Exploring Geometry in Architecture Sam, April 9, 2024May 3, 2024 In modern architecture, we use two and three-dimensional geometry to design buildings that can be found in both theoretical and physical states. Architecture is now looking into using more advanced computational geometry algorithms as design processes become more complex.In this article, we will identify and explain some of the different geometric principles. Step-by-step, from the most basic to advanced geometry used in the architectural design process. We will also provide examples of structures that have been designed using geometry.Table of Contents ToggleWhat is Geometry in Architecture?History of Geometry in Architecture Notable Geometric Buildings 1. The Great Pyramid of Giza. 2. Notre Dame Cathedral. 3. The Parthenon. 4. Philips Pavilion. 5. CN Tower. 6. Virupaksha Temple. 7. The Taj Mahal. 8. Palazzo Rucellai. 9. United Nations Headquarters. 10. Melnikov House. The Implementation of Geometry in Modern Architecture Why Has Geometry Been Sidelined in Most Modern Geometric Designs?1. The Evolution of Architecture 2. Technological Advancement Alternative Tools Modern Architects Use For Design Inspiration. 1. Artificial Intelligence 2. Nature3. Computer Aided Design (CAD) / 3D SoftwareImportance of Geometry in ArchitectureGeometrical Concepts in ArchitectureGeometric Shapes in Architecture1. Rectangles2. Cubes3. Triangles4. Squares5. Circles6. HexagonsOther Geometric Shapes in Architecture.Frequently Asked Questions (FAQs) on Geometry in Architecture.Which Geometry is Best for Architecture?Which Geometric Forms are Employed in Building?Which Architectural Shape is the Strongest?Which Shape is Most Frequently Utilized in Architecture ?Why Do Architects Use Geometric Shapes in Design?Recommended PostsConclusionWhat is Geometry in Architecture?Geometry in architecture simply means designing buildings according to geometric principles. With scattered examples of the important relationship between geometry and architecture through history and into the present time, an understanding of the effect of geometry on the behavior of a structure is a valuable tool for any architect or engineer.Geometry has been a topic of interest to great minds from varied fields for centuries. Mathematicians and scientists inquire about its form and shape, artists apply it in design and nature, and physicists and biologists search for order and symmetry in the universe. Amongst these, architects also have a vested interest in the topic. From its conception to the present day, geometry has been an influence in design and construction.Architects do not build on nothing. They must build on predetermined conditions, and these form a framework that the architect must work within.I believe that humans have a natural appreciation for beautiful geometric forms. This, in my opinion, is the reason we try to create precise geometric layouts while designing.In order to figure out this innate inclination to value outstanding geometric architectural forms, we must first examine the historical background of geometry in architecture.History of Geometry in Architecture Understanding the history of geometry is necessary before we can comprehend the geometry of architecture. Let’s get to that below:The “ideal” proportions for a structure are derived from the proportions of the human body, according to Marcus Vitruvius, a Roman architect who wrote Ten Books on Architecture in 20 BCE.Renaissance scholars like Leonardo Da Vinci, who portrayed his ideas in his drawing “Vitruvian man,” and Leon Battista Alberti, who wrote his own version of Ten Books on Architecture, rediscovered his teachings fifteen hundred years later.The Roman architect and writer Vitruvius made the argument that a building must satisfy three requirements in order to be considered good, those requirements are utility, firmness, and delight, in his work “De Architectura.”Buildings that are in tune with nature are the way to happiness, according to Vitruvius. And geometry served as our main means of deciphering the designs seen in nature. Things like symmetry and the relative sizes of pieces were among the things that nature taught us.This newfound knowledge of geometry allowed for its application to human inventions, including the best of our artistic endeavors.Leonardo Da Vinci’s vitruvian man is among the most renowned instances of the use of geometry in art and architecture. The goal of this artwork is to determine how the human form can be concurrently engraved inside a circle and a square.Leonardo Da Vinci’s Vitruvian Man.Source: Wikipedia.In the process, it becomes unclear if the human form is essentially derived from geometric principles, or if geometry is a useful tool for describing the human form.However, geometry is necessary not just to comprehend the human form but also to comprehend buildings.So, now let’s discuss the history of geometry in architecture. The ancients – that is the Greeks, and their successors the Romans – were the first to put the construction of a building on to a plane, and then to develop a theory of two and three