians, two pressing necessities prompted the invention of surveying: water, and religious observance. e development of intensive agriculture along the Nile valley relied upon an irrigation network of channels and chases. In turn, this intricate system required accurate measurement of distance and area, as well as minute changes in elevation. ese practices also aided in reestablishing, or scribing, property lines following the annual floods. Equally significant, surveying enabled the Egyptians to transcribe the divine order of the universe onto, and into, the natural world. Instruments designed to map the movement of the heavens also found use in charting the surface of the earth. Sacred texts contained mathematical formulae and their resultant proportional systems, their secrets guarded closely by a caste of architect-priests and their attendant surveyors – harpedonaptae, or ‘rope-stretchers’. Scholars believe that the Pharaohs themselves symbolically assumed this role: Egyptian mythology describes Seshat assisting pharaohs in ‘stretching the rope’, the ritual related to laying out the foundations of temples and other sacred structures in order to establish dimensional precision, thereby assuring celestial alignments. Murals and reliefs throughout Egypt depict various pharaohs wielding ropes associated with the literal act of ruling: knotted cords one-hundred royal cubits in length measured distance, while shorter cords twelve knots long form a right angle when arrayed as a triangle with sides three, four and five knots in length respectively (). Stonehenge provides another vivid example of measure in the service of order. Inhabitants repeatedly altered the site over the course of more than fifteen hundred years, and theories about its use and significance vary widely in past decades’ scholarship. Nevertheless, several self-evident attributes of the archeological evidence suggest one pre-eminent role: that of celestial observatory. From the center of its iterative rings of post-holes, trenching and trilithons, the so-called Heel Stone – a monolith to the northeast – marks the Grand gallery Queen’s chamber Un nished subterranean chamber King’s chamber
THE GROMA position of the summer solstice sunrise.An arranged quartet of lesser stones indicates major and minor solstice moonrise and moonset positions(3). Archeologists with the Stonehenge Riverside project contend that the mon- ument was part of a ritual landscape that extended upstream along the River Avon.Their theory suggests that the area surrounding nearby Durrington, Walls Henge,was a place of the living,while Stonehenge was a domain of the dead.Ajourney along the Avon to reach Stonehenge was part of a ritual pas- sage between this world and the underworld,to celebrate past ancestors and the recently deceased.Whatever its specific role,Stonehenge,like the phara- onic projects along the banks of the Nile built during the same period,demon- strates the practice of using geometry to both measure and replicate received South Ba的 notions of divine order within the earthly abode of humanity. The groma 个 The Romans,those most tenacious surveyors of the ancient world,laid out their empire with the aid of the groma(4).Composed of a cruciform arrange- Figure 3:Stonehenge was,among other things,a celestial observatory:its ment of plumb lines,it established perpendicular avenues aligned with the stones align to mark the positions of both sun and moon at summer solstice. cardinal axes-cardo and decumanus.This intersection determined the center of military camps,and subsequently the center of urban settlements estab- lished throughout Roman territories. The groma was the principal tool of the agrimensores-literally'field-mea- surers'-who settled property disputes and supervised the re-distribution of lands acquired by conquest.Together with the chorobates-water-level- and dioptra-sighting tube-the Empire employed the groma in all aspects of imperial and civic infrastructure:military surveyors used it to lay out the vast network of consular roads,as well as the far-flung encampments and defensive works maintained by Roman legionaries.These same tools helped to arrange the remarkable system of aqueducts that supplied the fountains, baths and privileged residences of urban centers.Architectural surveyors, in turn,laid out the streets,public spaces and buildings of cities and towns throughout the Empire. As with their Bronze Age predecessors,these practical manifestations of Roman surveying traced their origin to sacred rituals that superimposed pat- terns of cosmic order on the apparent chaos of the natural world.The cruci- form intersection prescribed by the groma derived from the inauguratio,the ancient ceremony that sanctifed the founding of a city.Presiding over the ceremony was an augur,a priest trained in the art of divining the heavens.He began by scrutinizing the full sweep of the horizon and naming all that he CARDO saw.Simultaneously,he drew a circle on the ground with his staff,represent- DECUMANUS ing the totality of the cosmos.The augur then divided the circle into quad- rants by inscribing the cruciform lines of the templum,the term for both the newly consecrated site,and the simple sketch on the ground.This single dia- gram aligned the site with the divine order of the universe,and delineated the Figure 4:Roman surveyors used thegrom to establish an orthogonal essential form of their cities.For the Romans,it reified the power of order. intersection aligned with the cardinal axes(afterP.Figerio,1933). 12
