The Indic MathematicaL Tradition - · PDF fileThe Indic MathematicaL Tradition Monthly Planner...

The Indic MathematicaL Tradition

Monthly Planner 2007,2008

With Panchangam Data

Compliments

Of Indic Studies Foundation

Designed By

Kosla Vepa

The Indic Mathematical tradition

Aryabhata I (the elder)आयर्भट

Born 2765 BCE (based on modern research)conventional dating (476 - 550 CE)

astronomer mathematician of the ancient world

Ancient Vedic AstronomyAncient Vedic Astronomy

First mentioned in the VedasFirst mentioned in the VedasThe Vedas can be dated to the 5th or 6The Vedas can be dated to the 5th or 6thth millennium BCE using millennium BCE using techniques now considered as a part of a discipline known as techniques now considered as a part of a discipline known as

ArchaeoArchaeo AstronomyAstronomy

One of the observations that the ancients made was the day and One of the observations that the ancients made was the day and the location of the Sun when it makes its way past the Celestialthe location of the Sun when it makes its way past the Celestial

equator to the northern half of the Celestial sphere. This is knequator to the northern half of the Celestial sphere. This is known own as the Vernal equinox. When this occurs the number of hours of as the Vernal equinox. When this occurs the number of hours of

daylight equals 12 or half the modern calendar daydaylight equals 12 or half the modern calendar dayThe Astronomy and the Astrology of India is based upon sidereal The Astronomy and the Astrology of India is based upon sidereal

calculations. Sidereal astronomy uses the distant stars as the calculations. Sidereal astronomy uses the distant stars as the frame of reference and the sidereal period is the time that it tframe of reference and the sidereal period is the time that it takes akes the object to make one full orbit around the Sun, relative to ththe object to make one full orbit around the Sun, relative to the e

stars. This is a more accurate computation of the true orbital stars. This is a more accurate computation of the true orbital period of any planetary body period of any planetary body ..

January 2007Monthly Planner

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

1New Year 's Day

2 3Purnima

4 5 6

7 8 9 10 11 12 13

14Makar Sankranti,, Uttarayana Punyakalam

15EkadasiMartin Luther King, Jr.

16 17 18

Amavasya

19 20

21 22 23Vasant Panchami

24 25 26Republic Day of India

27

28Ekadasi

29 30 31Dec 2006

S M T W T F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29 30

31

Feb 2007

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28

Done Priority Description Due DateDone Priority Description Due Date


The Armillary or Celestial sphere (Gola)

depicts the way the ancients saw the universe,asthey gazed at the sky. Armillary spheres have concentric rings to indicate planetary orbits, the zodiac band of constellations, and terrestrial and celestial measurement circles such as the Tropics of Cancer and Capricorn and the equator. Sometimes they are mounted with an Orrery inside. Sometimes they are mounted as garden sundials.

A Ptolemaic armillary sphere has an earth globe atthe center, surrounded by celestial circle and zodiac armillary rings, demonstrating the geocentric theory of the universe developed by Ptolemy and others in ancient Greece and Rome. The latest view is that Ptolemy was certainly not the first or the only onetodevelop a calculation algorithm based on a geocentric model. The Indics were already there, no pun intended, as were probably the Chinese

February 2007Monthly Planner


1Purnima

2Groundhog Day

3

4 5 6 7 8 9 10

11 12Lincoln's Birthday

13Ekadasi

14Valentine's Day

15 16Maha Shivaratri

17Amavasya

18Yugabda 5109

19President's Day

20 21 22Washington's Birthday

23 24

25 26 27Ekadasi

28

Jan 2007

S M T W T F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31

M ar 2007

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30 31



The Celestial sphereKnown also as the Armillary sphere or Gola in Sanskrit)

Showing the ecliptic and its inclination to the celestial equator and is the inclination of the earths axis to the axis perpendicular to the plane of the ecliptic