dimensional geometry that the building then followed. Almost every form constructed was able to be resolved into components of simple shapes which were then laid down on the plane.The Parthenon is a classic example. It’s an octostyle peripteral building, which means that it has a portico with 8 columns at the front, and is entirely surrounded by a single row of columns. This is a rectangular design and the components that make up the shapes of the pediments, entablature and decoration can all be broken down into triangles, circles and various other polygons.The theory of this geometry was well understood by the builders and they would use various straight edge and compass methods in making sure the dimensions and proportions were correct. This theory was then expanded to solid geometry with the work of Archimedes and Euclid. Most of the earlier work was forgotten about until the early Renaissance.One of the greatest advancements in architectural geometry occurred in the 17th century thanks to the work of German mathematician and astronomer Johannes Kepler.The significance of geometry in understanding the physical universe was demonstrated by Kepler’s work on the laws of planetary motion. These laws changed the way architects approached building design.Geometry is valued all over the world. Let’s take a look at a few buildings that clearly depict the application of geometry in building construction.Notable Geometric Buildings 1. The Great Pyramid of Giza. Architect: Hemiunu (fl. 2570 BC).Location: Giza, Egypt. The Great Pyramid of Giza.Source: Wikipedia.The geometry of building was highly valued by the ancient Greeks, Romans, and Egyptians. Their enduring architecture and structures are clear examples of this.One magnificent example is the enormous pyramid located at Giza. One thing is certain—the big pyramid base is a true geometric wonder—each side measuring around 230 meters (755 feet) with an inaccuracy of only a few inches. We have no idea how they built it; historians and experts are still baffled by its creation.The sides of the pyramid are angle” at 51 degrees and 51 minutes, creating a nearly perfect pyramid shape.Another intriguing geometric feature of the pyramid is its interior. Its downhill pathway, which is precisely 26.6 degrees, is in line with the north face of the pyramid and reflects the slope’s angle.2. Notre Dame Cathedral. Architects: Jean de Chelles, Pierre de Montreuil, Pierre de Chelles, Jean-Baptiste Lassus, Eugène-Emmanuel Viollet-le-Duc.Location: Paris, France.The Notre Dame Cathedral.Source: CNN.The cathedral, with its golden proportions at every level of construction, is the most exquisite example of French Gothic architecture. The upper columns’ widths exhibit a similar ratio, contributing to the design’s eye-catching quality.3. The Parthenon. Architects: Ictinus and Callicrates.Location: Athens, Greece.The Parthenon.Source: Smarthistory.Architectonic geometry is also well-known from the Parthenon in Athens, Greece. The temple’s design demonstrates the application of geometry in its harmony and balance. For instance: The structure has a perfect 9:4 height to width ratio, and its columns, friezes, and pediments are all based on mathematical calculations.4. Philips Pavilion. Architect: Iannis Xanakis.Location: Brussels, Belgium.Philips Pavilion.Source: Structurae.Xanakis took over the pavilion’s direction from Le Corbusier, and he used concrete to craft an unlikely set of nine hyperbolic paraboloids.Regretfully, the year after it was constructed, Xanakis’ memorial to technological advancement was destroyed.5. CN Tower. Architect: John Andrews.Location: Toronto, United States of America.CN Tower.Source: Wikipedia.Despite being contemporary, one of the world’s tallest freestanding buildings was created with the golden ratio in mind. The observation tower has a ratio of 0.618 to the overall height, with a variety of geometrical forms and shapes. The construction is well-balanced and the design is distinctive.6. Virupaksha Temple. Architect: Lakkan Dandesha.Location: Hampi, India.Virupaksha Temple.Source: Britannica.If you’re interested in the idea of fractal architecture, take a closer look at this Hindu temple in the Indian state of Karnataka. The patterns on the gopuram (entrance tower) divide and repeat as they ascend – just as in they do towards the edges of a snowflake or a leaf.7. The Taj Mahal. Architect: Ustad-Ahmad Lahori.Location: Uttar Pradesh, India.The Taj Mahal.Source: Britannica.Architectural geometry is best exemplified by the Taj Mahal in India. Because of its geometry, a lot of people even go so far as to consider the Taj Mahal to be among the most beautiful structures ever constructed.Even the smallest features, like patterns, and the greatest, like the symmetry of the building, exhibit geometry in the Taj Mahal.8. Palazzo Rucellai. Architect: Leon Battista Alberti.Location: Florence, Italy.Palazzo Rucellai.Source: Smarthistory.Leon Alberti published a dissertation on the proper use of geometry in building, and he created this palace. The structure demonstrates that Alberti lived according