cutaway drawing A method of creating a three-dimensional effect and showing the inside of a building by selectively removing parts of the outer skin, while maintaining the overall shape and structure of the building.
exploded-view drawing Where the elements of a building are ‘exploded’ to reveal their relationship with one another and how they fit and work together. Like the cutaway drawing, this was a Renaissance invention.
Fibonacci numbers Named after Italian mathematician Leonardo of Pisa, known as Fibonacci (c. 1170–c. 1250) – who introduced the concept into Western mathematics (although it had been known earlier to Indian mathematicians) – these are numbers that form a mathematical sequence, in which the following number is the sum of the previous two, so 0, 1, 1, 2, 3, 5, 8, 13. In art and architecture, the Fibonacci sequence is related to the perceived properties of the golden ratio.
golden ratio Also called the golden section or golden mean, this is a proportion believed to have some intrinsic aesthetic value that is in harmony with the universe. In practice, it has been defined as the effect created when a line is unequally divided, such that the whole is to the longer of the sections as that section is to the shorter.
human scale One of the scales in architecture in which a building is designed to work on a scale that makes humans feel in harmony with that environment. Other scales – monumental, for example – are created deliberately to work against it in order to create a specific psychological effect on those interacting with it.
Modulor system A system of measurement and proportion devised by Le Corbusier in the tradition of the writings of Vitruvius and da Vinci’s ‘Vitruvian Man’. It was based on the measurements of a 1.8-m (6-ft) tall man and was designed to help work out the ideal proportions for living and working spaces on a human scale.
orthographic drawing A means of representing a three-dimensional object in two dimensions. In architectural practice, this is a blanket term used to cover three types of drawing: section (a vertical slice through a building); plan (a horizontal slice); and elevation (a depiction of a façade).
Palladianism A style of Renaissance architecture derived from the buildings and written works of Andrea Palladio (1508–80). Particularly notable for symmetrical designs and use of Classical harmony, an early practitioner was the 17th-century English architect Inigo Jones, and Palladian principles and elements later became an essential part of the vocabulary of Neoclassical architecture across Europe.
Raumplan Adolf Loos’s (1870–1933) ‘space plan’, in which he put the design emphasis on individual rooms according to purpose, rather than for rooms to be squeezed into predetermined and restrictive floors. As he said, ‘My architecture is not conceived in plans but in spaces … For me there is no ground floor, first floor … Storeys merge and spaces relate to each other.’
vanishing point A key concept in the system of perspective – first appearing in the early 15th century – in which it is understood that while parallel lines can never meet in reality, in art they will appear to do so. So all parallel lines in a painting going in one direction will ultimately meet at a single point, the vanishing point, in order to create the illusion of three-dimensional space.
‘Vitruvian Man’ A drawing (c. 1487) by Leonardo da Vinci, derived from the writings of Vitruvius to depict the ideal proportions for geometry based on the human body.
A floor plan in architecture looks very similar to a map – it is a scaled drawing that includes all the fixed features of a defined area as if you were looking at it from above. However, for a drawing to be a plan it must have at least two other qualities. First, it is like a horizontal section – it ‘cuts’ along a horizontal plane (typically about 1.2 m/4 ft above the ground), showing the thickness of walls (with a hatched or black infill) and the interior space of a building (clear or textured to indicate a floor surface). Second, it includes outlines of features that are below that cut – fixed or permanent furniture, for example. For any single building, a number of plans need to be drawn to show the ground level, first floor, second floor, and so on, all of which can be quite different. A plan is usually monotone (often black on white) and is always measured and to scale. The plan has always been, and remains, one of the fundamental projections, or drawings, by which architects are able to develop a scheme because it demonstrates the arrangement and sequence of spaces.
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Plans are the fundamental drawings used to organize space, which, drawn to scale, provide information on solid elements (walls, stairs, doors) and the spaces between.
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Le Corbusier famously proclaimed that ‘the plan is the generator’. This plays on two meanings, ‘a plan’ being a kind of drawing, and ‘to plan’, meaning to consciously organize future action. By drawing a plan, space and the people who use it are organized in a particular way. This idea is not new, as we can see Classical, Gothic, Renaissance and 18th-century architects approaching the plan in a similar way.
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3-SECOND BIOGRAPHIES
HANNES MEYER
1889–1954
Swiss architect, head of the Bauhaus school (1927–30)
JACQUES-FRANÇOIS BLONDEL
1705–74
Highly influential French architect and theorist
ROBIN EVANS
1944–93
British architect and historian who wrote on the cultural and social significance of drawing architecture
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Nick Beech
An ability to read a plan is a key skill in architecture, since the plan represents how a building is organized.
