How it all started….
Have you ever asked yourself as to where we apply the knowledge that we learn in school?
When it comes to Math; this dilemma is even more prominent as we deal with abstract facts, proofs and much more complex ideas.. like Trigonometry, Algebra, functions and so on…
As a student, we always wonder where will be using all this …
So is an attempt to get some clarity to this; and to make ourselves more interested in Math.. We decided to use the platform of ISA Project.
Entering the quest….
We asked ourselves what will be the best topic to explore?
Will it be interesting?
Will we have enough information to proceed with the same?
After a lot of discussion, we decided, being born in a country like India, which is famous for its beautiful mansions, palaces, magnificent Temples and other iconic landmark buildings; exploring these Monuments will be a great place to start.
Thus the Topic ” Influence of Math in Architecture” was born 😊😊😊😊😊
(Obviously it was indeed a wonderful chance for us to browse, read and even visit buildings which are well known for mathematical influence in its structure.)
We decided to start with iconic monuments of our own country..
INDIAN MONUMENTS
We started with the Taj Mahal (Pride of our Nation)
one among the Wonders of the world
Made out of white marbles it a pure bliss to view …
The marbles are aligned in perfect synchronization with each other acting as perfect example for tessellation.
It exhibits symmetry and as the water fountain in front helps to create reflection, the overall effect is mesmerizing.
As it is such an iconic monument, lets explore our next monument..
Qutub Minar
Qutub Minar is the second tallest minaret in the world made up of bricks which is just marvellous to have a gander up on.
It was built by Qutab-ud-din-Aibak who was the head of the Delhi Sultanates.
The most interesting fact of this monument is that its base is of octagonal shape and it also has vertical line of symmetry.
If you want more information about the Qutub Minar, we suggest you refer the presentation that we made.
Next we decided that it would be best to take a monument that was a palace. Well there were so many options which caused a lot of decision making which also created some confusion.
At last we all agreed that the exquisite Mysore palace. Not only is the palace a sight to see but it is also one of the monuments that is closest to our state.
Mysore Palace
Well, I think we all would be willing to live in such a huge and magnificent palace but what if I told you that Mathematics was needed to construct this masterpiece.
Ok, we don’t blame you if you think we are joking but trust us, all of us were just star struck when we got to know that Mathematics is actually applicable in our lives to construct these marvelous structures.
This has actually gotten us to take Mathematics as a subject more seriously because it also plays a big role in art.
First off, the Mysore palace, unlike many other palaces out there, has a hybrid architecture. Which means it uses many different types of architectural styles.
It is about 145 feet high and is three storied. It also has some antiques which are about 900 years old, which is just gob smacking!!
Like the Qutub Minar this is the other monument that we explained in more detail in our presentation so we suggest you check it out.
While we were searching for monuments to include in our presentation Jantar Mantar really caught our eyes.
Jantar Mantar
At first when we hear about the Jantar Mantar, we think the name sounded like something that a magician would say; well that’s incorrect.
But what is really fabulous is that it kinda looks like two upside down hearts from an angle.
I think we can all agree on that? But what if we told you it was way more complex than just two upside down hearts? If you don’t believe then check out these facts we gathered.
First off this may sound a bit crazy but there were a total of 5 Jantar Mantars built between 1725 to 1735.
Also to spice things up it also contains 13 astronomical instruments, some of them the largest in their category; like how crazy is that?
It is also built on 18700 metres of land and its name literally means calculating instrument.
Lotus Temple
And last but not the least we also took a deeper look into the Lotus Temple
We, think most of you might have already gotten mesmerized by the stunning appearance it has gotten before we even start with the interesting facts, right?
Well, to start things off strong this temple costs a whopping $10 million. It is constructed with 27 free standing metal clad also known as the petals and it is characterized with nine sided architecture. The stunning temple is built on 26 acres of land.
Also 10,000 different sizes of marble were used in the construction of this temple and it is 40 meters tall and it has maximum capacity to accommodate upto 2500 people at a single time!
Our Little Field Trip
Like any other field trip we expected it to be a long tedious journey with lots of facts showered on us..but what awaited us was a pleasant surprise.
So to start things off; the bus journey was exciting and after 4 hours of travelling we finally reached Kannur which was our destination and we straight away headed towards the light house.
So at first glance, it kind of reminded us of the Qutub Minar and this seemed like a smaller replica of the Qutub Minar.
It was also really tiring to hike towards the top as the spiral staircase leading to it had a 100 steps but towards the end it proved to be worth it
The view from the top was just out of this world and it was overseeing the beautiful beach
Also right next to this amazing light house there was the light house museum which showcased us a lot of different parts of the light house which made us think “Huh, even to make a simple light house there is a lot of complexity and Mathematics has a big influence in it” which inspired us a lot.
After that it was time for us to move on to next part of our Mathematics inspired journey.
Next in our bucket list was to visit the Arakkal Musuem
This was built by the Arakkal family (which I think most of you must have figured out) and this showcased some really old antiques and weapons.
