Mathematics in architecture

Today this world is running on the path of digital technology. Mathematical precision is desired in every walk of life. Then why shouldn't mathematics be included in architectural design. It is very unfortunate that mathematics in architectural design is limited to architectural engineers only and is not taught in the B. Arch course. What comes up then is a design which is not most efficient as it could have been if mathematics were employed. I make myself clear with the following example. For designing windows what we look for is a balanced composition, and hardly calculate sill heights and lintel heights considering stack effect. I wonder how many of us really analyse our designs using laboratory techniques. For example we can analyse building models for airflow using a fan and smoke.Please see the picture attached.
Any kind of engineering design is tested many times before it is fabricated. This makes the design efficient. Can't we have the same for our architectural designs.


Mathematics in architecture

Nitesh! Please describe the concept of "architectural engineers" and "architects".

Mathematics in architecture

Hello Mr. Mathew, Architectural engineering focuses on the technical aspects of buildings (structural systems; heating, ventilating and air conditioning systems; and lighting and electrical systems) and the integration and coordination of building systems. Whereas architecture concerns with the aesthetics part also. However in this run for aesthetics, we architects are ready to compromise with the efficiency of the building to some extent. We want to put in some concepts in our designs which is hardly percieved by anybody. Finally what counts is the efficiency of the building. In our B. Arch course we are taught to apply our common sense to design, but i wonder how many of us make use of mathematics for applying concepts of illumination, climatology, structures etc in our designs. The B. Tech course in architectural engineering focuses on the technical aspects of buildings and the integration and coordination of building systems in a mathematical way (as is done in various other branches of enginering). Now the problem with architecture in India is that we have so many B. Arch graduates but we rarely find any peson with a B.Tech degree in architectural engineering.

Mathematics in architecture

Dear Nitesh,
Tell me, can water level be identified in terms of 1s and 0s? Can you make the intensity of fire discrete? I agree to that in our field some kind of scientific out look is not employed(as we perceive it in our studies).
But, in the practical world nothing can survive without technological inputs. For example, architects make some prototypes of bedrooms and try to incorporate it in their design. This approach cuts down on cost. Also, can improper arrangements of columns survive? Will a client pay you money for tunnel test and all those laboratory simulations? At least in 99% of the time? But to remind you we take into account such considerations, although not in its absolute influence on a particular setup but as some kind of thumb rules. Moreover, although window sizes may be standardised, no standard can be absolute and you have to change your design from time to time depending on the context of the problem.
Think about it. Although a swatch test is used for colour combination, what matters most is how the designer perceives the output. This is the actual role of an architect. If we go for fabrication in all buildings, will the Guggenheim Bilbao be possible? We are different from construction engineers and this field is combination of technology with arts.
To sum up, although your idea of technological input is right (actually its taking place), no supercomputer can fulfill the aesthetics aspiration of the user.
Thank you,

Mathematics in architecture

Dear Friends,
If we see mathematics as a language for expressing relationships of parts to the whole in this universe, the two views are easily resolved. In my personal opinion, mathematics should be taught to architecture students. But how it is taught is also really important  all too often we find that even subjects included in syllabi with the best of intentions soon become routines for pointless boredom if wrongly applied!
Srikumar M. Menon

Mathematics in architecture

Mathematics is a very vast field. It encompasses not only the study of numbers and enumeration, but it also tries to derive relationship between various quantities, developing patterns that can be visually depicted. It all depends on how we percieve the influence of mathematics on architecture to be.
The ancient greek architects were excellent mathematicians calculating proportions and optical corrections. Sequence, proportion, organisation are all principles that are equally employed in both the fields.
Unfortunately, even subjects like structures in architecture school are taught using formulas and numbers instead of understanding concepts. This makes it very dull and boring for art based students.
Using design tools is a completely different arena. Softwares are available to calculate light and heat patterns through CAD models. Even wind tunnel testing is done through this method. Physical models are not required. However, this is just a software and requires no understanding by the architect. It's an analytical tool.
As long as the architect is in tune with basic concepts of climate and its relationship with buildings, he will be generally right in designing opening sizes for example, and can always fine tune using software.

