Aaryabhata was a famous Indian mathematician and astronomer born in 476 CE in India. He wrote two important texts - the Aaryabhatiya and Aaryabhatiya Siddhanta. In his works, he calculated pi accurately, introduced the concept of zero, proposed that the earth rotates on its axis daily, and that the apparent movement of planets is due to the rotation of earth. He made many contributions to mathematics including arithmetic progressions, square and cube roots, and trigonometric functions like sines and verses. Aaryabhata is considered one of the great scientists of ancient India.

1. AARYABHATA
A LOOK AT HIS LIFE & WORK
BASED ON HIS TREATISES
BY: ARYANPREET SINGH
CLASS: 8-I

3. LIFE IN A SHORT
 BORN IN 476 CE
 HOMETOWN BELONGS TO A VILLAGE IN
ASHMAKADESH
 LEARNING STARTED AND ENDED AT KUSUMPURA
 WROTE AARYABHATIYAM IN 499 CE AT THE AGE OF 23
 DIED APPROX IN 550 CE( ACCORDING TO D.E.SMITH)
 ENJOYED THE LIFE ON MOTHER EARTH FOR APPROX
74 YEARS
 MANY PEOPLES USES OR WRITES/CALLS HIS
NAME AS AARYABHATTA WHICH IS NOT RIGHT.
HE HIMSELF MENTIONED HIS NAME AS
AARYABHATA IN GITIKAPAAD 1,GANITAPAAD
1,GOLAPAAD 50.

4. CONTINUE…..
 AARYABHATA WAS KNOWN TO ARABS BY NAME ARJABHARD
WHICH WAS LATER LATINIZED AS ARDUBARIUS. THE
MEANING OF BHATA=BRAVE OR SOLDGIER, AND OF
BHATTA=SCHOLAR/PHILOSOPHER/ AS SUFFIX TO A NAME OF
ANY BRAHMIN
 DISCIPLES: PANDURANGSWAMI, LAATDEO, NISHANKU
(ACCORDING TO BHASKARACHARYA-1). LAATDEO
REEXAMINED FAMOUS AND MOST ANCIENT TREATISE
SURYASIDDHANTA, MADE SOME CHANGES AND REVISED IT.
HE ALSO WROTE THE COMMENTARIES ON PAULISHA &
ROMAKA SIDDHANTA
 FOR ALL HIS CALCULATION HE CONSIDERED UJJAIN
(AVANTIKA) AS PRIME MERIDIAN,WHICH WAS ALSO MAIN
MERIDIAN IN ASTRONOMY.

5. HOW WE GOT HIS BIRTH
YEAR & LOCATION
 IN KAALKRIYAPAAD HE SAYS “ SHASHTYABDAANAAM
SHASHTIRYADAA VYATEETAAH TRAYASHCHA YUGPAADAAH
TRYADHIKAA VIMSHATIABDAAH MAM JANMANAA ATEETAAH”.
 MEANING “ WHEN 60*60 YEARS OF KALIYUGA HAD ELAPSED ALSO
THREE PREVIOUS YUGA(KRITA,TRETA,DWAPAR) ,AT THAT TIME 23
YEARS OF MY LIFE WERE ELAPSED.”
 3600 ELAPSED YEARS OF KALIYUGA CORRESPONDS TO
499CE=SHAKE 421
 AARYABHATA HIMSELF TOLD THAT “I AM QUOTING THE KNOWLEDGE
WHICH I HAVE GAINED AT KUSUMAPURA”. KUSUMAPURA WAS
IDENTIFIED AS PATALIPUTRA OR PATANA FROM THE COMMENTARY
OF BHASKARACHARYA 1 ON AARYABHATIYAM
 THIS CITY ‘S COORDINATES ARE 21.6166 N & 8502166 E
 ASHMAKADESHA SEEMS TO BE A DESHA SITUATED IN NW PART OF
OUR COUNTRY ACCORDING TO RAMAYANA & MAHABHARATA.
 SOME REAMARKS THAT ASHMAKADESHA IS IN KERALA.