m Sarsen Ring Trilithons North Barrow South Barrow Station stone position of the summer solstice sunrise. An arranged quartet of lesser stones indicates major and minor solstice moonrise and moonset positions (). Archeologists with the Stonehenge Riverside project contend that the monument was part of a ritual landscape that extended upstream along the River Avon. eir theory suggests that the area surrounding nearby Durrington, Walls Henge, was a place of the living, while Stonehenge was a domain of the dead. A journey along the Avon to reach Stonehenge was part of a ritual passage between this world and the underworld, to celebrate past ancestors and the recently deceased. Whatever its specific role, Stonehenge, like the pharaonic projects along the banks of the Nile built during the same period, demonstrates the practice of using geometry to both measure and replicate received notions of divine order within the earthly abode of humanity. The groma e Romans, those most tenacious surveyors of the ancient world, laid out their empire with the aid of the groma (). Composed of a cruciform arrangement of plumb lines, it established perpendicular avenues aligned with the cardinal axes – cardo and decumanus. is intersection determined the center of military camps, and subsequently the center of urban settlements established throughout Roman territories. e groma was the principal tool of the agrimensores – literally ‘field-measurers’ – who settled property disputes and supervised the re-distribution of lands acquired by conquest. Together with the chorobates – water-level – and dioptra – sighting tube – the Empire employed the groma in all aspects of imperial and civic infrastructure: military surveyors used it to lay out the vast network of consular roads, as well as the far-flung encampments and defensive works maintained by Roman legionaries. ese same tools helped to arrange the remarkable system of aqueducts that supplied the fountains, baths and privileged residences of urban centers. Architectural surveyors, in turn, laid out the streets, public spaces and buildings of cities and towns throughout the Empire. As with their Bronze Age predecessors, these practical manifestations of Roman surveying traced their origin to sacred rituals that superimposed patterns of cosmic order on the apparent chaos of the natural world. e cruciform intersection prescribed by the groma derived from the inauguratio, the ancient ceremony that sanctified the founding of a city. Presiding over the ceremony was an augur, a priest trained in the art of divining the heavens. He began by scrutinizing the full sweep of the horizon and naming all that he saw. Simultaneously, he drew a circle on the ground with his staff, representing the totality of the cosmos. e augur then divided the circle into quadrants by inscribing the cruciform lines of the templum, the term for both the newly consecrated site, and the simple sketch on the ground. is single diagram aligned the site with the divine order of the universe, and delineated the essential form of their cities. For the Romans, it reified the power of order. Figure 3: Stonehenge was, among other things, a celestial observatory: its stones align to mark the positions of both sun and moon at summer solstice. Figure 4: Roman surveyors used the groma to establish an orthogonal intersection aligned with the cardinal axes (after P. Figerio, 1933).
1-INTRODUCTION DEMONSTRATION 11 Organizational figures SIMPLE ORGANIZATION The images to the left illustrate three columns of related formal organizational figures in sequence.Each row proceeds from a basic conceptual premise.Corre- spondence along the columns exists as well. The first row shows three figures often associated with ideal geometries because of their regular form Diagram1:The square. Diagram 1-2:The circle. Diagram13:The triangle. (11-3).In this context,there is little difference between the square and most rectangles-they both have four sides,parallel and perpendicular.The same is true for the circle and other elliptical forms as well as most forms of the triangle. The second row shows three regular polygons related to the solids immediately above(14-6). In the third row,we encounter three archetypical shapes sometimes found in architectural composi- Diagram 14:The octagon. Diagram 1-5:The pentagon. Diagram 1-6:The hexagon. tions-the pentagram and other star forms being the rarer (17-9). The fourth and fifth rows demonstrate related satel- lite organizations rendering a hierarchy of shapes and path forms(110-15). Diagram1:A cruciform Diagram1-8:The pentagram. Diagram 1-9:A serpentine Figure1:Diagrams of organization figures(left). + Diagram 110:Cruciform Diagram:Radial satellites Diagram 1-12:Serpentine satellites Diagram113:Perimeter Diagram 1-14:Pentagon Diagram 115:Wing satellites. Figure 2:The same figures illustrated as solid extrusions satellites. satellites. 13
– DEMONSTRATION Organizational figures e images to the left illustrate three columns of related formal organizational figures in sequence. Each row proceeds from a basic conceptual premise. Correspondence along the columns exists as well. · e first row shows three figures often associated with ideal geometries because of their regular form (·–). In this context, there is little difference between the square and most rectangles – they both have four sides, parallel and perpendicular. e same is true for the circle and other elliptical forms as well as most forms of the triangle. · e second row shows three regular polygons related to the solids immediately above (·–). · In the third row, we encounter three archetypical shapes sometimes found in architectural compositions – the pentagram and other star forms being the rarer (·–). · e fourth and fifth rows demonstrate related satellite organizations rendering a hierarchy of shapes and path forms (·–). Diagram 1·1: The square. Diagram 1·4: The octagon. Diagram 1·7: A cruciform. Diagram 1·10: Cruciform satellites. Diagram 1·13: Perimeter satellites. Diagram 1·2: The circle. Diagram 1·5: The pentagon. Diagram 1·8: The pentagram. Diagram 1·11: Radial satellites. Diagram 1·14: Pentagon satellites. Diagram 1·3: The triangle. Diagram 1·6: The hexagon. Diagram 1·9: A serpentine gure. Diagram 1·12: Serpentine satellites. Diagram 1·15: Wing satellites. Figure 1: Diagrams of organization gures (left). Figure 2: The same gures illustrated as solid extrusions