**You may have come across some spectacular buildings, but have you ever stopped to wonder why they’re built that way? **

Math and architecture are more closely linked that you might think, so read on to discover what’s behind it all…

**1) The Great Pyramid of Giza, Cairo, Egypt**

The superlatives that describe the Great Pyramid of Giza speaks for itself: its the **largest** and **oldest** of the three pyramids and was the **tallest** man-made structure in the world for 3,800 years, but there’s also plenty of math behind one of the Seven Wonders of the Ancient World.

Did you know that in cubits (the first recorded unit of length), the pyramid’s perimeter is 365.24 – the number of days in the year? That the pyramid’s perimeter divided by twice its height is equal to **pi **(3.1416)? Or that the King’s Chamber measurements are based on a **Pythagorean triangle** (3, 4, 5)?

**2) Taj Mahal, Agra, India**

Sitting firmly at the top of many traveler’s wish lists, the Taj Mahal in India is a delight for tourists, with many waiting to get that iconic photo in front of this beautiful building. But look closer and you’ll find a great example of **line symmetry** – with two lines, one vertical down the middle of the Taj, and one along the waterline, showing the reflection of the prayer towers in the water…

**3) The Eden Project, Cornwall, UK**

The Eden Project, in South West England, opened in 2001 and now ranks as one of the UK’s most popular tourist attractions. Although visitors come to check out what’s inside, the greenhouses –

**geodesic domes**made up of

**hexagonal and pentagonal**cells – are pretty neat too.

‘The Core’ was added to the site in 2005, an education center that shows the relationship between plants and people. It’s little surprise that the building has taken its inspiration from plants, using **Fibonacci numbers** to reflect the nature featured within the site.

There’s even more math to be found in the building structure, which is derived from **phyllotaxis**, the mathematical basis for most plant growth (opposing spirals are found in many plants, from pine cones to sunflower heads).

**4) Parthenon, Athens, Greece**

Constructed in 430 or 440 BC the Parthenon was built on the Ancient Greek ideals of harmony, demonstrated by the building’s perfect proportions. The width to height ratio of 9:4 governs the vertical and horizontal proportions of the temple as well as other relationships of the building, for example the spacing between the columns.

It’s also been suggested that the Parthenon’s proportions are based on the **Golden Ratio** (found in a rectangle whose sides are 1: 1.618).

The Ancient Greeks were resourceful in their quest for beauty – they knew that if they made their columns completely straight, an optical illusion would make them seem thinner in the middle, so they compensated for this by making their columns slightly thicker in the middle.

**5) The Gherkin, London, UK**

The Gherkin’s unusual design features – the round building, bulge in the middle, the narrow taper at the top and spiraling design – create an impact in more ways than you might think. The cylindrical shape minimizes whirlwinds that can form at the base of large buildings, something that can be predicted by computer modeling using the

**math of turbulence**.

What’s more, the bulging middle and tapered top give the illusion of a shorter building that doesn’t block out sunlight, helping to maximise natural ventilation and saving on air conditioning, as well as lighting and heating bills. Built with the help of **CAD** (Computer Aided Design) and **parametric modeling**, the Gherkin is now a distinctive feature in London’s city skyline.

**6) Chichen Itza, Mexico**

Chichen Itza was built by the Maya Civilization, who were known as fantastic mathematicians, credited with the inventing ‘zero’ within their counting system. At 78 feet tall, the structure of El Castillo (or ‘castle’) within Chichen Itza is based on the **astrological system**.

Some fast facts: the fifty two panels on each side of the pyramid represent the number of years in the Mayan cycle, the stairways dividing the eighteen tiers correspond to the **Mayan calendar** of eighteen months and the steps within El Castillo mirror the **solar year**, with a total of 365 steps, one step for each day of the year.

**7) Sagrada Familia, Barcelona, Spain**

Designed by Antoni Gaudi, the Sagrada Familia is one of Spain’s top tourist destinations. There’s plenty of math to get your teeth into too. Gaudi used

**hyperbolic paraboloid structures**(a quadric surface, in this case a saddle-shaped doubly-ruled surface, that can be represented by the equation z = x2/a2 – y2/b2), which can be seen within particular façades.

The Sagrada Familia also features a **Magic Square** within the Passion façade – an arrangement where the numbers in all columns, rows and diagonals add up to the same sum: in this case, 33. The **Magic Constant**, or 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.