This place also had a really amazing interior as opposed to the exterior and once you visit this palace we assure you that you won’t leave it without learning a thing or two.
This palace took 100,000 rupees to construct in the olden times which is actually a huge amount right now.
So after being mesmerized by the Arakkal museum the last leg of our journey was the visit to the iconic Peralassery temple pond.
The shape of the pond fascinated us as this was made by meticulous arrangement of the basic shapes like Squares and triangles, and the resultant view was spectacular. This pond boosted our imagination to the limitless possibilities that; we can construct any kind of structures with the use of Mathematics.
As we were all impressed by the influence of Mathematics in various architecture, we decided not to restrict ourselves by exploring the monuments in India alone. So we decided to extend beyond…
Monuments around the world
Spain
Alhambra Palace
Our first destination is the country of bull fights, Spain. The architecture in Spain is splendid right from the spectacular museums, to the holy cathedrals. Our classmate just visited España (Spain) a few weeks ago and this inspired us to learn more about the architectural style found there.
Let us go to the crimson castle that got turned into a court, the Alhambra palace. Each historic palace was built by different dynasties and this one was built by the Nasrid dynasty. Found in the city of Granada, this palace has symmetry not only in the architecture, but also in stucco (plaster used for coating wall surfaces) and tile works.
The tiles are filled with radial works and dihedral reflection. The second type is the periodic patterns. As the name suggests it involves repeating image or well phrased as translational symmetries. The angles that appear in rotations for the patterns are 60°, 90°, 120°, 180°.
Well if you know about Taj Mahal, in India, there is a pool of water right in front of it which reflects the beauty of Taj Mahal. Similarly, for our Alhambra palace too there is a pool of water in front of the patio. The reflections show dihedral symmetries.
SAGRADA FAMILIA
Have you ever seen an unfinished church? Yes, we too were surprised when we heard this and there is a beautiful version of this in Barcelona, designed by Antoni Gaudí, the BASILICA I TEMPLE EXPIATORI DE LA SAGRADA FAMILIA… yes, it is quite a mouthful…
The architect used hyperbolic paraboloid structures (a surface represented by the equation z = x²/a² – y²/b²).
These terms were actually new to us and here are a few we would like to share:
Hyperboloids = found in the openings of windows and vaults
Paraboloid = links surface between vaults and roofing
Helicoid = represents the rising movement … Eg: spiral staircase
Ellipsoids = rounded capitals of the main columns were generated from this.
The pillars in here looks like trees dividing into branches.
Double twisted columns were used for stability.
The roof of these buildings is what we love the most about La Sagrada Familia. They appear in wave like structure and this is the best example of conoids.
For further information refer our PPT Spain
Malaysia
I don’t think that there is anyone who does not like street art, is there? Let us stop for a break at the country famous for street art, Malaysia. Malaysian culture is diverse and the buildings are spectacular.
Masjid Negara
The capital of Malaysia, Kuala Lumpur is famous for Masjid Negara, the national mosque. This mosque was built in 1965 after achieving their independence from Great Britain. Its key features are a 240 ft. minaret and a 16 pointed star concrete main roof. The reflecting pools and fountains spread throughout the compound.
Its tessellations comprise of geometrical shapes and a wide range of symmetry is seen.
Petronas Tower
You must have heard about the plane crash that almost destroyed the twin towers in the US. Well there is one similar twin skyscraper in Kuala Lumpur called as the Petronas towers (Petronas twin towers). There is a sky bridge that connects both the towers.
The roof of the tower is made up of many triangular structures. This structure is symmetrical and as the name suggests, the towers are twinning.
For further information refer our PPT Malyasia
United Kingdom
We were researching to find a brilliant place from UK to complete our project..
At last we found what we were seeking,the 30 St Mary Axe or in other words the place where the magnificent building, The Gherkin is situated.
It has a gherkin shape narrowing at each end where the building curves inwards at the bottom. The glass dome at the very top of the building gives a wonderful 360 degree view of London. The building, which is 590 feet (180m) tall has a total of 41 floors
The building is covered in glass windows, but not all the way down to the ground. At ground level you see the criss-cross of the supporting girders with the lowest windows and doors set back behind them.
The building is made by a unique way called parametric modeling. The glass panelled windows are joined together in triangulation (one of the strongest structural shapes known to man that also cuts down on the amount of steel used), that spiral round to the top dome, controlling any wind-excited sways. The shafts also allow for extra light passing through the building, making it a more uplifting experience for the people working inside.
10,000 tonnes of steel and 24,000 sq m of glass was used in its external construction and regardless of its round façade the only round piece of glass to be used is the ‘lens’ that sits at the very top!!!
A 6 hour journey from London takes you to Cornwall, where the Eden Project is located. It is a 35 acre reclaimed clay pit, which has been transformed into an oasis of greenery.