to his theories; pilasters and entablatures divide the façade into harmonious proportions.9. United Nations Headquarters. Architect: Harrison and Abramovitz.Location: New York, United States of America.Headquarters of the United Nations Headquarters.Source: Open House New York.Le Corbusier used the Modulor scale of proportions to design the UN building, which is a slab block. In order to facilitate conversion between the metric and imperial systems, the Modulor was designed to be based on the height of a man with his arm raised over his head. Though its unique shape has always caused controversy, UNHQ is an iconic building.10. Melnikov House. Architect: Konstantin Stepanovich Melnikov.Location: Moscow, Russia.Melnikov House.Source: Wikipedia.This is one of the few cylindrical structures that has withstood the test of time; it was built by Soviet artist and architect Melnikov, who refused to construct in the style that Stalin insisted upon.The structure consists of two cylinders with asymmetrically arranged hexagonal windows, constructed from bricks arranged in a honeycomb lattice pattern.The Implementation of Geometry in Modern Architecture Burj Khalifa.Source: Wikipedia.Geometry is a source of inspiration for modern architects, who use it to create unique and dynamic patterns in their works. Modern architecture has made use of parametric design, a computer technique that creates intricate forms through algorithms. Using techniques for parametric modeling, architects can design complex patterns into their structures.We utilize geometry to ensure, at least in theory, that our structures remain upright, that our plans are understandable to people around the world, and that we don’t overcrowd our cities with unsightly, unbalanced construction.Modern architects also employ geometry by adopting “biomorphic” geometric forms, or shapes that are a replication of forms seen in natural environments. Of course, when Vitruvius and his adherents employed the proportions of the human body, they were doing this to some degree.Many of the traditional “rules” on harmonious proportions in architecture are still valid, but they are no longer rigidly adhered to; in fact, doing so is actively encouraged.Modern architecture does not employ geometry in the same rigid ways as it did in the past. While they still adhere to geometry’s laws in order to produce designs that are harmonious and balanced, they also make an effort to defy the principles wherever they can.Why Has Geometry Been Sidelined in Most Modern Geometric Designs?This change, in our opinion at Archilinx, occurred for two main reasons:1. The Evolution of Architecture Contemporary architecture is not confined to conventional, inflexible shapes. In order to design more proactive buildings, architects now commonly employ curves, irregular shapes, and organic forms. Compared to rigid geometric shapes, these designs frequently call for greater adaptability and inventiveness.Although it is no longer the master, geometry is still very important in building. On the contrary, it’s merely one of the instruments that architects employ nowadays to achieve their goal.2. Technological Advancement Modern architects are able to create more intricate and imaginative designs due to access to cutting-edge technology and building methods.In addition to these, there are other tools and resources modern architects utilize for design inspiration. What other resources do architects employ in addition to geometry to generate ideas? Well, let’s look at that below:Alternative Tools Modern Architects Use For Design Inspiration. Modern architects are inspired by more than simply geometry; they use a variety of techniques, tools and resources.Let’s discuss those tools below:1. Artificial Intelligence There is no denying that artificial intelligence is the way of the future. Architecture is not an exception to the way AI is already fundamentally altering every industry.Interesting AI-generated architecture concepts are already visible. In their bios, some people began referring to themselves as “AI architects.”Using AI technology, architects are now able to create new ideas and concepts that were previously unimaginable.2. NatureArchitects often draw inspiration from nature. Their colors, patterns, and shapes serve as frequent sources of inspiration for architects.Rather than utilizing geometry, an architect can, for example, base a building’s design on how a tree branches out.3. Computer Aided Design (CAD) / 3D SoftwareModern architects are able to produce endless ideas, construct parametric solutions, and preview how a structure would look under various conditions thanks to technology advancements in 3D modeling applications.The architect was able to move beyond conventional geometry because of this independence.Given their abundance of resources, one may ask, why do architects still utilize geometry? Let’s find out below:Importance of Geometry in ArchitectureThese points below demonstrate how geometry plays a variety of roles in architecture, including practical, aesthetic, and technological aspects. Let’s briefly discuss