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INTRODUCTION: India is dotted with plethora of monuments, which include temples, Buddhist stupas, churches,mosques, rock-cut caves, minarets, palaces and forts,out of which one is QUTUB MINAR constructed in the reign of Slave Dynasty in Mehrauli surrounding Delhi, capital of India. Even though the capital shifted from Mehrauli after the Slave d.ynasty rule came to an end, many other dynasties contributed significantly to Mehrauli's architecture. The most visible piece of architecture remains the Qutb complex which was initiated by Qutub ud din Aybak with subsequent additions by Iltutmish and Alauddin Khilji. The Qutub complex is today a UNESCO world heritage site and also the venue for the annual Qutub Festival. Mausoleum of 13th century, Sufi saint, Khwaja Qutbuddin Bakhtiar Kaki is also situated near the Qutub Minar Complex, and the venue for the annual Phoolwalon- ki-sair Festival. The dargah complex also houses graves of later Mughal emperors, Bahadur Shah I, Shah Alam II, and Akbar II, in an adjacent marble enclosure. To the left of the dargah, lies Moti Masjid, a small mosque, built for private prayer by the son of Aurangzeb, Bahadur Shah I. Foundation Programme - 1 - Geometry Research Project
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INTRODUCTION:

India is dotted with plethora of monuments, which include temples, Buddhist stupas, churches,mosques, rock-cut caves, minarets, palaces and forts,out of which one is QUTUB MINAR constructed in the reign of Slave Dynasty in Mehrauli surrounding Delhi, capital of India. Even though the capital shifted from Mehrauli after the Slave d.ynasty rule came to an end, many other dynasties contributed significantly to Mehrauli's architecture.

The most visible piece of architecture remains the Qutb complex which was initiated by Qutub ud din Aybak with subsequent additions by Iltutmish and Alauddin Khilji. The Qutub complex is today a UNESCO world heritage site and also the venue for the annual Qutub Festival.

Mausoleum of 13th century, Sufi saint, Khwaja Qutbuddin Bakhtiar Kaki is also situated near the Qutub Minar Complex, and the venue for the annual Phoolwalon-ki-sair Festival. The dargah complex also houses graves of later Mughal emperors, Bahadur Shah I, Shah Alam II, and Akbar II, in an adjacent marble enclosure. To the left of the dargah, lies Moti Masjid, a small mosque, built for private prayer by the son of Aurangzeb, Bahadur Shah I.

Balban's tomb belonging to Balban, Slave dynasty ruler of Delhi Sultanate was constructed here in the 13th century can still be seen though in a dilapidated condition. Architecturally important structure as it is the first true arch in Indo-

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Islamic architecture, Another tomb, that of Balban's son, Khan Shahid, who died before he could be crowned, is also located near by in Mehrauli Archeological Park.

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QUTUB COMPLEX:

The Qutb complex (Hindi: कु़तुब परिस, Urdu: پرِسر قطب ), also spelled Qutab or Qutub, is an array of monuments and buildings at Mehrauli in Delhi, India, the most famous of which is the five-storeyed, and 72.5 m high Qutb Minar built in 1192 AD, by Qutbuddin Aibak, viceroy and general in Mohammed Ghori of Ghazni's army to mark their victory over Delhi. Qutbuddin later became the first ruler of the Slave Dynasty, and after his death the Minar was added upon by his successor Iltutmish (aka Altamash) and much later by Firoz Shah Tughlaq, a Tughlaq dynasty, Sultan of Delhi in 1368 AD. The complex initially housed a complex of twenty-seven ancient Jain temples which were destroyed and their material used in the construction of the Quwwat-ul-Islam Mosque next to the Qutb Minar, in the Qutb complex [1], built on the ruins of Lal Kot Fort built by Tomar Rajput ruler, Anangpal in 739 CE and Qila-Rai-Pithora, Prithviraj Chauhan's city, the Rajput king, whom Ghori's Afghan armies had earlier defeated and killed, at the Second Battle of Tarain [2].

