# exploring mathematics within architecture

In my written study, I am going to be looking at three different architecture pieces which will have different mathematical concepts behind them. The three mathematical concepts that I will be looking at within architecture is the Fibonacci sequence, fractal design and parabolic curves which are used in many designs. For example, the Villa Savoye by Corbusier has a fa?ade which, if you draw over it, includes lots of geometry including the Fibonacci sequence and other mathematical parts. I am also going to look at the Lideta Mercato which incorporates the fractal design through copying patterns off of a traditional Ethiopian cloth.

This fractal design is different to the rest as it looks at a traditional object and designs from a certain place. My final architecture piece that Im going to be looking at is loceanografic which has parabolic curves and can be seen as the roof of the structure. All of the points are halfway between the directrix and the focus vertex which means the distance from a certain point and a certain line will always be equal.

In my work, I would like to use at least one or two different mathematical concepts which would be the basis of my designs and by exploring these different types of math within these buildings will expand my knowledge of how to use them in designing architectural pieces. I hope that by researching the three architectural structures, it will help me towards my final piece and could add a different perception to the piece as well as sophistication.

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Corbusiers work is about showing the essence of modern architecture during the 1900s through his designs and writings by thinking about both the nature of modern life and how architecture plays a part in the new machine age. Corbusier famously says the house should be a machine for living in which is shown through his forms, layout, materials used and the site of where the villa is. The villa savoye was designed by Corbusier and Pierre Jeanneret in 1929 and built in a flat, green landscape on the outskirts of Paris which provided an escape from the busy city. The space in which he built it was unrestricted meaning that he could be as creative as he wanted however, he designed a floating box which made the site surrounding the building seem vast and showed off the modernist villa.

The initial idea for this design came from all his previous buildings as well as his book vers une architecture which is a collection of essays by Corbusier exploring the concept of modern architecture as well as Lesprit noveau which is a magazine he founded where he published many of his essays and later on incorporated them into the villa savoye and many other buildings later on. In his essays he devised his Five Points of Architecture which he saw as a universal system that any architecture could use as well as it being applied to any architectural site. The Five Points of Architecture are pilotis, roof terraces, a free plan, a free fa?ade and ribbon windows. The pilotis is a grid of concrete or steel columns which replace supporting wall and allowed the building to be raised off of the ground and enable air to circulate beneath the villa as well as allowing the soil beneath to be used. The roof terraces act as a kitchen garden and a sun terrace which is covered in vegetation allowing the produce to be moisture and acts as a heat and cold insulator for both summer and winter. It allows nature to be within an urban setting. The free plan allows interior space to be shared across the villa making it feel like a grand space due to the lack of supporting walls. The ribbon windows cut through the non-supporting walls along the fa?ade of a building and provides natural lighting along with a view of all the buildings surroundings. Finally, the free fa?ade allows the open and closed sections to enable the connection and separation of an exterior design from the structure. These five points were all met within the villa savoye