Geometry, Nature and Architecture
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The document discusses the relationships between nature, geometry, and architecture. It provides examples of geometric patterns found in nature, such as hexagonal honeycomb structures and symmetrical flower patterns. Geometry has historically been used in architecture for spatial layout, decoration, and meeting structural requirements. Examples discussed include ancient Egyptian pyramids, Greek temples, Islamic tiling patterns, Chinese tulou structures, and Gothic cathedrals. Modern architects like Gaudi incorporated complex geometries in works like the Sagrada Familia, drawing inspiration from nature.
![• Some Hindu temples have a fractal-like structure where parts resemble the whole, conveying a
message about the infinite in Hindu cosmology.
What is fractal?
a curve or geometrical figure,
each part of which has the
same statistical character as
the whole. They are useful in
modelling structures (such as
snowflakes) in which similar
patterns recur at
progressively smaller scales,
and in describing partly
random or chaotic
phenomena such as crystal
growth and galaxy formation.
Kandariya Mahadeva Temple (c. 1030), Khajuraho,
India, is an example of religious architecture with
a fractal-like structure which has many parts that
resemble the whole.[2]](https://image.slidesharecdn.com/maamhiraqureshi-181229122054/85/Geometry-Nature-and-Architecture-28-320.jpg)
![• In Renaissance architecture, symmetry and proportion were deliberately emphasized by architects such
as Leon Battista Alberti, Sebastiano Serlio and Andrea Palladio, influenced by Vitruvius's De
architectura from Ancient Rome and the arithmetic of the Pythagoreans from Ancient Greece.
The interior of the Pantheon by Giovanni Paolo Panini,
1758
The Pantheon in Rome has survived intact, illustrating
classical Roman structure, proportion, and decoration.
The main structure is a dome, the apex left open as a
circular oculus to let in light; it is fronted by a short
colonnade with a triangular pediment. The height to
the oculus and the diameter of the interior circle are
the same, 43.3 meters (142 ft), so the whole interior
would fit exactly within a cube, and the interior could
house a sphere of the same diameter. These dimensions
make more sense when expressed in ancient Roman
units of measurement: The dome spans 150 Roman
feet; the oculus is 30 Roman feet in diameter; the
doorway is 40 Roman feet high.[18] The Pantheon
remains the world's largest unreinforced concrete
dome.](https://image.slidesharecdn.com/maamhiraqureshi-181229122054/85/Geometry-Nature-and-Architecture-31-320.jpg)
Geometry, Nature and Architecture
- 1. DEPARTMENT OF ARCHITECTURE ARCHITECTURAL ANALYSIS BATCH 2017
- 2. GROUP MEMBER NAMES: MASOOMA DAWOOD MAHAM KHAN MISDA SABA MAHNOOR MUMTAZ BUSHRA KHAN FATIMA SOLENGI ALIZA AKHTAR HUMZA RASHID DANNIAL
- 3. GEOMETRY , NATURE AND ARCHITECTURE What is Nature? the phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations and the basic or inherent features, character, or qualities of something What is Geometry? Geometry is Greek word where Geo means earth and metry means measure. And its the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. What is Architecture? Architecture is said to be mother of Art where the process of planning , designing and construction buildings or any other structures are involved.
- 4. EXAMPLES: NATURE: Sky, Sun , Water and sand Clouds, cotton and human Trees in forest
- 5. SQUARE CIRCLE STAR TRIANGLE PENTAGON HEXAGON OCTAGON GEOMETRY:
- 7. INTERIOR VIEW OF SHEIKH ZEYAD MOSQUE, ABU DHABI
- 8. HOUSE
- 9. HOW NATURE AND GEOMETRY RELATES ARCHITECTURE? GEOMETRY IN NATURE: As we know geometry is Greek word which means earth-measure. In the nature all the things occurs, has specific proportions, Geometry, scale and geometry. All of nature evolves out of simple geometric patterns incorporated within the molecular "seed" structure. Each of these basic patterns contains information that enables animals, plants, minerals (and humans) to develop into complex and beautiful forms, each with an intrinsic awareness of its location in space and time.
