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.

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:

6. ARCHITECTURE:
MOSQUE 3D VIEW

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

13. GEOMETRY IN LOTUS

14. These flowers illustrate perfect
symmetry found in many plants in
nature

15. S
U
N
F
L
O
W
E
R

16. SYMMETRY IN LEAVES

17. PINECONE:
The beautifully repetition and movement of pattern

18. Symmetrical slices:

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

20. SNOWFLAKE:
Ghost of
melting
snowflake.

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

36. Deconstructivism Architecture

37. Modern Architecture

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.