About 23.5 degrees

March 2007Monthly Planner


1 2 3Parti al Lunar Eclipse

HoliPurnima

4 5 6 7 8 9 10

11Daylight Saving Time Begins

12 13 14 15Ekadasi

16 17St. Patri ck's Day

18Solar Eclipse

19Chaitra, Ugadi ,Hindi, Telugu New year

Ramayana week

20 21Vernal Equinox

22 23 24

25 26Sri Ram Navami

27 28 29Ekadasi

30 31

Feb 2007

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28

Apr 2007

S M T W T F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30



The structure of Vedic Literature (continued)EachVeda consists of Samhitas, Brahmanas, Aranyakas -

speculation in the solitude of wilderness eventually taking shape as the Upanishads,

To these were appended what were later called the Vedangascomprising of

Shiksha (phonetics) Sandhi rules

Chandas (meter)

Nirukta (etymology)

Vyakarana (grammar)

Jyotisha (astronomy and calendric functions)

KalpaSutras(Ritual procedures and the associated mathematics)

Note the emphasis on brevity throughout, sandhi to make the content more compact, phonetics for mnemonic purposes. Panini’s Ashtadhyayi is a tour de force as the worlds oldest

Grammar text and Nirukta for associativity in remembering the meaning of words

April 2007Monthly Planner


1April Fool's Day

Mahavira Jayanti

2Purnima

3 4 5 6 7

8 9 10 11 12 13 14Tamil New Year, Baisakhi, Vishu

15 16 17Partial Lunar Eclipse

18 19 20 21

22Ramanuja JayantiSankara Jayanti

23 24 25 26 27 28Ekadasi

29 30Narasimha Jayanti

Mar 2007

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30 31

May 2007

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30 31



Proposed chronology of the Vedics

A work in progress

Event Individual Date

Birth Veda Vyaasa ~3300 BCE

Birth Apastambha 3200 BCE

Birth Baudhayana 3200 BCE

Era Kaliyuga 3102 BCE

Birth Aryabhata 2765 BCE

Lifespan Gautama Buddha 1888-1807 BCE

Coronation Chandragupta Maurya 1554 BCE

Coronation Asoka Maurya 1472 BCE

Coronation Kanishka 1294-1234 BCE

Era Andhra Satavahana 833 BCE -327 BCE

Coronation Chandragupta of Gupta dynasty 327 BCE

Pancha Siddhanta VarahaMihira 123 BCE

Reign Vikramaditya 102 BCE to 78 BCE

Birth Brahmagupta 30 BCE

Writings Bhaskara II Siddhanta Siromani 486 BCE

May 2007Monthly Planner


1Purnima

2Buddha Purnima

3Annamacharya Jayanti

4 5

6 7 8 9 10 11 12Hanuman Jayanti

13EkadasiMother's Day

14 15 16Amavasya,Jyeshtafirst of 2, adhik maas

17 18 19Armed Forces Day

20 21 22 23 24 25 26

27Ekadasi

28Memorial Day

29 30Poornima

31

Apr 2007

S M T W T F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30

Jun 2007

S M T W T F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29 30



Precession of the equinoxes

At the end of a tropical year from one vernal equinox to the next with respect to the fixed stars , the earth appears to fall short by 50.26 seconds of longitude.

That means it takes approximately 25876 years for the precession to complete 360 degrees or 1 revolution of the vernal equinox as it traverses a different Nakshatra every 955 years.

Voila , here we have a 26000 year clock and by noting the Nakshatra in which the vernal equinox occurred we can tell when the event occurred. By dividing each Nakshatra into 4 padas we can refine the unit of time to 240 years . This is a fairly reliable method of dating events such as the composition of the Rg or the date of the Mahabharata war

