**If you’re into Math and you’re into Architecture then this is the post for you. See which buildings made the hit-list for the most mathematically interesting places across the world, take a trip and go see them for yourself. **

A while ago we posted about the “9 Most Mathematically Interesting Buildings in the World.” You had so many good suggestions for other fascinating buildings that we decided to investigate some more.

Read on to learn about 7 more mathematically interesting buildings and see if your suggestion made the cut!

**1) The Parabola House, Tokyo, Japan**

The minimal design and a **ceiling based on the mathematical shape of a ****parabola** make this house, designed by Japanese architectural firm Atelier Tekuto, truly unique.

The house is 6m by 27m in length—a long and narrow site—with a “three-dimensional” ceiling that dips and rises, giving the house a sense of openness and movement, like flowing air.

Since the family who lives in the parabola house spends most of their time in the living room, this room was situated on the top floor to exploit fantastic views of Mt. Fuji.

*Image via Wikipedia*

**2) Borobudur, Central Java, Indonesia**

This spectacular 8^{th} century Buddhist Monument is a shrine for the Lord Buddha and is built as a massive stupa. The foundation is a square, approximately 118 meters on each side and has nine platforms, 504 Buddha statues and over 2,500 relief panels.

The basic unit of measurement used in Borobudur’s construction was the *tala, *which is thought to be the length of a human face from hairline to chin. A survey conducted in the 1970’s revealed multiple ratios of 4:6:9, indicating that the **architect had used fractal and self-similar geometry in the design.**

Researchers believe the recurring ratio and the use of the *tala* measurement have Buddhist cosmological and astronomical significance.

*Northwest view of Borobudur, image via Wikipedia*

**3) Rushton Triangular Lodge, Northhamptonshire, United Kingdom**

Designed by a Roman Catholic in 1593, the Triangular Lodge is an affirmation of faith that uses the Holy Trinity as architectural inspiration.

The lodge has walls that are 33 feet long with three triangular windows each, three Latin texts each 33 letters long inscribed on the façade, three floors and a triangular chimney. The main room on **each floor is hexagonal, leaving three triangular corner spaces**.

The architect carved many mysterious numbers in the walls, like 1580—thought to be the date of his conversion—1626 and 1641. Experts suggest that not only are the latter dates divisible by three, but but when the design date (1593) is subtracted from them, the results are 33 and 48—the years of Jesus’ and Mary’s deaths.

Suggested by reader Mike.

*Image via lukewestall*

**4) United Nations Headquarters, New York, NY, United States**

Since the publication of Luca Pacioli’s *Divina Proportione* in 1509 made the properties of the Golden Ratio widely available , artists and architects have been fascinated with its use in construction. The Golden Rectangle has side lengths that conform to the Golden Ratio, or 1:(1+ √5)/2 (approximately 1:1.618).

One of the most recent examples of the Golden Rectangle in architecture is the United Nations building in New York—comparing the building’s width with its height reveals that **every ten floors create a Golden Rectangle.**

An interesting feature of the Golden Rectangle is that when a square is removed, another golden rectangle remains; this can be repeated infinitely—just try it with some pencil and paper.

Suggested by reader John Golden.

*Image via Paolo Rosa*

**5) The Pantheon, Rome, Italy**

Though the Pantheon you see in Rome today looks a great deal different than when it was originally built between 27 and 25 BCE, it still impresses with it’s mysterious construction and the fact that it is still the world’s largest un-reinforced concrete building.

The Pantheon is called a “perfect space” because the **diameter of the rotunda is exactly equal to its height**; this is meant to suggest geometrical perfection in a perfect universe. The only interior light comes from the 27 foot wide oculus which symbolizes the sun as the source of all light on earth.

How the dome has managed to bear its own weight through the centuries without collapsing is still a mystery–most architects speculate that the answer may lie in an unknown formulation of the cement.

Suggested by readers Vincent Cirella and Adam.

*Image via emilio labrador*

**6) Angkor Wat, Siem Reap, Cambodia**

It has long been theorized that the architect of Cambodia’s magnificent 12th century temple complex based its design on themes of calendrical, historical and astrological significance.

But in the 1990’s a professor from the University of Michigan discovered that some of **Angkor Wat’s sections are extremely precise**: the northern and southern outer corridors measure 202.14 meters long and the eastern and western measure 114.22 and 114.24, respectively.

Using these measurements, the professor was able to work out the standard measurement used in the construction of Angkor Wat (a cubit) and decode numerous sacred and historical details.

**She also discovered that the architect had cleverly repeated numbers throughout the building**, for example, each half of a split bridge connecting Angkor Wat to the outside world measures 216 cubits and is decorated with 216 columns.

Suggested by reader Libby Brown.

*Image via rla579*

**7) Sydney Opera House, Sydney, Australia**

The original design for Sydney’s iconic Opera House was unveiled in 1957, the work of Danish architect Jorn Utzon who conceived of the Opera House as a set of staggered sails or shells.

The shells were originally conceived as series of parabolas but the design proved to be prohibitively expensive and a host of other mathematical solutions were proposed, such as circular ribs or an ellipsoid shape.

Eventually the design team hit on the solution that would make the Opera House so universally admired: **the sails were to constructed as sections of a massive sphere**. This allows shells of varying sizes to be cast from the same mold–if all the shells were put together, they would form a sphere of 75.2 meters in radius.

Suggested by reader mo.

*Image via jimmyharris*

**Bonus Building: Turku Power Station, Finland**

Many buildings like the Eden Project use the Fibonacci sequence in their construction.

This power station in Finland uses the sequence in an unconventional way–as art! At night, the chimney is **lit up with Fibonacci numbers in 2 meter high neon lights**.

It was commissioned by the Turku City Environmental Art Project and artist Mario Merz says it is **“a metaphor of the human quest for order and harmony among chaos.”**

Image via Pavlin Petkov

**If you’re still hungry for more mathematically interesting buildings, let us know if you’ve got more suggestions!**

**If you liked this, you might also like: 8 Ancient Labyrinths to Quiet Your Mind. **

*Main image: Angkor Wat temple as the night falls by experez*

Wow! I want to visit Angkor Wat to see that place too, I hear is so amazing!

Always amazing to see the mathematical and engineering accomplishments achieved on ancient buildings.

Very amazing! I like the Borobudur most.

@Mara: Thanks for the interesting list. My favorite (OK, I’m biased, being Australian) is the Opera House.

Actually, the statement about the UN Headquarters and the Golden Ratio is not actually correct. It is closer to 14 floors (compared to the width) that gives the ratio of around 1.62.

See Devlin’s article which mentions this.

This article has been included in the Carnival of Mathematics.

Hi,

I refer to your article above on the Pantheon and the statements “How the dome has managed to bear its own weight through the centuries without collapsing is still a mystery–most architects speculate that the answer may lie in an unknown formulation of the cement.”

Perhaps some of the readers may want to try to read the following articles to have a better understanding :

On the Structure of the Roman Pantheon, Robert Mark and Paul Hutchinson, 1986

http://www.jstor.org/pss/3050861

The Pantheon, By David Moore, P.E., 1995

http://romanconcrete.com/docs/chapt01/chapt01.htm