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The complex was added to by many subsequent rulers, including Firoz Shah Tughlaq and Ala ud din Khilji as well as the British.[3]

The most famous monument situated in the complex is the Qutb Minar; other important constructions in the complex are the Quwwat ul-Islam Mosque, the Alai Gate, the Alai Minar, the Iron pillar, and the tombs of Iltutmish, Alauddin Khilji and Imam Zamin; surrounded by Jain temple ruins [4].

Today, the adjoining area spread over 100 acres, with a host of old monuments, including Balban's tomb, has been developed by Archeological Survey of India (ASI) as the Mehrauli Archeological Park, and INTACH has restored some 40 monuments in the Park [5]. It is also the venue of the annual 'Qutub Festival', held in November-December, where artists, musicians and dancers perform over three days. Qutb Minar complex, with 38.95 lakh visitors, was India's most visited monument in 2006, ahead of the Taj Mahal, which drew about 25.4 lakh visitors [6].

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Qutub Minar:

This is the portion above the main entrance to Qutab Minar

(Muhammad Ghori managed to defeat Prithviraj Chauhan in battle in 1192. Ghori left his slave Qutub-ud-din Aibak as his viceroy, who captured Delhi the subsequent year. After Ghori's death in 1206, Aibak proclaimed himself the ruler of Delhi and founded the slave dynasty. Qutb-ud-din contributed significantly in terms of architecture by getting Mehrauli built. His most prominent contribution is the starting of Qutab Minar. This 72.5m tall tower was built across three generations and finally completed in 1220AD. The Slave dynasty ruled till 1290, among them was Razia Sultan who ruled for just three years, but became a historic figure for being the first empress in India.)

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The Qutub Minar is located 15 km south of New Delhi and is a majestic monument and is the tallesttower of India. It is minar in perfection, known to have no parallel in the world. The tower was namedafter Qutbud-Din to herald the victory of the slave dynasty in the 13th century. The construction of thismonument was started in 1200 A.D. but was completed by Iltumitsh. Originally, it was built as a minarfor calling the faithful to the mosque for prayer but later it was known as a victory tower, see Figure 2.Spearing its way proudly into the sky, Qutub Minar with a height of 72.5 meters commands apanoramic view of the green fields extending into a sprawling city. The Qutub Minar was built as avictory memorial by the Muslims who captured Delhi. Minar is the root of the English word "minaret"meaning "Little Minar" or pillar.Qutb-u'd-Din Aibak laid the foundation of Qutub Minar in 1199 A.D. for the use of Mu'azzin (crier) togive calls for prayer and raised the first storey, to which were added three more storeys by hissuccessor and son-in-law, Shamsu'd-Din IItutmish. All the storeys are surrounded by a projected

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balcony encircling the Minar and supported by stone brackets, which are decorated with honeycomb design, more conspicuously in the first storey. The beautiful calligraphy on the bands of Qutub adds to its grandeur.

Qutub Minar is 72.5 m high with 379 steps and it has a diameter of 14.3 m at the base and 2.8 m at theapex. The magnificent monument has five storeys at present, which can be easily distinguished from theoutside by the projecting balconies with stalactitic brackets. Initially, it was a four storeyed tower. Thetopmost tower was damaged in 1368 when two more storeys were added (see Figure 4). The architectureof the Qutub is of Islamic style. The lower most storey has alternate angular and circular flutings, thesecond storey with rounded and the third with angular ones, the alignment of the flutings remaining in thesame line. The ornamentation of the varied styles in the different storeys adds to the grandeur. The lower three storeys of the Qutub are made mainly of buff colored quartzite. But the upper two

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storeys, which were damaged and reconstructed, are made mainly of marble with a subordinateamount of quartzite; Quartzite of the Alwar Series of Delhi system (Pre-Cambrian) is available locally.The marble was brought from different parts of Rajasthan, India. Sculptured Vindhyan sandstone isreported to be brought after destroying the Hindu temples, was also used in the construction of theQutub. From the Nagari and Persian inscriptions on the minar, it is evident that it was partiallydamaged in 1326 and 1368 by lighting and was promptly repaired by the Muslim rulers. Qutbu'd-Din Aibak laid the foundation of Minar in AD 1199 for the use of mu'azzin (crier) to give callsfor prayer and raised the first storey, to which were added three more storeys by his successor andson-in-law, Shamsu'd-Din IItutmish (AD 1211-36).