Precession of the equinoxes and the pole star

June 2007Monthly Planner


1 2

3 4 5 6 7 8 9

10 11Ekadasi

12 13 14Flag Day

15Adhik Maas last day

16Amavasya,Jyeshtashukla

17Father's Day

18 19 20 21Summer Solsti ce

22 23

24 25 26 27 28 29 30Purnima

May 2007

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30 31

Jul 2007

S M T W T F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31



Precession of the Equinoxes

July 2007Monthly Planner


1 2 3 4Independence Day

5 6 7

8 9 10Ekadasi

11 12 13 14Amavasya, Asadha shukla

15 16Dakshinayana Punyakala

17 18 19 20 21

22 23 24 25Ekadasi

26 27 28Guru(Vyaasa) Purnima

29 30 31Jun 2007

S M T W T F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29 30

Aug 2007

S M T W T F S

1 2 3 4

5 6 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30 31



Deciphering the age of an event

Observations about the Nakshatra in which the Vernal Equinox occurs tell us the era in which the observations took place (Archaeo-Astronomy)

This is only one of the possible astronomical markers

Look to manuscripts written by Astronomers and Mathematicians, since they have a penchant for precision in their observations and remarks

We are at the beginning of discovery of our forgotten past

August 2007Monthly Planner


1 2 3 4

5 6 7 8Ekadasi

9 10 11

12Amavasya,Sravanashukla

13 14 15Independence Day

16 17 18

19 20 21 22 23 24EkadasiVaralakshmi Vratam

25

26 27 28PurnimaRaksha Bandhan

29 30 31

Jul 2007

S M T W T F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31

Sep 2007

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30



Dating of the Vedas

Hermann Jacobi

John Playfair In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BC.3

Playfair’s argumentation, “Remarks on the astronomy of the Brahmins”, Edinburg 1790, is reproduced in Dharampal: Indian Science and Technology in the Eighteenth Century, Academy of Gandhian Studies, Hyderabad 1983 (Impex India, Delhi 1971), p.69-124.

September 2007Monthly Planner


1

2 3Labor Day

4Krishna Janmashtami

5 6Ekadasi

7 8

9 10 11Amavasya, Bhadrapada shukla

12 13 14 15Ganesh Chaturthi

16 17 18 19 20 21 22Ekadasi

23Autumnal equinox

24 25 26Purnima

27 28 29

30

Aug 2007

S M T W T F S

1 2 3 4

5 6 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30 31

Oct 2007

S M T W T F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31



The difference between the sidereal day and the solar

day from Wikipedia.

For the same reason the sidereal year is longer than the solar or tropical year by

about 20 minutes.

We will come back to this when we discuss the

precession of the equinoxes

October 2007Monthly Planner


1 2 3 4 5 6Ekadasi

7 8Columbus Day (Observed)

9 10Amavasya,Aswinashukla

11Navratri begins

12 13

14 15 16 17Saraswati Puja

18 19Madhva Jayanti

20

21Vijaya Dashami

22Ekadasi

23 24 25Purnima

26 27

28 29Karva chaturthi (Karva chauth)

30 31Halloween

Sep 2007

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30

Nov 2007

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30


TheIndic

NakshatraSystem

attributed toGargeya in the Atharva

Veda

Western Asterism name Indian Nakshatras (Sidereal Zodiac) Sector in deg,min deg,min