A section slices through a building to produce a two-dimensional representation of a building’s profile, as well as an elevation of its interior. Sections are generally understood to be vertical cuts through a building, although a plan is, in effect, simply a horizontal section. Sometimes difficult to read for the untrained eye, a section serves as a medium of communication between architects, consultants and other professionals to define the exact vertical measurements of a structure. The section as a dominant form of architectural representation emerged in the 16th century from the archaeological contemplation and sketching of the ruins of ancient structures. It was the barren and cracked walls and vaults of buildings – such as the Baths of Caracalla or the Colosseum in Rome – that gave rise to the idea of ‘slicing’ open a building to reveal its internal workings through the medium of drawing. In a 1527 treatise on military architecture, Albrecht Dürer was the first to present a section aligned with a plan and an elevation, thus promoting the idea of these three orthographic types of drawings belonging together as a set.
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The section is a drawing produced from an imaginary, usually vertical, cut through a structure, revealing its outline and the interior visible behind the cut.
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The Modernist architect Adolf Loos prioritized the section over the plan when designing a building. With his Raumplan (space plan) theory, he intended to liberate the building from its fixed vertical divisions into floors, assigning different heights for each room according to its use and social importance within the building. Loos claimed to design by adding cubes on top and next to each other, rather than working with flat floor plans.
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3-SECOND BIOGRAPHIES
ALBRECHT DÜRER
1471–1528
German printmaker, painter, draughtsman and writer. A key driver of the Renaissance in Northern Europe
ADOLF LOOS
1870–1933
Austrian Modernist architect and writer, who promoted a focus on function and economy in architectural design
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Anne Hultzsch
A section view of a building reveals its load-bearing structure as well as an internal elevation.
Generally speaking, an elevation denotes a particular side of a building, or one of its façades, which can be front, back, or any of the sides. More specifically, it describes the type of drawing made from projecting a building’s façade at right angles onto a vertical plane parallel to that façade (or an imaginary flat surface, if the façade is curved). Along with an accompanying plan and section, the elevation is consistently scaled, and thus forms part of the orthographic set of drawings used to define a structure’s exact measurements. Vitruvius wrote in De Architectura (c. 15 BC) that an ‘elevation is a picture of the front of a building, set upright and properly drawn in the proportions of the contemplated work’. From the Renaissance onwards, but especially in 18th- and early 19th-century drawings, elevations were often combined with perspective to show more depth and reveal recesses and projections, also emphasized by using shading. More recently, in the 20th century, axonometric projections have taken over a similar role, while today computer-generated three-dimensional models allow for unlimited numbers of orthographic projections in any plane.
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As a drawing, an elevation depicts the front of a building in an orthogonal projection, showing accurate dimensions of all its parts.
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In The Projective Cast (1995), architect and historian Robin Evans suggested that the reliance on orthographic drawing, including the elevation, has promoted the prevalence of rectangular shapes in buildings. As the projective plane employed to construct an elevation is flat and straight and not curved, it encourages the design of flat and straight elevations in buildings. With the rise of computer-aided design and three-dimensional modeling, in recent decades architectural design has produced more non-orthogonal schemes.
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3-SECOND BIOGRAPHIES
JOHN HEJDUK
1929–2000
American architect/artist with an interest in the creative and theoretical possibilities of architectural drawing
ROBIN EVANS
1944–93
British architect, teacher and historian, known for pioneering work on architectural drawings
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Anne Hultzsch
An elevation presents accurate measurements of a building’s façade, as well as an easily recognizable image.
Symmetry is perhaps the most easily accessible idea within the wider realm of architectural geometry and number systems. The principle is a familiar one, that one side of an image is a close match of the other. Egyptian pyramids can be described as embodying this principle, as can other examples from antiquity such as the Parthenon in Athens or Rome’s Pantheon. Classical buildings will almost always feature an equal number of columns along a façade so that the entrance can be placed centrally – an unequal number of columns or compositional devices would force the entrance to be placed off-centre. The 16th-century Italian architect Palladio took ideas of symmetry to an extreme, notably in his Villa Capra (1560): each of its four façades is identical, and the plan of the building (a small circle within a larger square) is entirely symmetrical either side of both axes. Neoclassical architects after the Renaissance employed symmetry as part of their design language, including Lord Burlington in Britain (Holkham Hall and Chiswick House) and the USA’s John Russell Pope (Jefferson Memorial). The Capitol building in Washington, DC, built and extended throughout the 19th century, is a prime example of the power of symmetry.
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Symmetry is the principle that a building, in plan or elevation, is broadly mirrored either side of a central axis.
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As a rule of thumb, Classical architecture tends to embody the principle of symmetry, whereas Gothic and medieval architecture is more variable. The (largely) 19th-century Palace of Westminster in London, a Gothic design, is distinctly asymmetrical in form, in spite of the strict compositional rhythms of its surface. The works of some architects today – notably Frank Gehry and Daniel Libeskind – are celebrations of asymmetry.