**8 ) Guggenheim Museum, Bilbao, Spain**

Bilbao may not be the first place you’d think to travel to in Spain, but the Guggenheim Museum certainly gives you a good excuse to pay this northern port city a visit. Since opening to the public in 1997, the Guggenheim Museum Bilbao has been celebrated as one of the most important buildings of the 20th century and it’s not hard to see why.

Intended to mimic a ship, the titanium panels, which look like fish scales, were designed to appear random but actually relied on **Computer Aided Three Dimensional Interactive Application** (CATIA). In fact, computer simulation made it possible to build the sorts of shapes that architects from earlier years could have only imagined.

**9) Philips Pavilion, Brussels, Belgium**

Known for great beer, delicious waffles and moules frites, if you visited Belgium’s capital Brussels in 1958, you would have most likely come across the Philips Pavilion instead. Commissioned by electronics company Philips, the Pavilion was a mind-boggling collection of **asymmetric hyperbolic paraboloids** and steel tension cables, intended to be used as a venue to showcase technological progress after the Second World War.

**Got more suggestions of famous buildings built on math? Post up your comments and let us know!**

*If you liked this, you might also like: 7 Most Advanced Ancient Civilizations in the World*

*Great Pyramid photo credits: girolame*

Are their any mathematical influences involved with the Potala Palace in Lhasa, Tibet??

What about the Alhambra in Spain?

IM Pei’s Louvre Pyramid

Two towers (WTC)

UN Building (Golden Rectangle)

The Dubai scyscraper

Disney amphitheatre in LA

Epcot Center dome

Renaissance Center, Detroit…

… eventually most buildings are interesting!

I have this one with loads of parabolas in. A student of mine found it. But he or I have no idea where in the world it is or what it is. Allegedly 21 parabolas can be seen. Can anyone shed any light on it?

http://tinyurl.com/28fh4at

Thanks.

Anyone want to include the Pantheon??

And who says that the modern world was so good? There are lots of mathematics, science and technology going on from the old times=)

Sydney Opera House.

Gaudi was a genius, but not a mathematician.

He used gravity and inverted models to design the cathedral.

There is an example in the small, first floor museum there.

His inspiration was in organic forms.

A true master, many other pieces of his genius dot Barcelona.

Gaudi was a great architect, i love looking at his builidings

wat a lovely collection of pictures along with information…

Do u have explore in south india

I was going to suggest some of the temples at Siem Reap, Cambodia. Angkor Wat really is astounding. But then I remembered that most of the temples at the site there draw upon Southern Indian influences. The ancient Hindu temples at towns like Thanjavore, Trichy, Madurai and Mamallapuram are in fact far older than their Khmer cousins, though they never seem to get the architectural credit, despite an uncanny resemblance.

The triangular lodge, Northamptonshire, UK

Barcelona is chock full, there are so many Gaudi buildings there I bet we could do a Top 20 for Barcelona alone!

Great list. And thank GOD it wasn’t another Top 10!

The Pantheon in Rome is by far the most mathematically significant… not even close. You really should do some research before posting. Most can be considered pretty incredible. Also you have include Le Corbusier’s 1927 Villa Stein for the use of the Golden Ratio. You really just chose some easy ones, not very interesting to non math minds. Loved that it was not a top ten though!

Naqsh-e Jahan in Isfahan, Iran.

Specifically the Sheikh Lotfollah Mosque. A glorious place with mysterious angles, obsessively analysed by Jason Elliot in “Mirrors of the Unseen”.

the author carried the Parthenon to excess. The inner columns could not be thicker than the externals. This is a contradictory to the mathematic rules of golden Ratio and the aesthetic sensation.

What about Eiffel Tower in Paris?

Designed by A G Eiffel.

Errected for the 1889 Paris exposition.

Raised in 1959 to 321 m (1052 ft.)

Height: 300 m (984 ft.)

pyramids ,sphinex,all museum of ancient egyptian they are all wonderfull and great ,come to Egypt and enjoy a lot of interesting places &magic sun,desert, nile river,green village,seas ,no place like Egypt

I will share this with my students. Ty. Ingrid

Fascinating !

– Is it PARTHENON or Panteon ?

– A memorable structure and icon of the Brussel’s 1958 Fair was the ‘ATOMIUM’

– London’s “Festival of Britain” 1951 featured the ‘SKYLON’, which just like the UK economy at the time, had “no visible means of support”.

-Unfortunately, I have no available photos. Perhaps someone might post.

Ian.

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You forgot Hagia Sofia, Turkey