"The fluid lines are nothing more than the adaptation of the shape to a new concept of more dynamic, flexible and alternative space. A multiple and fragmented geometric perspective, which reveals the opinion of numbers and formulas".
“While I was growing up in Iraq, math was part of my daily life. We played with mathematical problems as we had fun with paper and pencil: doing math was a bit like drawing ".
Zaha Hadid
Great Persia stretched from the territories of the Tigris and Euphrates, today identifiable with Iraq, to Uzbekistan, homeland of al-Khwarizmi, founder of modern algebra during the ninth century.
A great mathematical tradition, the Persian one, continued with Omar al-Khayyam, al-Tusi and others, which Hadid knew.
Zaha Hadid, born in Baghdad, who passed away in 2016, was also a mathematician, graduated from Beirut, before moving to London in 1972 to study at the Architectural Association.
Zaha Hadid has left an indelible mark on modern avant-garde architecture, with a revolutionary language and a style that over time will be characterized by a curved, complex, dynamic and fluid linearity.
He challenged geometry, countering the supremacy of the right angle in traditional architecture, indeed avoiding angles in general.
It has given life to dynamic and fluid spaces, creating bold structures made possible, in the design phase, by the concomitant digital revolution (sometimes implementing the same programming software for projects) and making use, in their realization, of the use of materials innovative.
The 3rd class of the lower secondary school is the real learning place in which to approach the algebraic language.
Not that the students are completely fasting it, having obtained a taste, even a rigorous one, in the previous two years, but now the students have to expand the toolbox of mathematical tools to tackle higher studies.
However, an explanation / learning practice is well established which mostly involves the presentation and memorization of formulas and algebraic processes.
With an iterative process, consolidated by dozens and dozens of exercises, the formulas settle in the neurons of preteens.
In reality, as we all know, this does not always happen.
The limit of this approach to the study of algebra is that of being too theoretical, of not being able to finalize this powerful mathematical tool towards something concrete that allows us, absurdly, to interpret reality.
Over two millennia separate us from a totally different approach to algebra.
Already the Babylonian students faced the same problems in geometric terms: their processes, calculations, their solutions were "visualized" by the use of specific figures.
For the Greeks, too, the essential concern was to make sense of such expressions.
I have always tried, in my teaching method, to treasure the history of mathematics and therefore its evolution over time.
So when it was time to introduce the remarkable products, for example the square of the binomial, I certainly did not limit myself to writing the classic formula on the blackboard (square of the first term, more or less double product of the first for the second term, plus square of the second term) but I invited the students to act like their Babylonian colleagues of two thousand years ago.
They then had to draw a segment, divide it into two unequal parts (a + b) and build the relative square on that segment. The surface of the square was divided into four “appropriate” parts: two squares with different surfaces and two rectangles with the same surface.
Calculating the area of the starting square (square of the binomial "a + b") therefore meant taking note that it could be obtained by adding the area of two squares and two equesthesia and therefore equivalent rectangles (double product).
The added value of this approach was completed by making use of GeoGebra, a powerful free mathematical software.
The student literally “saw” the function studied and its graph in both two and three dimensions.
Unfortunately, the use of GeoGebra tends to get lost in subsequent higher studies.
A real shame for the student.
"Mathematics: The Winton Gallery": project by Zaha Hadid Architects in London
The highlight of the exhibition, which occupies a total area of 913 square meters, is a Handley Page experimental airplane from 1929, whose aerodynamics ideally summarizes the concept behind the gallery: how mathematics helps us solve real and tangible problems.
In this sense, the project by the ZHA studio - inspired by the geometries of the air flows that are created around an airplane in flight, developed through fluid dynamics simulation programs and further underlined by an innovative lighting curated by Arup - is intended to express how mathematics shapes nature, influences the environment in which we live and regulates practically all the creative activities and disciplines of humanity, including architecture.
A 1929 Handley Page Gugnunc hangs from the ceiling: an aircraft that served as inspiration for the design of the gallery. The wing design of the Gugnunc was influenced by cutting-edge aerodynamic research and is used in the gallery to illustrate how mathematics can be used to solve practical problems.
The purpose of this work is the study of the air turbulence that is created around the plane while it is in flight and deliver the results to aerospace engineers who will improve the aerodynamics and lift of the aircraft: ultimately therefore improve flight safety.
A gradual approach
Evidently the equations studied by the ZHA are much more complex (the study of the spatial turbulence field presupposes the elaboration of the Navier Stokes equation, used in air transport, to which the trigonometric equations for parametric surfaces must be added) but the elementary notions for understand the Winton Gallery project are these.
The three-dimensional curved surfaces simulate the air flows that surrounded the plane in flight.
Every aspect of reality can be studied and understood through mathematics.
Sometimes, to go further, someone's creativity is needed: the union of art and mathematics can only fill our gaze with pride.
The project for the Gallery dates back to 2014 but Zaha Hadid did not have time to inaugurate it: she died in 2016 at the age of 66, of a heart attack.
She received many international awards and the prestigious Pritzker Prize, equivalent to the Nobel Prize for architecture, in 2004, the first woman to obtain it.
He has designed and built all over the world: I remember in Italy the Maxxi in Rome, the Generali Tower in Milan, the Naples Afragola high-speed station.
The Persian mathematician Omar al Kayyam, 1048-1131, who proposed a general systematic theory of third degree algebraic equations and their geometric solutions, was also a poet who was able to seduce.
Those who were oceans of perfection and science
Those who were oceans of perfection and science
and by shining virtues they became Lamps to the world,
they did not step out of this dark night:
they told fairy tales, and then fell back to sleep.
When they cut off the shoot of my life
When they cut off the shoot of my life
my parts will be scattered far from each other.
If from my mud then they will model a pitcher
make it full of wine and I will return to sight.
Bibliography and Sitography
Zaha Hadid Complete works 1979-today, edited by Philip Jodidio 2020 TASCHEN
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