1. Beta Arietis Aswini 00 00 13 20

2. 41 Arietis Bharani 13 20 26 40

3. Eta Tauri Karthika 26 40 40 00

4. Alpha Tauri Rohini 40 00 53 20

5. Lamda Orionis Mrigasira 53 20 66 40

6. Alpha Orionis Aridra 66 40 80 00

7. Beta Geminorum Punarvasu 80 00 93 20

8. Delta Cancri Pushya 93 20 106 40

9. Alpha Cancri Aslesha 106 40 120 00

10. Alpha Leonis Magha 120 00 133 20

11. Delta Leonis Pubba 133 20 146 40

12. Beta Leonis Uttara 146 40 160 00

13. Delta Corvi Hasta 160 00 173 20

14. Alpha Virginis Chitra 173 20 186 40

15. Alpha Bootis Chothi 186 40 200 00

16. Beta Librae Vishakam 200 00 213 20

17. Delta Scorpi Anuradha 213 20 226 40

18. Alpha Scorpi Jyeshta 226 40 240 00

19. Lamda Scorpi Moola 240 00 253 20

20. Delta Sagittari Poorvashad 253 20 266 40

21. Delta Sagittari Uthrashad 266 40 280 00

22. Alpha Aquilae Sravana 280 00 293 20

23. Alpha Delphini Dhanishta 293 20 306 40

24. Lamda Aquar Satabhisha 306 40 320 00

25. Alpha Pegasi Poorvabhadra 320 00 333 20

26. Alpha Andromeda Uttrarabhadra 333 20 346 40

27. Zeta Piscium Revathi 346 40 360 00

November 2007Monthly Planner


1 2 3

4Daylight SavingsTime Ends

Ekadasi

5 6Election Day

7Naraka Chaturdasi

8Deepavali

9Amavasya,Kartikashukla

10Vikram New Year 2064

11Veterans Day

12 13 14 15 16 17

18 19 20Ekadasi

21 22Thanksgiving

23 24Purnima

25 26 27 28 29 30

Oct 2007

S M T W T F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31

Dec 2007

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30 31



Dating of the Mahabharata

The following key dates are found to be consistent with the sky inscriptions observed by Veda Vyasa:

Krishna's departure on Revati Sept. 26, 3067 BCE Krishna's arrival in Hastinapura on Bharani Sept. 28, 3067 BCE Solar eclipse on Jyeshtha amavasya Oct. 14, 3067 BCE Krittika full moon (lunar eclipse) September 29, 3067 BCE War starts on November 22, 3067 BCE (Saturn in Rohini, Jupiter in

Revati) Winter solstice, January 13, 3066 BCE Bhishma's expiry, January 17, 3066 BCE Magha shukla ashtamiA fierce comet at Pushya October 3067 BCE Balarama sets off on pilgrimage on Sarasvati on Pushya day Nov. 1, 3067

BCE Balarama returns from pilgrimage on Sravana day Dec. 12, 3067 BCE

On the day Ghatotkaca was killed moon rose at 2 a.m., Dec. 8, 3067 BCE

December 2007Monthly Planner


1

2 3 4Ekadasi

5 6 7 8

9Amavasya,Margasi rsashukla

10 11 12 13 14 15

16 17 18 19Gita jayanti Vaikunta Ekadasi

20 21 22Winter solstice

23Purnima

24 25Christmas

26 27 28 29

30 31New Year's Eve

Nov 2007

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30

Jan 2008

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30 31



Month Suns LongitudeDeg min

Duration days

Gregorian2007/2008

1. Vaisakha 23 15 30.9 Apr. 18

May 17,16

June 15

July 13

Aug. 18

Sept. 12

Oct. 10

Nov. 10

Dec. 24

Jan. 19

Feb. 18

12. Caitra 353 15 30.3 Mar. 19

2. Jyestha(adhika) 53 15 31.3

3. Asadha 83 15 31.5

4. Sravana 113 15 31.4

5. Bhadrapada 143 15 31.0

6. Asvina 173 15 30.5

7. Kartika 203 15 30.0

8. Margasirsa 233 15 29.6

9. Pausa 263 15 29.4

10. Magha 293 15 29.5

11. Phalguna 323 15 29.9

Months according to Indian Panchang Synchronization and Leap MonthsThe fundamental problem with the Indian

panchang as with all lunisolar calendars is the synchronizaton (or a lack thereof) between the solar and lunar periodicities and just as we add a leap day every four years to the Gregorian calendar m we have to add a leap month or adhika maas every 2.5 years. There are 2 synchronization cycles known as the MetonicCycle and the Saros. According to the Metoniccycle (Meton . was a Greek of 430 BCE), every 2.5 years an extra lunar month, will have to be added to keep up to 365 days. In 19 years,7 lunar months are aided to make it more accurate, i.e. 19 x 12 + 7 = 235 lunar months. Since a lunar month is about 29.531 days which gives a total of 235 x 29.531 = 6939.68 days. However Yajnavalkya was the first to demonstrate a 95 year (19*5)synchronization cycle in the Satapatha Brahmana . Yajnavalkya was another one of those who could be termed a Man for all seasons,a multi faceted personality, a species of Homo sapien that appeared to populate the pages of ancient Indian History in much profusion

January 2008Monthly Planner


1New Year's Day

2 3 4Ekadasi

5

6 7 8Amavasya, Pausa shukla

9 10 11 12

13 14Makar Sankranti

15 16 17 18 19

20 21Martin Luther King, Jr.

