Indian architecture followed principles of vastu shastra, aligning buildings with cosmic movements. Cities like Harappa and Mohenjo-Daro were precisely planned using mathematical drawings. Jaipur's design was based on a nine-square mandala representing the universe, with the royal palace at the center. Ancient Greek architectural orders like Doric, Ionic, and Corinthian influenced styles worldwide, and the golden ratio of 1.618 was incorporated into designs like the Parthenon and buildings as diverse as the Taj Mahal and United Nations headquarters.

7. Indians employed planning principles and proportions that rooted the buildings to the cosmos, considering the movements of sun, stars, and other heavenly bodies. vastu shastra , the ancient Indian canons of architecture and town planning employs mathematical drawings called mandalas

12. During the Indus Valley Civilization at the sites of Harappa and Mohenjo-Daro constructions took place following precise mathematical calculation

14. x x

26. Pythagoras theorem used in architecture: The Samrat Yantra, at Jaipur, designed by Jai Singh, measuring 147′ at its base and 90′ high could calculate time within two seconds accuracy per day. .

27. Jaipur was designed using the pithapada mandala as the basis. In this mandala of nine squares that represent the universe, earth occupies the central square. In the city, which consists of nine large squares, the central square is assigned to the royal palace. They calculated and planned city map using recursion: Length of City / Length of Middle Town : 771.1/340.5 ≈ 2.26; Length of Middle Town / Length of Castle: 340.5/151 ≈ 2.26

30. Great Mosque of Kairouan

32. The grand Imam Mosque

33. DORIC ORDER Examples of the Doric order are Parthenon the temple for the goddess of wisdom.

34. LONIC ORDER Some examples of the Lonic order are the temple of Apollo at Didyma/Turkey. The temple of Athena Nike was also the Lonic order.

35. CORINTHIAN ORDER The Corinthian order was the latest order. The oldest example of the Corinthian order was the temple of Apollo at Bassae. The Greeks made little use of this order.

36. Here (a + b) / a = a/b= Φ ≈1.6180339887 Golden ratio is (a+b):a or a:b which is 1: Φ i.e. 1: 1.6180339887…

41. The Greek used it extensively for beauty and balance in the design of the Parthenon and other architecture:

42. Φ was used it in the design of Notre Dame in Paris, which was built in the 1163 and 1250

43. In India, Φ was used in the construction of the Taj Mahal,

44. Φ was used in the UN building

45. The CN Tower in Toronto has contains the golden ratio in its design. The ratio of observation deck at 342 meters to the total height of 553.33 is 0.618 or phi, the reciprocal of Phi!