Indian Calendar

 INDIAN CALENDAR

Elements of the Indian Calendar

• Coordinate system

                      

The ecliptic plane is the plane that contains the orbit of the Earth around the Sun

The sun is said to be in a nakshatra or Rasi if the line joining the Earth with Sun goes through that nakshatra (star) or rasi (constellation)

The celestial sphere is an imaginary sphere centered on the Earth used to measure the positions of the stars  through angles Azimuth and Altitude

The moon and almost all the planets are found within a belt of width 8 degrees on either side of the ecliptic plane, and this belt is known as the Zodiac or the Rasichakra

Solar and Lunar Years

• Solar year (Samvatsara) is the time taken by the Earth to complete one revolution around the Sun. That means, after exactly one solar year, the Sun will return to the same star (background of stars). It is equal to 365.2564 days.
• Lunar year (AnuVatsara) is 12 cycles of Full Moon to Full Moon (or New Moon to New Moon). It is equal to 354.3671 days. 
  

Thus, there is a discrepancy of 10.9 days in the Solar and Lunar years. After every Five years the Sun and the Moon come to the same position in the background of stars. This 5-year cycle is used to synchronize the solar and Lunar calendars by adding two Lunar months (Adhika masas).

Five components of Panchanga: These five components uniquely 

• Tithi
• Nakshatra
• Vara
• Karana
• Yoga
  

The Sun moves at the rate of 1 degree per day, with respect to the Earth. The Moon moves at the rate of 13 degrees with respect to the Earth. The difference between the longitudinal positions of the Sun and the Moon is Tithi

The Moon is in the green color longitude (i.e. the line joining centres of Earth and Moon in this longitude). The Sun is in blue color Longitude. The Integer part of the angle between these two longitudes is called TITHI.

The Nakshatra, at any instant, refers to the particular portion of the ecliptic in which the moon is situated. In the above picture, the moon is situated in Nakshatra #3 i.e., Krittika

There are 27 Nakshatras (lunar mansions) in Vedic astrology. They are: 1. Ashvini, 2. Bharani, 3. Krittika, 4. Rohini, 5. Mrigashirsha, 6. Ardra, 7. Punarvasu, 8. Pushya, 9. Ashlesha, 10.Magha, 11.Purva Phalguni, 12.Uttara Phalguni, 13.Hasta, 14. Chitra, 15.Swati, 16.Vishakha, 17. Anuradha, 18. Jyeshtha, 19. Mula, 20. Purva Ashadha, 21. Uttara Ashadha, 22. Shravana, 23. Dhanishtha, 24. Shatabhisha, 25. Purva Bhadrapada, 26.Uttara Bhadrapada, and 27. Revati

Indian Mathematicians

 Indian Mathematicians

1. Panini - Algorithms
2. Pingala - Binary Mathematics
3. Aryabhatta - Square root, cube root, place value system, sine table, quadratic equ., trigonometry
4. Varaha Mihira- Fine ancient Siddhantas, Trigonometric identities, combinatorics, Magic square
5. Bhaskara-I - Indeterminate equations, approximate formula for sine function, astronomy
6. Brahmagupta - Arithmetic with zero and negative numbers, pythogorean triplets, etc
7. Virahanka - Fibonacci numbers, Morci meters,
8. Bhaskara-II - Sine functions, surds, permutations and combinations, ideas of calculus, astronomy
9. Nilakantha Somayaji - Irrationality of pi, BAsic ideas of calculus, PLanetary theory, Sine series

Unique Aspects of Indian Mathematics

 Unique Aspects of Indian Mathematics

Unique features

• Indian mathematics is a seamless blend of poetry, literature, logic, and mathematical thinking weaved into a single work. It is not compartmentalized as in modern education. There is no fear or stress in learning mathematics
• Indian mathematics seamlessly blended into daily life:  Temple inscriptions, literary works, discussions on religion, spirituality, etc
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Vaisesika Darsana

 Vaisesika Darsana

• Mainly deals with 'Exposition of reality'
• Systematic framework to describe all the 'Nameable and knowable' entities
• Kanaada gave 370 sutras to describe the 'second stage of creation' (First stage of creation, as per Indian Tradition, involves creation of ether, time, space and elements- earth, water, fire and air. Second stage of creation involves creation of multitude of physical entities)
• Three-pronged approach
• Uddhesa: Classification framework
• Lakshana: Definition of properties
• Pariksa: Examination using perception and inference
• Framework of Vaisesika school

• Dravyas, guna and karmas have general and special aspects, as given below
  

• Dravya constitutes the basic building block of the physical reality. It can be roughly translated as substance or matter, with more broader scope
• Classification on the basis of extent

• Classification based on occurence as singular or in classes

• Attributes of substances

Attributes are inherent properties associated with the substances (DRAVYA). 

They do not have independent existence nor cause for conjunction or disjunction process

17-24 attributes are identified and classified into three sets.

1)  Attributes related to finite substances- color, taste, smell , touch, fluidity, viscidity, etc

2) Attributes related infinite substances - cognition, pleasure, pain, desire, aversion, volition, merit, demerit, impression and sound

3) Attributes associated with both finite and infinite substances- number, quantity, separateness, conjunction and disjunction

From the above table, we can understand the general properties and special properties. Earth has a special property of smell. Ether has a special property of Sound. Water has a special combination of taste-color-touch

 

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