22Purnima

23 24 25 26

27 28 29 30 31

Dec 2007

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30 31

Feb 2008

S M T W T F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29



“In the 5th Mandala of Rig Veda, the 40th sukta and 5th Rik, Rishi Atri describes a total solar eclipse.

Rig Veda- HYMN XL. 5. Indra. Surya. Atri.

O Surya, when the Asura's descendant Svarbhanu, pierced thee through and through with darkness, All creatures looked like one who is bewildered, who knoweth not

the place where he is standing.Vedic astrology refers to moon’s ascending node or descending node at time of potential solar eclipse as Rahu or Swarbhanu, a demon. The passage certainly describes a total solar eclipse, magically imposed by

Rahu, and people and animals being scared of the solar eclipse event .The same material is expanded in

Kaushitiki or Sankhyayana Brahmana. 24.4.“

Dr.S.Balakrishna

February 2008Monthly Planner


1 2Groundhog Day

3 4 5 6 7Amavasya, Magha shukla

8 9

10 11Vasant panchami

12Lincoln's Birthday

13 14Valentine's Day

15 16

17Ekadasi

18President's Day

19 20 21Purnima

22Washington's Birthday

23

24 25 26 27 28 29

Jan 2008

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30 31

Mar 2008

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30 31



Definitions (see figure)

Ecliptic - the great circle on the celestial sphere that lies in the plane of the earth's orbit (called the plane of the ecliptic). Because of the earth's yearly revolution around the sun, the sun appears to move in an annual journey through the heavens with the ecliptic as its path.

Celestial sphere or armillary imaginary sphere enveloping the earth appears to turn as the earth rotates

Celestial equatorequinox (ē´kwĬnŏks) , क्तांतीोुत्त (Kranthivruth)either of two points on the celestial sphere where the ecliptic and the celestial equator intersect.

Periodicity of the saptarishi or Great Bear constellation or the UrsaMajor equatorial coordinate system Line of DeclinationLine of right ascension

March 2008Monthly Planner


1

2 3Ekadasi

4 5 6Amavasya,Phalgunashukla

7 8

9 10 11 12 13 14 15

16 17EkadasiSt. Patrick's Day

18 19 20Vernal Equinox

21Holi

22

23Easter Sunday

24 25 26 27 28 29

30 31

Feb 2008

S M T W T F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29

Apr 2008

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30



Some more definitions

Sidereal Day

An apparent sidereal day - the time it takes for the Earth to turn 360 degrees in its rotation; more precisely, is the time it takes a typical star to make two successive upper meridian transits. This is slightly shorter than a

solar day. There are 366.2422 sidereal days in a tropical year, but 365.2422 solar days, resulting in a sidereal day of 86,164.091 seconds (or: 23 hours, 56 minutes,

4.091 seconds).The reason there is one more sidereal day than "normal" days in a year is that the Earth's orbit around the Sun offsets one sidereal day, giving observers on Earth 365 1/4 days, even though the planet itself rotated 366 1/4 times (the Earth rotates in the same direction around its axis as it does around the Sun:

seen from the northern sky, counter-clockwise).Midnight, in sidereal time, is when the First Point of Aries crosses the upper

meridian.A mean sidereal day is reckoned, not from the actual transit, but from the

transit of the mean vernal equinox (see: mean sun).

April 2008Monthly Planner


1April Fool 's Day

2Ekadasi

3 4 5

6Amavasya,Cha itra shukla, Cha ndrama na uga di

Daylight Saving Time Begins

Hindi Telugu Ne w Year (Cha itra)

7 8 9 10 11 12

13Ram Navmi

14 15 16Ekadasi

17 18 19

20Hanuman jayanti

21 22 23 24 25 26

27 28 29 30Mar 2008

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30 31

May 2008

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30 31



Comparison of The Àryabhatiya of Àryabhata and Astronomic values.