All the storeys are surrounded by a projectedbalcony encircling the minar and supported by stone brackets, which are decorated with honey-comb

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design, more conspicuously in the first storey. Numerous inscriptions in Arabic and Nagari charactersin different places of the minar reveal the history of Qutb. According to the inscriptions on its surface itwas repaired by Firuz Shah Tughlaq (AD 1351-88) and Sikandar Lodi (AD 1489-1517). Major R. Smithalso repaired and restored the minar in 1829.

In the Qutub Complex, there is one unfinished minar called Alai Minar, which was later madeThe ides was to make a talled and more magnificent minar than the Qutub but it failed.

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However, the unfinished minar gives an excellent opportunity to look into the constructions practicesand material being used. It was the intention of Ala-ud-din Khalji (1296-1316) to construct a minar,double both in diameter and height of the existing one, under the name Alai Minar. Its constructionwas begun, and a rough unfinished stump is insitu at Qutub complex, but the minar did not seem to have reached any stage of completion.

FUNCTION OF A MINARET:

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As well as providing a visual cue to a Muslim community, the main function of the minaret is to provide a vantage point from which the call to prayer is made. The call to prayer is issued five times each day: dawn, noon, mid-afternoon, sunset, and night. In most modern mosques, the adhan is called from the musallah, or prayer hall, via microphone to a speaker system on the minaret. Minarets also function as air conditioning mechanisms: as the sun heats the dome, air is drawn in through open windows then up and out of the minaret, thereby providing natural ventilation.

STRUCTURE:

The Qutab Minar is tall, with 379 steps leading to the top. The diameter of the base is 14.3 meters, while the top floor measures 2.75 meters in diameter. Surrounding the building are many fine examples of Indian artwork from the time it was built in 1193. A second tower was in construction and planned to be taller than the Qutb Minar itself. Its construction ended abruptly when it was about 12 meters tall.The name of this tower is given as Alai Minar and construction of recent studies shows that this structure has been tilted in one direction. It is made of red sandstone all the way except for two stories at the top. This part is of white marble and was made by Firoz Shah Tughlaq. He had decided to put a prominent finish to the magnificent minar.

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INTERESTING FACTS ABOUT QUTUB MINAR:

1. Qutab Minar is the tallest brick minaret in the world.

2. The Qutub Minar and its adjoining monuments are all listed as UNESCO World Heritage Site.

3. The diameter of Qutub Minar is 14.32 m at the base and 2.75 m on the top. The height of Qutub Minar is 72.5 m.

4. There are 379 stairs inside the tower, which lead to the top.

5. The foundation of the tower was laid down by Qutubu’d - Din Aibak in 1199 AD.

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6. The purpose behind the construction of Minar was for the use of mu'azzin (crier) to give calls for prayer.

7. The first storey was completed during the reign of Aibak.

8. Many historians believe that the Qutub Minar was named after the first Turkish sultan, Qutb-ud-din Aibak. But there is a different view also. Other historians contend that it was named in honour of the Sufi Saint Qutbuddin Bakhtiar Kaki

9. The next three stories were added by Shamsu'd-Din Iltutmish, the son - in - law of Qutubu’d - Din Aibak.

10. The fifth and the last storey were constructed by Firuz Shah Tughlaq.

11. All the stories are surrounded by protruding balconies, encircling the tower.

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12. The Minar contains numerous inscriptions in Arabic and Nagari characters, which narrate its history.

13. As per the inscriptions on its surface, it was repaired by Firuz Shah Tughlaq and Sikandar Lodi.

14. The Minar was also repaired and restored by Major. R. Smith in 1829.

15. According to the Archeological Survey of India, the site at which Qutab Minar is located was once occupied by 27 Hindu and Jain temples.

