Maths and architecture are very closely linked. In today’s blog post I thought I would talk about some famous buildings and describe how maths is related to them.

#### The Great Pyramid of Giza – Cairo, Egypt

The Great Pyramid of Giza, one of the Seven Wonders of the Ancient World, is the **largest** and the **oldest** of the three pyramids and was the **tallest** man-made structure in the world for 3,800 years.

In cubits (the first recorded unit of length) the pyramid’s perimeter is 365.24, which is the number of days in the year! Also, if you divide the pyramid’s perimeter by twice its height, you will get **pi**! The last amazing fact is that the measurements in the King’s chamber are based on the famous **Pythagorean triangle** 3, 4, 5.

#### Taj Mahal – Agra, India

The main mathematical feature of the Taj Mahal is its impeccable **symmetry**. It is symmetric about a vertical line down the middle, as well as a horizontal line along the waterline, as one can see its reflection in the water.

#### The Eden Project – Cornwall, UK

The Eden project opened in 2001 and is composed of two biomes containing plants from many different climates and environments.

The greenhouses are geodesic domes made up of hexagonal and pentagonal cells.

Furthermore, in 2005 an education centre was built. This building draws inspiration from plants, using **Fibonacci numbers** to reflect the nature onsite. Also, the structure of is derived from phyllotaxis which is the mathematical basis for most plant growth – a pattern of opposing spirals.

#### Parthenon – Athens, Greece

The Parthenon was constructed in 430/440 BC on the Ancient Greek ideals of harmony, which is shown in the perfect proportions of the building, for example the width to height ratio of 9:4, the spacing of the columns, etc.

In the Ancient Greek’s quest for beauty, they wanted to make their columns appear completely straight. However, to achieve this they made their columns slightly thicker in the middle due to the fact that if they had not, an optical illusion would make them seem thinner in the middle.

In addition, it’s been suggested that the Parthenon’s proportions are based on the Golden Ratio.

#### Chichen Itza – Mexico

The Mayan civilisation were incredible mathematicians. The structure shown above, called El Castillo, within Chichen Itza is based on the **astrological system:**

- The 52 panels on each side of the pyramid represent the number of years in the Mayan cycle;
- The stairways dividing the 18 tiers correspond to the Mayan calendar of 18 months;
- The steps within El Castillo mirror the solar year, with a total of 365 steps i.e. 1 step for each day of the year.

#### Sagrada Familia – Barcelona, Spain

This structure was designed by Antoni Gaudi and is one of Spain’s top tourist destinations. Gaudi used hyperbolic paraboloid structures, which can be seen within particular façades.

This quadratic and doubly ruled surface given by the Cartesian equation:

What does this look like? **Pringles **resemble a hyperbolic paraboloid!

Additionally, the Sagrada Familia features a **magic square** within the Passion façade. This is an arrangement where the number in all columns, rows and diagonals add up to the same sum, which in this case is 33. The **magic constant** M is the constant sum in every row, column and diagonal and can be represented by the following formula:

M = n(n^{2}+1)/2

(All pictures from Wikipedia)

M x