Astronomy Constants AD 2000.0 Aryabhatiya 1604 BC

Rotations per solar orbit 366.25636031 366.2563589 366.25635656

Days per solar orbit 365.25636031 365.2563589 365.25635656

Days per lunar orbit 27.32166120 27.3216638 27.32166801

Rotations per lunar orbit 27.39646289 27.39646514 27.39646936

May 2008Monthly Planner


1Ekadasi

2Ekadasi

3

4 5Amavasya,Vaisakhashukla

6 7 8 9 10

11Mother's Day

12 13 14 15Ekadasi

16 17Armed Forces Day

18 19Buddha jayanti

20 21 22 23 24

25 26Memorial Day (Observed)

27 28 29 30 31Ekadasi

Apr 2008

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30

Jun 2008

S M T W T F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30



ASTRONOMIC AUTHORITY

Àryabhata(from Clarke and Kay)

Surya Siddanta

Years in Cycle 4,320,000 4,320,000

Rotations of the earth 1,582,237,500 1,582,237,828

Days 1,577,917,500 1,577,917,828

Lunar Orbits 57,753,336 57,753,336

Kay notes 57,753,339 lunar orbits rather than 57,753,336 per Clarke.

Synodic Months 53,433,336 53,433,336

Mercury 17,937,920 17,937,060

Venus 7,022,388 7,022,376

Mars 2,296,824 2,296,832

Jupiter 364,224 364,220

Saturn 146,564 146,568

June 2008Monthly Planner


1 2 3Amavasya,Jyeshtashukla

4 5 6 7

8 9 10 11 12 13 14EkadasiFlag Day

15Father's Day

16 17 18Purnima

19 20 21Summer Solsti ce

22 23 24 25 26 27 28

29Ekadasi

30May 2008

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30 31

Jul 2008

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30 31



Dating of the Vedas

Koenrad Elst – “In a rather shoddy way, Friedrich Max Müllerlaunched the hypothesis that the Rg-Veda had to be dated to about 1200 BC, and even though he later retracted it, that arbitrary guess has become the orthodoxy”. A precursor to the habitual circular reasioning adopted by current day European indologists

Maurice Winternitz remained skeptical of his own assumptions - We cannot explain the development of the whole of this great literature if we assume as late a date as round about 1200 BC or 1500 BC as its starting-point.” 1

Hermann Jacobi

John Playfair see next slide

B G Tilak Orion Cosco Publications, reprint 1984, original 1895

S Balakrishna – Vedic Astronomy articles

www.vedicastronomy.net

July 2008Monthly Planner


1 2 3Amavasya,Asadhashukla

4Independence Day

5

6 7 8 9 10 11 12

13Ekadasi

14 15 16 17 18Guru Purnima (Veda Vyaasa)

19

20 21 22 23 24 25 26

27 28Ekadasi

29 30 31

Jun 2008

S M T W T F S

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30

Aug 2008

S M T W T F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29 30

31



ChaitraVaishakhJeshtaAshadhShrawan(Sawan)Bhadrapad(Bhado)AshwinKartikMargshirshPaushMaghaFalgoon (Fagan)