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USE OF CALLIGRAPHY:

Arabic calligraphy is associated with geometric Islamic art (the Arabesque) on the walls and ceilings of mosques as well as on the page. Contemporary artists in the Islamic world draw on the heritage of calligraphy to use calligraphic inscriptions or abstractions in their work.

Instead of recalling something related to the reality of the spoken word, calligraphy for the Muslim is a visible expression of spiritual concepts. Calligraphy has arguably become the most venerated form of Islamic art because it provides a link between the languages of the Muslims with the religion of Islam. The holy book of Islam, al-Qur'ān, has played a vital role in the development of the Arabic language, and by extension, calligraphy in the Arabic alphabet. Proverbs and complete passages from the Qur'an are still active sources for Islamic calligraphy.

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Geometry in Qutub Minar:

There are many prospects to see geometry in an architectural piece or anything in nature. It can be symmetry, tessellations, basic shapes, curves, lines, angles, etc....I will be showing geometry in Qutub Minar in terms of tessellation, basic geometrical shapes, symmetry, etc...

What makes the minar so tall???....

The tall and ever attractive monument of Delhi which can be seen from most parts of the city is called the Qutab Minar. Every body has the same question when one sees the structure for the first time. The question that is often being put up is "Why the monument is that big?" or "Was there any specific reason to build such a tall building or it was just a wish of the person who built it?" Well, the exact reason is assumed to have something related to commemorating the victory. Mughals used to build victory towers to proclaim and celebrate victories. Some say

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the minaret was used to offer prayer but it is so tall that you can hear the person standing on the top. Also, the minaret is not joined on to Qutuddin's mosque and the Iltutmish's mosque.

Qutab Minar is among the tallest and famous towers in the world. The minaret is 234 feet high and the highest individual tower in the world. Other towers in the world are the Great Pagoda in Pekin, China and the Leaning Tower of Pisa in Italy but these towers are not as high as the Qutab Minar in Delhi.

According to history books, the minar was started by Prithviraj or his uncle Vigraharaja who won Delhi from the Tomar Rajputs. However, it is assumed and historians believe that Qutubuddib and Iltutmish finished it though the minar may have been commenced by Prithviraj or Vigraharaja. The minar was completed in 1200 A.D and since then the tall structure has been there upright and ever beautiful keeping an eye to Delhi just like a sentry. When Alauddin returned from the wars in the Deccan, he had this thought in mind that he would build a victory tower somewhat similar to the Qutab Minar. The ruins of this very initiative can be seen adjacent to the Qutbuddin's mosque because Alauddin died at the very start of the construction work and no one carried on to finish the initiative taken by Alauddin.

Qutab Minar is another great masterpiece of Mughal architecture. It has a number of floors or storeys which has beautiful carvings like the one on the tomb of Iltutmish. There are inscriptions all round the tower and these inscriptions reveal that Iltutmish finised the tower. The structure of the wall is made as such that it widens from top to bottom, just to make the minar stronger.

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Moving upstairs inside the minar will give you a wonderful experience and counting the stairs is always a fun for visitors. It has 378 steps which takes good amount of energy to reach at the top. The top of the tower gives an insight to Delhi because you get to see the bird's eye view of the city. To point a few sight seeing from the top, you will find views of the Hauz Khaz on the left and the walls of the Jahanpanah and Siri on the right. It was this very top of Qutab Minar that was used by Khilji and Tughlaq kings to watch the wild Mongol hordes when they threatened Delhi. The top also served as the watch top for Tughlaq who watched Timur's army camp on the Wellingdon Airport. Other important monuments that is visible from the top are the walls of Tughlaqabad, Humayun's Tomb, Purana Qila, Firoz Shah Kotla and Jama Masjid.

The minar did receive some damage because of earthquakes on more than a couple of occasions but was reinstated and renovated by the respective rulers. During the rule of Firoz Shah, the minar's two top floors got damaged due to earthquake but were repaired by Firoz Shah. In the year 1505, earthquake again struck and it was repaired by Sikandar Lodi. Later on in the year 1794, the minar faced another earthquake and it was Major Smith, an engineer who repaired the affected parts of the minar. He replaced Firoz Shah's pavilion with his own pavilion at the top. The pavilion was removed in the year 1848 by Lord Hardinge and now it can be seen between the Dak Bungalow and the Minar in the garden. The floors built by Firaz Shah can be distinguished easily as the pavilions was built of white marbles and are quite smooth as compared to other ones.