Set up by an ecological charity to promote education about the natural world, it’s home to two huge biomes that bring a taste of the rainforest and the Mediterranean to south-west England. Each biome consists of adjoining domes that is made up of hundreds of hexagonal and pentagonal inflated panels that are held together by steel frames. At 300 feet tall they’re the world’s tallest greenhouses.
The design of the roof is based on Fibonacci spirals, a mathematical pattern found throughout nature.
For further information refer our PPT United Kingdom
These are just some of the many monuments around the world, which have enthralled people for centuries with their architectural beauty and intelligent use of designs and materials in construction. Let us not forget that the base for all these amazing monuments’ beauty is the use of Mathematics in their design. And the final result is there for all of us to see.
We were so impressed with the results we were able to find; that we decided to go a step further and contact students from other countries to know about monuments in their countries with influence of Mathematics in their architecture.
As you might have guessed; interacting with students and getting details from their point of view was far more interesting than reading the same facts from Wikipedia and other sites.
The following are our inference based on the facts shared to us by our foreign friends
EGYPT
What comes to your mind when you hear EGYPT?
For me its always a big desert with huge pyramids, mummies and cat idols that comes to my mind.
I guess for most of us its the same, right?
Well, such deep impression is made in our minds about the huge pyramids and the stories related to it.
So what other than these famous pyramids will we select in our search of monuments?
Pyramids are the only intact structure from our oldest list of World wonders. They were build as memorial tombs for Kings, called as Pharaohs.
The structure comprises of basic geometrical shapes like Triangles, Squares and Hexagon connected effectively in innovative way.
The base shape decides the name of the pyramid. Based on the number of sides in the base shape; same number of triangles will be used, which will be connected at a point called apex. This resultant shape is called Pyramid. Simple, Right?
Well see the examples below
Pyramids also exhibits proportionality between their sides.
If the apex of the pyramid is directly over the center of a regular base as it is above, it is called a right pyramid.
If the apex is not over the center of the base, it is called an oblique pyramid, and the faces are not congruent.
The volume of a pyramid is V=1/3bh, where b is the area of the base and h the height from the base to the apex.
Another architecture seen in Egypt is the obelisk. An obelisk is a stone rectangular pillar with a tapered top forming a pyramidion, set on a base, erected to commemorate an individual or event and honour the gods.
The ancient Egyptians placed pairs of obelisks at the entrances of their temples. The columns were associated with the Egyptian Sun God and perhaps represented rays of light.
Obelisks also helped archaeologists to translate hieroglyphics.
For more information have a direct peep to the PPT shared with us by our friends in Egypt
Well,our juniors got so impressed with the pyramids and the history related with it; that they decided to make models of the same. It was fun to guide them, to make the pyramids, we started of by introducing them about different types of pyramids, we explained about the concept of nets (the 2D version drawn in paper; which when folded in correct places will help us to form 3D shapes) and helped them in making Pyramids of various sizes.
Well it was an incredible experience to be a teacher instead of student..though it was tiring and a big tester for our patience…it was worth when we saw the end result.. our own cluster of Pyramids. 😊😊😊
UNITED STATES OF AMERICA
A pioneer in almost all fields; a country filled with landmark monuments, America.
Washington Monument
The first monument introduced was Washington Monument; which is the highest Obelisk. It was erected as a memorial for America’s first President “George Washington”.
The Washington monument has a special relationship between its base width and height. They maintain a 1:10 ratio. It exhibits symmetry too.
Normally Obelisks are filled with hieroglyphs describing the life history of the person. But surprisingly Washington Monument is devoid of any inscriptions.
US Capitol Building
The next monument is US Capitol Building , the home to US Congress.Its as beautiful and vast as our Mysore palace. It exhibits symmetry and congruence in its construction. It was built in September 18, 1793. Located on approximately 274 acres, it is the seat of the legislative branch of the US Federal Government.
The building is 555 ft tall and 751 ft long. Its height above the base line on the East front to the top of the Freedom Statue is 188 feet. The building covers over 4 acres, with the highlight of the building being the Rotunda located below the Capital Dome. The rotunda is 96 ft in diameter and rises 180 ft from the floor to the canopy, with a volume of approx 1.3 million cubic feet! It is quite a wonder to behold!
One of the unique features of the rotunda is the Whispering Gallery, from where whispers can be heard in other parts of the Gallery. This effect usually happens in circular, hemispherical or elliptical enclosure, often under a dome or a vault. The sound is carried by waves that travel around the circumference clinging to the walls. Be careful of what you whisper in the rotunda!
For further information check out the PPT
Below are some of the snaps of our friends in US watching our PPT, about Monuments in India
Below are some of the snaps of our friends in Egypt watching our PPT, about Monuments in India
Take a look at us, while we were enjoying the PPT prepared by our US friends
Last but not the least, we took photo of ourselves while we were writing this Blog 😁😁
Hope you enjoyed the journey with us… Do share your findings too!
Adios Amigo !!! Good Bye Friends!
Splendid Symmetry 