English calendar weekdays Indian calendar weekdays

SundayMondayTuesdayWednesdayThursdayFridaySaturday

RaviwarSomwar (Chandrawar)MangalwarBudhwarGuruwarShukrawarShaniwar

August 2008Monthly Planner


1Amavasya, Sravana Shukla

2

3 4 5 6 7 8 9

10 11 12Ekadasi

13 14 15 16Purnima, Raksha Bandhan

17 18 19 20 21 22 23Krishna Janmashtami

24 25 26 27Ekadasi

28 29 30Amavasya, Bhadrapada shukla

31

Jul 2008

S M T W T F S

1 2 3 4 5

6 7 8 9 10 11 12

13 14 15 16 17 18 19

20 21 22 23 24 25 26

27 28 29 30 31

Sep 2008

S M T W T F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30



Zodiac sign Sanskrit Name Sector begin Sector end

Aries Mesha 00 30

Taurus Vrishabha 30 60

Gemini Mithuna 60 90

Cancer Karka 90 120

Leo Simha 120 150

Virgo Kanya 150 180

Libra Tula 180 210

Scorpio Vrishchika 210 240

Sagittarius Dhanus 240 270

Capricorn Makara 270 300

Aquarius Kumbha 300 330

Pisces Meena 330 360

September 2008Monthly Planner


1Labor Day

2 3 4 5 6

7 8 9 10 11Ekadasi

12 13

14 15Purnima

16 17 18 19 20

21 22Autumn begins

23 24 25Ekadasi

26 27

28 29Amavasya,Aswinashukla

30Aug 2008

S M T W T F S

1 2

3 4 5 6 7 8 9

10 11 12 13 14 15 16

17 18 19 20 21 22 23

24 25 26 27 28 29 30

31

Oct 2008

S M T W T F S

1 2 3 4

5 6 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30 31



… a region of the sky, within official borders set in 1928 by the IAU. • Often recognizable by a pattern or grouping of stars. • Some patterns, like the Winter Triangle, span

several constellations.

A Constellation is

October 2008Monthly Planner


1 2 3 4

5 6 7 8 9Vijaya dasami

10 11Ekadasi

12 13Columbus Day (Observed)

14Purnima

15 16 17 18Karva chaturthi

19 20 21 22 23 24Ekadasi

25

26Daylight SavingsTime Ends

27Naraka Chaturdasi, Deepavali

28Amavasya,KartikaShukla

29Vikram New Year 2065

30 31Halloween

Sep 2008

S M T W T F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30

Nov 2008

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30


Asterisms (Sapta Rishi as an example)

• The big dipper • Actually part of Ursa Major • The Big Bear

• Or Big Raccoon?Bharateeya Jyotishya shaastra states

that each Nakshatra name corresponds to a group of stars called star mansions or Asterisms.

Image fom: http://www.physics.csbsju.edu/astro/constellations/ursa_major_l.html

The Indic Mathematical traditionThe Indic Mathematical tradition

November 2008Monthly Planner


1

2 3 4Election Day

5 6 7 8

9Ekadasi

10 11Veterans Day

12 13Purnima

14 15

16 17 18 19 20 21 22

23Ekadasi

24 25 26 27Amavasya,Margasi rsashuklaThanksgiving

28 29

30

Oct 2008

S M T W T F S

1 2 3 4

5 6 7 8 9 10 11

12 13 14 15 16 17 18

19 20 21 22 23 24 25

26 27 28 29 30 31

Dec 2008

S M T W T F S

1 2 3 4 5 6

7 8 9 10 11 12 13

14 15 16 17 18 19 20

21 22 23 24 25 26 27

28 29 30 31


Kosla Vepa

Note


Precession of the equinoxes and the pole star

December 2008Monthly Planner


1 2 3 4 5 6

7 8 9Ekadasi, Gita Jayanti

10 11 12Purnima

13

14 15 16 17 18 19 20

21Winter solstice

22Ekadasi

23 24 25Christmas

26 27Amavasya,Pausa shukla

28 29 30 31New Year 's Eve

Nov 2008

S M T W T F S

1

2 3 4 5 6 7 8

9 10 11 12 13 14 15

16 17 18 19 20 21 22

23 24 25 26 27 28 29

30

Jan 2009

S M T W T F S

1 2 3

4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25 26 27 28 29 30 31



I dedicate this research to the Goddess Sarasvati

And the river that bears her name

And the Brahmi civilization that flourished on the banks of the river for over 3000 years giving rise to the first phonetic

and syllabic scriptOm Sarveshaam Swastir Bhavatu

Sarveshaam Saantir Bhavatu

Sarveshaam Poornam Bhavatu

Sarvesham Mangalam Bhavatu

Date post:	06-Feb-2018
Category:	Documents
Upload:	lyphuc
View:	226 times
Download:	0 times

The Indic MathematicaL Tradition - · PDF fileThe Indic MathematicaL Tradition Monthly Planner...

Documents