The minar is not that erect as it used to be because of wears and tears over the past several years. Closely looking at the mina rives you an idea that it is somewhat tilled

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towards one side. The minar is very sincerely looked after by the authorities much like the same as other historic monuments in the country.

USE OF BASIC SHAPES:

Qutub Minar uses the basic shapes like cylinder, frustum of a cone, angular elevations, semicircles and beautifully carved shapes in forms of tessellations and Islamic carvings. It is made of red and buff sandstone. Aibak constructed the first floor and the tree more storeys were added by Iltutmish. All the storeys are surrounded by a projected balcony encircling the Minar and supported by stone brackets, which are decorated with honeycomb design, more conspicuously in the first storey. The first storey and its balcony have the curved and

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fluted design. The second storey has only curved design while the third storey has only fluted design. The Qutub Minar is decorated with floral motif and arabesque. The inscriptions on the surface of the Minar suggest that Firoz Shah Tughlaq (AD 1351-88) and Sikandar Lodi (AD 1489-1517) repaired it. Firoz Shah renovated the top floor and added marble to the building.

HIGHLY SKILLED USE OF CURVES, LINES AND ANGLES TO BRING OUT INTRICATE CARVING AT QUTUB MINAR, ALSO INSCRIBED ARE QUOTES

FROM THE HOLY KURAN. THE USE OF GEOMETRY SHOWS THE DEXTERITY AND COMMAND OF SCULPTORS OVER DESIGN.

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Details of Jainist stone carvings inside the remains of the Quwwat ul-Islam Mosque.SKILLFUL USE OF CURVES,

ANGLES TO CARVE OUT BEATIFULL DESIGNS.

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ISLAMIC CALLIGRAPHY:In the world of Islam the art of writing has always a great role. Amongst all arts calligraphy can be considered as the most typical art form to express in Islamic Art. The Quran itself has stressed on art of beautiful writing. The growth of Islamic Calligraphy was seen in both art and architecture, Use of lines, curves to generate beautifully

carved inscriptions is the important part of QUTUB MINAR.

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TESSELLATION IN QUTUB MINAR:

USE OF TRIANGLES AND STAR.

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USE OF HEXAGONS AND STARS TO CREATE A BEAUTIFUL TESSELLATION.

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SYMMETRY IN QUTUB MINAR:

THERE IS HIGHLY SKILLED USE OF SYMMETRY IN QUTUB MINAR WE HAVE LINEAR SYMMETRY IN ALL THE FIVE FLOOR OF QUTUB MINAR. THERE IS ROTAIONAL SYMMETRY ALL AROUND THE DESIGN OF TOWER.

WE ALSO HAVE MIRROR SYMMETRY AT MANY PLACES IN QUTUB MINAR.

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CONCLUSION

THIS PROJECT MADE ME AWARE OF USE OF GEOMETRY AT ELEMENTARY LEVEL IN TERMS OF CONSTRUCTION, DESIGN, TESSELLATIONS AND SYMMETRY IN QUTUB MINAR.

I GOT AN OPPORTUNITY TO DO A RESEARCH ON A MONUMENT LIKE QUTUB MINAT. I AM SINCERELY

THANKFUL TO FACULTIES FOR GIVING ME THIS TASK.

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BIBLIOGRAPHYBOOKS FROM NIFT RESOURCE CENTRE:

ISLAMIC TESSELLATIONS ISLAMIC PATTERN

BRIEF HISTORY OF INDIAN ARCJITECTURE

MUGHAL ARCHITECTURE

INTERNET RESOURCES

GOOGLE BIBO

TOURISM SITES: INCREDIBLE INDIA

PHOTOGRAPH RESOURCES:

WWW.FLICKR.COM

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