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3-SECOND BIOGRAPHIES
LORD BURLINGTON
1694–1753
English nobleman, architect and promoter of Palladianism
INIGO JONES
1573–1652
English architect responsible for bringing Italian Classical style to England
FRANK GEHRY
1929–
Canadian-American architect, designer of the Guggenheim in Bilbao, Spain, and the Walt Disney Concert Hall, Los Angeles
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David Littlefield
Symmetry, often symbolic of geometric purity, can manifest itself in elevation and in plan.
Background for the development of perspective as a graphical-representation technique dates from the art of the late medieval period. As art began to adopt more representational techniques, Renaissance artists such as Leonardo da Vinci and Albrecht Dürer studied the methods required for constructing realistic perspective images. In the 17th century, Blaise Pascal and Gérard Desargues were among the first mathematicians to explore perspective in a way that would establish it as a vital tool in architecture, art and engineering. With the development of the theory of projective geometry in the 19th century through the work of Jean-Victor Poncelet, Karl von Staudt, August Ferdinand Möbius and Jakob Steiner, perspective became a formal mathematical inquiry. In these studies the most important elements are the distance of objects from the eye of the observer and the illusion of depth within the constructed space, which is created through one or more vanishing points. Today, with advances in computer-generated three-dimensional modelling, a perspective image is easily constructed with the use of appropriate software. These can be rendered in any number of ways according to the purpose, as photorealistic or any other suitable style.
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Perspective is a two-dimensional representation of three-dimensional space that architects use to depict the environments they create.
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Early theories of how the eye perceives the world were explored by the Greek mathematician Euclid, who stated that the eye projects visual rays onto an object and the resulting perception of the world occurs as a dynamic activity of the observer. Alhazen, a Muslim scientist, made significant contributions to the principles of optics in the early 11th century, one of which was the idea that we see because rays of light enter the eye.
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3-SECOND BIOGRAPHIES
EUCLID
fl. 300 BC
Greek mathematician, the ‘father of geometry’, author of Optics, the earliest surviving Greek work on perspective
LEONARDO DA VINCI
1452–1519
Italian Renaissance polymath, who experimented with perspective in his paintings
ALBRECHT DÜRER
1471–1528
German painter, engraver, mathematician and theorist of perspective
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Dragana Cebzan Antic
Perspective is used to depict the space inside and outside of the building that usually shows an image as it would be seen from the eye level view.
Axonometric drawings are a relatively recent technique (c. 19th century), first developed as tools for the analysis of structures. They look like strange, distorted perspective drawings – paradoxically, because axonometric drawings are mathematically precise. In perspective, parallel lines converge, while in axonometric, parallel lines remain parallel – they never meet. This is because in axonometric projection all measures at all three planes – height, width, depth – remain constant. Therefore, all component parts of a structure and the spaces between are given a precise, measurable relationship. This makes it very powerful for the architect. An axonometric image can either be given as a bird’s-eye view, looking down onto the corner of a building, or a worm’s-eye view, looking up into the corner of a building. Various techniques are used to show parts of a building that would otherwise be hidden by walls, ceilings, or roofs, including: cutaways, as if parts of the building have been peeled off; wire frame, showing all the edges where surfaces meet, as if the building were made of wire; and exploded, as if the building were an assemblage of parts that had been extruded along horizontal and vertical planes.
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Axonometric projection in its various forms – isometric, diametric, trimetric and oblique – is a powerful tool for analysing and constructing three-dimensional space on a two-dimensional surface.
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Axonometric drawing was first formalized in the 19th century as ‘isometry’ (‘equal measure’) by the natural philosopher William Farish. French Rationalist architects of the period found it useful in analysing ancient structures, and it became a key form of projection for Modernists, suiting their view of architecture as rational and machine-like. Common in Europe until the Renaissance development of perspectival projection, axonometric drawing continued to be used elsewhere, notably in China.
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3-SECOND BIOGRAPHIES
AUGUSTE CHOISY
1841–1909
French Rationalist architect
THEO VAN DOESBURG
1883–1931
Dutch artist, architect and founder of De Stijl, who used axonometric projection to powerful visual effect
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Nick Beech
James Stirling (1926–92) made axonometric projection an art form: here, the History Faculty Library at Cambridge University.
In architectural practice, scale refers most commonly to the relationship that exists between a building and its representation in terms of size and complexity. It is used in plan or model scales, say 1:100, which means that one part in the plan or model is equal to 100 parts of the real thing. Scale also describes the idea of proportionality, as when we speak of a building being ‘out of scale’. This points to a break in continuity of a common set of size relationships preeminent in a place – for instance, if a large-scale 10-storey office complex occupying a whole block is inserted into a residential neighbourhood of smaller-scale four-storey buildings, it will create an imbalance in the relative scale. Finally, there is the concept of human scale, which pertains to the idea that an environment can either promote or inhibit human comfort and interaction. Leonardo da Vinci’s so-called ‘Vitruvian Man’ (c. 1490) as well as Le Corbusier’s ‘Modulor’ (1948) – a scale of proportions based on the human form, the Fibonacci numbers and the golden ratio – were both attempts to link human proportions to an ideal scale in buildings.