them:Sustainability: Using parametric design techniques, architects can explore intricate geometric configurations that adapt to particular environmental conditions, maximizing energy efficiency and environmental performance in buildings.Symmetry: Both in general building layouts and in details like facades and interiors, geometry is used to produce compositions that are balanced and symmetrical.Proportion: When designing buildings, architects frequently employ geometric concepts like the Fibonacci sequence and the Golden Ratio to create proportions that are harmonious.Structural Stability: Shapes like triangles and arches are frequently utilized to transfer loads and resist forces, and geometry is a key factor in determining the structural integrity of structures.Spatial Organization: Architects utilize geometric shapes and patterns to properly arrange interior spaces and establish straightforward routes for inhabitants to travel through.Lighting: Buildings can benefit from optimal natural lighting through the use of geometry. Techniques like light shelves, skylights, and clerestory windows use geometric concepts to regulate the amount and distribution of sunshine.Contextual Relevance: Geometry in architecture is sensitive to and respectful of its surrounding environment, which includes the urban fabric, the surrounding terrain, and the surrounding cultural context.Cultural Significance: The optimal geometry frequently includes components with symbolic, historical, or cultural significance.Aesthetic Expression: To create visually arresting and culturally significant buildings, geometric patterns, motifs, and ornamentation are regularly included into architectural design.Acoustics: To improve or reduce sound transmission in architectural environments, specific geometric forms and arrangements are used, which enhances acoustic performance and comfort.Given the significance of geometry in architecture, which well-known concepts of geometry have architects employed in designing their buildings?Geometrical Concepts in ArchitectureArchitecture is made up of several geometric concepts. Let us first define and discuss the most widely used geometric concepts in architecture below:Points: A point is used to identify a location in a plane represented by an ordered pair, and it has no magnitude and dimensions.Lines: A line is the path traced out by a moving point and has these properties: it is completely known if we are given two distinct points, it is straight, and it extends indefinitely in both directions.Angles: Angles are the unit of measurement used to determine how far apart two lines are from one another.Shapes: A shape is a geometric form that can be created through a combination of lines, planes, or an actual physical boundary around a real or mathematical object.Symmetry: In order to achieve harmony and balance in their designs, architects employ the geometric concept of symmetry. Symmetry is a balanced arrangement of shapes or patterns on both sides of a central axis.Tessellation: Tessellation is a tool used by architects to produce complex patterns in buildings. Tessellation is a process to cover a plane with a pattern.Solids: Solids are three-dimensional structures made up of a combination of different shapes, such as spheres, cylinders, cones, and cubes.Perspective: Creating the appearance of depth and space on a surface that is two-dimensional through optical illusion is known as perspective.Modular Systems: a technique for dividing a space or form into recurring elements in architectural design to create rhythm and proportionProportions: The link between an object’s size in one section and its size in another part or as a whole is known as its proportions.Golden Ratio: Architects use the golden ratio to create balance and proportion in their designs. The ratio 1.618, is the most aesthetically acceptable ratio for the human eye. Golden ratio proportions can be found in the geometric shapes used by architects in their constructions, such as the Parthenon in Athens, Greece, which features a facade that follows this pattern.Architects and engineers employ these ideas to design safe, secure, and visually beautiful buildings.Geometric Shapes in ArchitectureIn architecture, using geometric shapes is not only a matter of taste. The structural and functional ramifications of every geometric shape can affect a building’s overall design.Let’s begin with the rectangle, a commonly used shape in architecture.1. RectanglesThe basic geometric shapes, including the rectangle, are considered the “blocks” of our surroundings. This is because such shapes are the foundation of all other complex shapes. In the same manner, a simple four-sided rectangle provides an interesting basis for many architectural forms.Rectangles offer a great opportunity in the creation of balanced, stable, and tranquil designs. This is due to the fact that as a rectangle is not offset, the majority of load-bearing structures will take on a rectangular form. The use of the rectangle has been pivotal within architectural design. It is one of the most simplistic shapes