- 10. Followings are the some example of the geometry in nature: The bees make their hives in regular hexagon.
- 11. Proportions of human body Proportions in shell
- 12. Honeycomb
- 14. These flowers illustrate perfect symmetry found in many plants in nature
- 17. PINECONE: The beautifully repetition and movement of pattern
- 19. This beautiful fossil sand dollar from Madagascar has incredible detail. The original shell consisted of small, thin, interlocking calcareous plates that have completely turned to stone. This fossil shows the 5 point "flower" symmetry common to the animal in the Echinodermata phylum. This sand dollar is slightly less than 3" in diameter and protrudes 1" at its center high point. Fossil Sand dollar
- 21. The holes in radiolarian and diatom shells respectively exist for differing reasons. Both types of skeleton are formed from silicon compounds. In diatoms, the holes collectively take on the role of a sieve, a two-way filtration mechanism across which water and nutrient molecules permeate the cell.
- 22. .
- 23. Just think about a spider's web. That is a complicated geometric design. And it is created, usually, in a perfect manner. Even though I majored in Drawing and Painting in college, and even though I am a Graphic Artist at work, I could not draw a design that perfectly, freehand. Yet a spider, using only his body, continually creates geometrically complex advanced shapes that few, if any, human adults could perfectly duplicate, without the aid of machines, or tools such as a pencil and ruler...and even with a pencil and ruler, it would be very complicated, and possibly even impossible, for most people to exactly duplicate.
- 24. The symmetrical wings and the beautiful geometric pattern on wings. Star fish
- 25. GEOMETRY IN ARCHITECTURE: Geometry and architecture are related. History: From Pythagoreans of 6th century BC onwards; • In ancient Egypt • In ancient Greece • India • Islamic world • Renaissance architecture etc. MOTIVES: Architect uses geometry for the following motives: • To define spatial form of building. • To layout buildings and their surroundings according to mathematical, aesthetic and sometimes religious principle. • To decorate buildings with mathematical objects such as tessellations. • To meet environmental goals such as to minimize wind speed around the bases of tall building. • To create forms considered harmonious What is Tessellations? A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.
- 26. EXAMPLES FROM HISTORY: In Ancient Egypt, Ancient Greece, India, and the Islamic world, buildings including pyramid, temples, Mosques, palaces, mausoleum were laid out with specific proportions for religious reasons. • In Islamic architecture, geometric shapes and geometric tiling patterns are used to decorate buildings, both inside and outside. The complex geometry and tilings of the muqarnas vaulting in the Sheikh Lotfollah Mosque, Isfahan, 1603–1619
- 27. Design of a muqarnas quarter vault Geometrical tile ornament (Zellij), Ben Youssef Madrasa, Maroc
- 28. • Some Hindu temples have a fractal-like structure where parts resemble the whole, conveying a message about the infinite in Hindu cosmology. What is fractal? a curve or geometrical figure, each part of which has the same statistical character as the whole. They are useful in modelling structures (such as snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth and galaxy formation. Kandariya Mahadeva Temple (c. 1030), Khajuraho, India, is an example of religious architecture with a fractal-like structure which has many parts that resemble the whole.[2]
- 29. • In Chinese architecture, the tulou of Fujian province are circular, communal defensive structures WHAT IS TULOU? A tulou or "earthen building", is a traditional communal Hakka people residence found in Fujian, in South China, usually of a circular configuration surrounding a central shrine, and part of Hakka architecture. Exterior of TulouInterior of Tulou
- 30. Inside the Yanxiang Lou, a large round tulou in Xinnan Village
- 31. • In Renaissance architecture, symmetry and proportion were deliberately emphasized by architects such as Leon Battista Alberti, Sebastiano Serlio and Andrea Palladio, influenced by Vitruvius's De architectura from Ancient Rome and the arithmetic of the Pythagoreans from Ancient Greece. The interior of the Pantheon by Giovanni Paolo Panini, 1758 The Pantheon in Rome has survived intact, illustrating classical Roman structure, proportion, and decoration. The main structure is a dome, the apex left open as a circular oculus to let in light; it is fronted by a short colonnade with a triangular pediment. The height to the oculus and the diameter of the interior circle are the same, 43.3 meters (142 ft), so the whole interior would fit exactly within a cube, and the interior could house a sphere of the same diameter. These dimensions make more sense when expressed in ancient Roman units of measurement: The dome spans 150 Roman feet; the oculus is 30 Roman feet in diameter; the doorway is 40 Roman feet high.[18] The Pantheon remains the world's largest unreinforced concrete dome.