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Scale describes the size relationship between a whole and its parts, or between an object and its representation.
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The meaning of scale is today challenged by seemingly scale-less computer-aided design, in which we zoom into and out of drawings with a scroll of a mouse. While in paper drawings scale is determined by the draftsperson, virtual CAD models enable the viewer to smoothly switch scales in real time. As this is not automatically accompanied by an increase or reduction of detail shown, scale is in danger of becoming peripheral to architectural production.
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3-SECOND BIOGRAPHIES
LEONARDO DA VINCI
1452–1519
Italian painter and polymath with strong interests in architectural theory and design
LE CORBUSIER
1887–1965
Swiss-French architect, designer and urbanist, a pioneer of modern architecture
30-SECOND TEXT
Anne Hultzsch
Mathematical ratios, buildings and their components, even the human form, depend on the concept of scale.
Celebrated and derided, vilified and deified, Le Corbusier polarized opinion among fellow architects and the general public, and his work is still reassessed and reevaluated today. Born Charles-Édouard Jeanneret-Gris in Switzerland, in 1920 he reinvented himself as Le Corbusier, his name becoming almost a brand for his activities as an artist, theorist, writer, furniture designer, architect and town planner.
Early experience in the offices of Auguste Perret (the pioneer of reinforced concrete) and Peter Behrens (where he would have come across Walter Gropius and Mies van der Rohe) had a great influence on him. After a period as an artist, in 1922 he set up a practice in Paris with his cousin Pierre Jeanneret and worked mostly on private villas, notably the Villa Savoye at Poissy, which embodied his Five Points of Architecture. Using steel, glass, reinforced concrete and the aesthetic of an ocean liner, this is now regarded as the quintessential Corbusier construction.
In 1923 he published the influential Vers une Architecture [Toward an Architecture], which outlined his concept of a planned city that would eliminate the slums and squalor that could lead to social unrest. Le Corbusier went on to work on various ambitious urban-planning projects, publishing his ideas in La Ville Radieuse (The Radiant City) – which was influenced by the garden-city movement – which culminated in his work on Chandigarh, the new capital of the Punjab in India, for which he devised the plan and many of the buildings.
He also developed his Modulor system as a guide to proportion in domestic building based on human proportions. He applied this to the Unités d’Habitation tower blocks – his machines à vivre – which were built in various French cities, the one in Marseilles being the best known. On the back of these, Le Corbusier has been blamed for the blight of grim, alienating tower bocks all over northern Europe – although his supporters argue that his ideas have been misunderstood and misappropriated. However, he was without question also capable of reaching the sublime, which he did most effectively in the chapel of Notre Dame du Haut at Ronchamp. A departure from Corbusian standardization, it is at once simple and complex, using plain materials with an upturning heaven-seeking roof, yet the space within is made mysterious and transcendent, full of veiled light from a series of asymmetric windows punctuating the thick, unadorned walls.
Born in La Chaux-de-Fonds, Switzerland
1907
Worked in Paris for architect Auguste Perret
1908
Studied architecture in Vienna with Josef Hoffman
1910–11
Worked in Berlin with architect Peter Behrens
1911
Travelled to the Balkans and Greece; made drawings of Classical Greek architecture
1914–15
Worked on a theoretical project known as the Domino House
1918
Returned to Paris and took up painting after meeting Cubist Amédée Ozenfant; published their manifesto on Purism and the journal L’Ésprit Nouveau (1920–5)
1922
Worked on Immeubles Villas, tower blocks of social housing, and designed private houses
1922
Put forward his unrealized scheme for the Ville Contemporaine
1923
Published Vers une Architecture
1925
Devised the Plan Voisin, an unrealized urban-renewal scheme for Paris
1925
Published L’Art Décoratif d’Aujourd’hui which railed against craft traditions and ornamentation
1927
Designed Villa Stein
1929–31
Designed Villa Savoye, an exemplar of his Five Points theory as defined in Vers une Architecture
1935
Published La Ville Radieuse, redefining his theories of urbanism
1946–52
Designed Unités d’Habitation – residential housing projects
1948
Published Le Modulor, an anthropometric scale of proportions
1950–4
Designed chapel of Notre Dame du Haut, Ronchamp
1952–9
Developed Chandigarh, India’s first planned city
1953
Designed monastery of Ste-Marie de la Tourette, Éveux
25 August 1965
Died at Roquebrune-Cap-Martin, France
