Architecture
Geometry All Around Us
Architecture is a Language of Geomtery
Geometry
provides a tool for
creating architecture
Geomtery: All around us in our buildings
Human language is so common that it is practically
invisible, Whereby we naturally assume that it
somehow corresponds with the world. What would
we do without languages.
Architecture (& geometry) occupies a similar place to
language.
The configuration and manipulation of materials to
enclose and control space is universal to all human
cultures.
Human “geomtery" is in every aspect of our built
world in the same way as language.
Geometry in Architecture?
• Proportions between the parts of a building, a painting,
or a sculpture. In particular, we'll look for the golden ratio
and the musical ratios.
• Use of geometric symbols, such as the circle, mandala,
triangle, square, pentagram, hexagon, or octagon, and their
use in so-called Sacred Geometry.
• Geometric Constructions, like squaring the circle, the
Gothic Master Diagram, the sacred cut, and constructions of
the pentagon.
• Shapes of Frames; how they are chosen and how they
affect the contents of a painting.
• Art Motifs, especially recurring geometric themes that we
see over and over in art.
• Math content; any geometry or other math that is closely
related to the ordering or architecture
• People, ones that played a key role in developing the ideas
related to this course, and especially those that were both
mathematicians and artists or architects.
What is Architecture
The structuring
of space using
physical
materials by
use of
geometry
Where did it all start from
The development
of civilisation is
paralleled to our
understanding of
geomtery
Ancient Geometry
An Architect created this pyramid some 5,000 years ago.
•The Egyptians used triangles extensively to build the pyramids.
•Although the shape is a pyramid the building is mainly built from
rectangular blocks
•The Egyptians also used geometry to align their buildings to the
sun and stars
Ancient Geometry
An Architect created this temple some 2,500 years ago.
Are the columns cylinders?
Geometry was critical in placing this building in the landscape
Geometric order in buildings
Geometric structure in buildings
Geometric order and decoration
Here the architect used geometry to arrange the decoration in the
window.
How many different shapes can you find in the diagram?
Layers of Geometry in decoration
There are also many different layers of geometry used to create
the decoration in the window.
Layers of Geometry in decoration
See how the patterns are all formed from different shapes.
Layers of Geometry in decoration
How many shapes can we see in this picture ?
Layers of Geometry in decoration
How many shapes can we see in this picture ?
Layers of Geometry in decoration
How many shapes can we see in this picture ?
Geometry and proportion and beauty
This house design is
considered a model of
beauty because of the
use of geometry.
How many different
squares and rectangles
can you count in the
diagram on the bottom
right?
Geometry and proportion and beauty
This architect used the
same geometry and
proportion to create
this plaza and buildings
Can you see which
shapes he has used
from the diagram
below?
Geometry and proportion and beauty
The same architect
used geometry and
proportion to create
this building
Organic Geometry
This architect used nature to inspire his geometric forms and design. He thought
that buildings and geometry should be based on what we find in nature.
Organic Geometry
To achieve his geometry he would make models of his buildings upside down to
work out how to hold them up.
Geometry in modern buildings
Who can tell me what geometry was used to design this building?
The Sydney Opera House
These pictures might give you a better clue?
The Sydney Opera House
The outside shells are formed from parts of a sphere.
Geometry and Nature
The architect of this house used geometry not to replicate nature but to create
harmony with nature
This architect only used one shape to create this building what was it?
How many different examples of this shape can you find?
Geometry and building
Architects use geometry to understand how to put their buildings together.
Sometime the shapes in between the structure is as important as the structure
itself. Describe some of the shapes between the building frames above.
Geometry and building
This building looks complex at first .... But look closely at it .... What shapes can
you see that is repeated to make this complex geometry?
Geometry and building
Triangles..... Perhaps we can look at the previous image and you can see that the
whole building is made from triangles in different patterns. This is similar to the
medieval buildings that also used geometry to decorate their buildings.
Geometry and building
This building is a simple geometry on the outside .... But look closely at it .... What
shapes can you see inside to make this complex geometry?
Geometry and building
This building is the same building from inside.... There are 3 layers of geometry
that make this building...... Can you see the different layers?
Buildings that use distorted geometry
This building is made from squares and rectangles that have been “melted” into
another form.
Can you see the melted shapes?
How far can we stretch geometry
As far as our imagination and tools allow