Mathematics in architecture

Hi,
It's nice to see your message. In a way, you are very much right and even I sometime think about this, about the reason why mathematics is neglected in architecture courses. We need it very badly, as we have a subject called mechanics in our syllabus, which is purely based on mathematical calculations, and many of the people who are in college try to avoid this subject or they don't put their whole interest in it. But, when we design the building we need this subject very much, I think people should get into mathematics which is very useful for designing buildings.

Mathematics in architecture

Hi, Friends!!
This is a very common debate that I have with my fellow students of architecture at NCA, LAHORE. We are always comparing our Art College NCA with the Engineering University UET Architecture Department.
We architects as the name implies are supposed to learn and understand the basic principles, and rules of quality construction, inspiring and functional design and beauty and attraction of aesthetics. But we are not suppose to go in to detail as such as to learn the application of engineering in architecture. No doubt, any renowned architect is nothing without the equally competent structural engineer and vice versa. We are taught design at our respective schools, but we architects are given the freedom of choice of learning what ever aspect of construction we want to learn and excel in future.
In a team there are a number of jobs that people do, not all are supposed to design. Even architects working under the principle architect only work to make the design better in working detail. NOW!, here comes our skills and talents which we our selves developed at our high school or in professional college or in the field, due to our interests and understandings.
Thanks!;)

Mathematics in architecture

Hello Nitesh,
Mathematics is indeed a basic need in architectural curriculum, not just as a theory subject but as a 'skill course'. Fortunately, being a student in architectural department in an engineering college, I had this subject in first couple of semesters. This, I think, should be introduced in the curriculum of architecture all over the country.
The flow of mathematics and pattern is a useful tool for many of the greatest designers. Buckminster Fuller derived many of his ideas from a rigorous study of mathematical and physical principles. And so did many other great architects to derive their innovative methods. From my point of view a wide fundamental knowledge about mathematics doesn't hurt while making architectural design. Of course I would agree that too much focus on a specific area might make blind for other aspects of the design process. Probably a good architect must be an universal dilettante, knowing at least a little about everything.
The concept of B.Arch. and B.Tech. in architecture is also very much clear. Basically, what distinguished architectural engineers, from other 'architects' is that engineers are much better trained in the new mathematics and physics than the architects. They had the ability to consider systematically questions most architects could only deal with intuitively or ignore. Therefore we seriously need a balanced combination of the two.
Regards,

Mathematics in architecture

Hi Nitesh,
I am preparing a seminar on this topic because mathematics is an important concept in architecture. Architects of the present, as well as of the past, are aware of both aspects of architecture i.e. arts & science. But very few of them are ever able to imply it in his/her works (like Le Corbusier, etc.)
Can anybody give me some MODERN examples of buildings where some concept of mathematics is applied, such as the golden mean, Fibonacci series, red series (Le Corbusier), proportions etc.?

Mathematics in architecture

Nitesh,
Architecture is an art, not a precise science. Mathematical precision and standardisation are only needed to ensure interchangeability of products made by mass production manufacturers.
Using only "Mathematics" to design with means design without human comfort (physiological and psychological)... What you perhaps feel the need for is "Ergonomics" (the scientific study of human efficiency) and you could use this to help design your buildings. :))) FOOTNOTE to Apurva Mishra: "Le Modular" by Le Corbusier is of some interest but not useful or original. The "Internationale Systeme" (aka Metric) is what I call "The Fascist Fractal" because every number must either be 10 or a fraction of 10. Yes, Le Corbusier understood the French Internationale Systeme made for bad design because it was not based on human measurements, but being typically French in behaviour (...anything AngloSaxon is an anathema), he shut his mind to the fact that the British Imperial system of measurement is humanbased and both infinitely more flexible and more aesthetic than Metric.:)))