- 32. Facade of Santa Maria Novella, Florence, 1470. The frieze (with squares) and above is by Leon Battista Alberti.
- 33. Ancient Egypt times the Pyramid is best example of structure in proportion and geometry. A pyramid is a structure whose outer surfaces are triangular and converge to a single point at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilateral, or of any polygon shape. As such, a pyramid has at least three outer triangular surfaces (at least four faces including the base). The square pyramid, with a square base and four triangular outer surfaces, is a common version. • Ancient Greek times were the times where people gave amazingly proportioned structure which has been proved itself in every ages or construction.
- 34. After the 19th Century: At the end of the nineteenth century, • Vladimir Shukhov in Russia • Antoni Gaudí in Barcelona pioneered the use of hyperboloid structures; in the Sagrada Família, Gaudí also incorporated • hyperbolic paraboloids, • tessellations, • catenary arches, • catenoids, • helicoids, • ruled surfaces. In the twentieth century, styles such as • modern architecture • Deconstructivism explored different geometries to achieve desired effects.
- 35. HYPERBOLOID STRUCTURE hyperbolic paraboloids, catenary arches,catenoids, • helicoids, ruled surfaces
- 38. Sagrada Família location: Barcelona, spain Building type: roman catholic church (basilica) Constructed since: 136 years The Sagrada Familia was and still is a constructional challenge: it is one of the largest testing grounds for construction methods in the world.
- 39. “I am a geometrician, meaning I synthesise.” A. Gaudí Gaudí took his inspiration from two sources; the Christian message and nature. One was derived directly from the Holy Scriptures, tradition and liturgy. The other came from the observation of the natural world, providing him with a conceptual and methodological framework. Gaudí did not copy nature but analysed the function of its elements to formulate structural and formal designs which he then applied to architecture.
- 40. Perhaps Gaudí saw that he had to find a clear and unequivocal manner to point the way forward for the construction work that he would leave unfinished. The architect planned many parts of the temple to be built combining geometric forms chosen for their formal, structural, lighting, acoustic and constructional qualities. The majority of the surfaces are ruled surfaces, making their construction easier. The main contributions Gaudí made to architecture that can be seen in the Sagrada Familia are:
- 41. To achieve greater stability and a slender and more harmonious effect, Gaudí designed all the branching columns as double-twisted columns formed by two helicoidal columns. The base of each column has a cross-section that is a polygon or star which as it twists to the right and the left transforms into a circle higher up.
- 42. As well as ruled surfaces, Gaudí developed a system of proportions to be applied to all the dimensions of all parts of the Sagrada Familia. He repeatedly used simple ratios based on twelfths of the largest dimension, as in 1 to ½, 1 to ⅔, 1 to ¾… etc. to provide proportions for the width, length and height of every part of the temple. For example; dividing the total length of the temple (90 metres) by 12 gives us a module of 7.5 metres, which is used in the design of the floor plan and the heights of the Sagrada Familia. Different measurements can be compared to better appreciate his use of numerical series, not only the general dimensions of the temple but also the diameters and heights of the columns, the diameters of the window openings and vaults, etc. For example; the total height of a column is always, in metres, double the number of points of the cross- sectional polygon of its base: a column with a 12- point star as its base is 24 metres high; a column with an 8-point star base is 16 metres high, etc.