1. Geometry in Architecture
THE MATH and application in MODERN ARCHITECTURE
By Alma Zalo

2. The preview. Examples of Architectural designs inspired by Mathematics
The motive and/or insight behind some designs.
Advantages of such designs and the added-value.
Is it all about the aesthetic value?

3. Petronas Towers – Kuala, Malaysia
Agora Tower – Taipei ,Taiwan

4. The never ending illusion
Flatiron building, also Fuller building- NY, USA
Ripley’s Building - Ontario

5. The dancing building – Prague, Czech Republic
The crooked House – Sopot, Poland

6. The connection with Math.
Designing such enormities is a delicate balancing act. A building not only needs to be structurally sound and aesthetically pleasing, it also has to comply with planning regulations, bow to budget constraints, optimally fit its purpose and maximize energy efficiency.
The design process is a complex optimization problem. Advanced digital tools can analyze and integrate the bewildering array of constraints to find optimal solutions.
Math describes the shapes of the structures to be built, the physical features that have to be understood and, as the language of computers, forms the basis for every step of the modelling process.

7. 30 St Mary Axe; nicknamed as The Gherkin, In London, 41 floors,
minimize whirlwind around its base, shape maximizes ventilation,
uses half the energy others towers the same size use
Mobius Strip Temple - In China

8. Incorporating technology
With the help of computers you can model aspects of a building, from its physics to its appearance. Computer models can simulate things like the way the wind blows around the building or sound waves bounce around inside it.
Graphic programs can explore different mathematical surfaces and populate them with panels of different textures. The information you get from these models can be pulled together in architectural CAD tool called parametric modelling.
Parametric models allow you to change a variety of geometrical features while keeping fixed those features you have decided should not change..
A design team can explore a huge range of design options in a very short period of time;
change geometric features of a building and see how the change affect aerodynamic properties,
can explore how complex shapes that are hard to build can be broken down into simpler ones,
can quickly calculate how much material is needed to estimate the cost.
The results…

9. The London City Hall on the river Thames.
Note the giant helical stair case inside
The use of glass and a giant helical staircase in the interior are
supposed to symbolize the transparency and the accessibility of the democratic process.

10. More on CAD
Surfaces that can be described by mathematical equations — such as slices of cones, tori, or spheres — often form the basis of designs.
This is advantageous when it comes to creating virtual models, as mathematically generated surfaces are easily represented on a computer.
Rather than describing a structure by a large number of individually stored co- ordinates, you only need to store an equation.
The exact shape of the surface can be controlled by varying the parameters in the equation The motive and/or insight behind some designs.

11. A Mathematically generated surface
z = e-a(x^2+y^2)
z is the vertical axis in the 3-D coordinate system.
The number a determines the shape of the surface.
The first surface has a=1
The second surface a=5
The third surface has a=7.

12. The tallest of the super tall…
World Records;
At over 828 meters (2,716.5 feet) and more than 160 stories, Burj Khalifa holds the following records:
Tallest building in the world
Tallest free-standing structure in the world
Highest number of stories in the world
Highest occupied floor in the world
Highest outdoor observation deck in the world
Elevator with the longest travel distance in the world
Tallest service elevator in the world

13. About that aesthetic value…

14. Exam question! What is the name of the tallest building in the world?
The Burj Khalifa.

15. References
EMAAR. The Tower. n.d <
Freiberger, Marianne. Perfect buildings: the Maths of modern architecture. Ed. Plusadmin <
Nastasi, Alison. 10 Amazing Examples of Architecture Inspired by Mathematics <