but can have such a profound influence on the overall aesthetic of a building.2. CubesDue to the power and resilience that a cubic building evokes, the cubic form is thought to be very significant in architecture. The geometry of cubic objects is obvious. They look stable and secure because of this.Because every corner is uniformly planned, these buildings provide for easy orientation. For buildings where a controlled, orderly flow is desired, cubic forms are especially appropriate.3. TrianglesTriangles in architecture have been used to great effect. In recent history, buildings are designed with a frame to take the weight of the building, thereby enabling vast open spaces in the interior.A good example of this can be seen in a typical sports hall design with a pitched roof. The most optimum way of creating a frame that will take a great load is to use triangles. This is because they are not deformable, and if the joints are pinned, no member of the frame will experience a force other than that which is induced by the weight it supports.This will let architects use as little framework as possible so as not to obstruct the interior space, and also a good frame can be a feature of the building. This can now be seen in the shapes of many public buildings using modern materials and methods, such as the British Museum.4. SquaresThe use of squares has been prevalent in architectural designs and compositions. The geometrical properties of a square have always been able to be designed within architecture.The oldest examples were found in ancient times. Egyptians and Greeks employed squares in virtually all of their monumental structures. Temples, palaces, and their surrounding public areas were frequently based on an overall plan constructed from a square grid of streets and walls.In symbolizing the attributes of stability and rational order, the square provided a powerful representational tool. The design and placement of actual structures were often based on the plan of a large square.5. CirclesThough they are less frequent in architecture than rectangles, circles and spirals have their uses. Circles are a common design element used by architects to give a structure a sense of flow and continuity.6. HexagonsHexagons are not as frequently used by architects as other forms, although in recent years, their use has increased.When utilized appropriately, hexagons give a design individuality and intrigue.Other Geometric Shapes in Architecture.There are numerous geometric shapes that can be conceived besides the square or cubic forms. These consist of building structures that are trapezoidal, elliptical, or round.In representational areas, elliptical shapes are frequently utilized. Buildings with trapezoids foster an energetic and dynamic environment. Because of this, architects frequently use them while designing sports or recreation centers.Frequently Asked Questions (FAQs) on Geometry in Architecture.Which Geometry is Best for Architecture? In the field of architecture, the notion of a “ideal geometry” is arbitrary and contingent upon the building’s intended use, architectural style, cultural background, and the architect’s and client’s individual tastes. There are many different elements that influence the ideal geometry in architecture, such as practicality, aesthetic choices, cultural settings, and environmental considerations. Since the optimal geometry differs significantly between architectural projects, there is no universal answer.Which Geometric Forms are Employed in Building? The most popular shapes for large-scale construction are triangles, arches, and rectangles.Which Architectural Shape is the Strongest? The triangle is the strongest because it maintains its shape, has an extremely sturdy foundation, and a robust support system.Which Shape is Most Frequently Utilized in Architecture ? In architecture, rectangles are the most often utilized geometric shape. Their popularity in architectural design stems from their simplicity and ease of use.Why Do Architects Use Geometric Shapes in Design? Geometric shapes can convey a variety of ideas or statements in design. For instance, a triangle that has been distorted can indicate danger, whereas a circle might stand for a continuing cycle or continuous operation. Recommended PostsThe Marriage of Form and Function in ArchitectureOverview of Functionalism in ArchitectureOverview of Functionality in ArchitectureOverview of Avant-Garde ArchitectureBest 24 Ways to Achieve Functional Aesthetics in Your HomeConclusionGeometry and architecture have been connected for centuries and are still relevant in modern architecture.When creating buildings, it is crucial for you as an architect or planner to take into account the impact of fundamental geometric shapes.The choice of various forms vary among individuals so you ought to consider carefully the shapes you utilize in your designs because of this. It won’t be until then that you can satisfy the demands of the users and get the intended result.Total0Shares Share 0 Tweet 0 Pin it 0 Share 0 Articles
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