6. COMMENTATORS &
MENTIONERS
 PRABHAKAR- 525 CE
 BHASKARACHARYA 1- 629 CE
 SOMESHWARA- BETWEEN 968-1200 CE
 SURYADEVA YAJJVAN- 1191 CE
 NILAKANTHA SOMAYAJI- 1502 CE
 DAMODARA- 1400 CE
 ABU RAYHAN MOHAMMED IBN AL-BERUNI WROTE
TAHQIQ-M L’IL HIND ( ALBEUNI’S INDIA) & MENTIONED
AARYABHATA MANY TIMES. ALSO MENTIONED THAT AL-
FAZARI & YAQUB IN ARABIC TRANSLATED THIS TREATISE

7. AARYABHATA’S TREATISES
 AARYABHATIYA IS FIRST TREATISE
 AARYABHATIYA SIDDHANT IS SECOND,NOT EXTANT.
VARAHAMIHIRA, BRAHMAGUPTA, GOWINDSWAMI,
BHASKARACHARYA 1 MENTIONED ABOUT THIS TEXT .
THIS TEXTS SEEMS TO BE RELATED TO
SURYASIDDHANTA. IT WAS BEING USED AS A
TEXTBOOK ALL OVER THE COUNTRY. ACCORDING TO
RESEARCHERS BRAHMAGUPTA TOOK THIS TREATISE
AS A BASIS FOR HIS “KHANDA KHADYAKA”.
 DIFFERENCES; AARYABHATIYA CONSIDERS DAY AS A
INTERVAL BETWEEN TWO SUCCESSIVE SUNRISE.
WHEREAS AARYABHATIYA SIDDHANTA CONSIDERS A
DAY AS AN INTERVAL BETWEEN TWO SUCCESSIVE
MIDNIGHTS

8. OTHER MENTIONS
 DR EDWIN THIBAUT
 G R KAYE IN HIS “HINDU ASTRONOMY” CALLS HIM AS
PROPOGATOR OF NEW SCHOOL OR ERA
 NATURE MAGAZINE ARTICLE ON 20/27 DEC 2001 AS
“SCIENCE IN TURSE-VERSE” ABOUT HIS SINE
FUNCTIONS AND TABLES. AARYABHATA HAS
EXPLAINED HOW TO FORM SUCH TABLES IN SINGLE
VERSE

9. CHARACTERISTICS OF
AARYABHATIYA
 NEW PRESENTATION SYSTEM OR CONVERSION OF WORDS INTO
NUMBERS OR VICE-VERSA
 VALUE OF PI
 RADIAN MEASURMENTS- WHERE HE CONSIDERED DIAMETER OF
CIRCLE AS 3438 MIN AND USED THAT CIRCLE TO FIND JYA (SINE)
 AHARGANA SYSTEM LIKE JULIAN DAY NUMBERS
 YUGAPADDHATI: HE CONSIDERED YUGA=43,20,000 YEARS= ONE
MAHAYUGA AND DIVIDED IT INTO EQUAL PERIOD OF 10,80,000 YEARS
FOR EACH YUGA I.E KRITA ,TRETA, DWAPAR, KALI
 CONSIDERED THAT “ AT KALIYUGA BEGINNING ALL PLANETS CAME INTO
A STRAIGHT LINE”
 SPHERICAL SHAPE OF EARTH. USED THE WORD
ROTATION=BHUBHRAMA
 HOW TO MAKE GOLYANTRA, NOT EXTENSIVELY BY HIM BUT BY
BHASKARACHARYA IN HIS COMMENTARY
 SINE TABLE
 INDETERMINATE EQUATION OF FIRST ORDER (KUTTAKA
GANITAM=PULVERIZER)
 ACCURATE ASTRONOMICAL CONSTANTS

10. TIME AND DISTANCE RECKONING
 1 BRAHMA DAY=14 MANVANTAR, 1 MANVANTAR=72 YUGAS.
UPTO MAHABHARATA WAR END ON THURSDAY 6 MANU,27
YUGAS,3 YUGPAAD HAD ELAPSED(1.5)
 1 BHAGAN=12 SIGNS;1 SIGN=30 DEGREE,1 DEGREE=60
KALAA=60 ARC MIN;1 KALAA=60 VIKALAA=60 ARC SEC, 1
VIKALAA=60 TATPAR; 1 DAY=60 NAADI=60 GHATIKA=24 HRS, 1
NADI=60 VINADIKA=24 SEC, 1 VINADIKA=24 SEC=6 BREATHS. 1
YEAR=12 MONTHS, 1 MONTH=30 DAYS (3.1,3.2)
 1 SOLAR YR=1 HUMAN YR. 1 HUMAN YR*30= 1 PITRUVARSHA, 1
PITRUVARSHA*12= 1GOD YEAR. 1200 GOD YR=1 NORMAL
GRAHAYUGA, 1008 SUCH MAKES 1 DAY OF BRAHMA(3.7 & 8)

11. DASHAGITIKA
 1. 1: PRAANIPATYAIKMANEKAM KAM SATYAAM DEVTAAM
PARAM AARYABHATASTRINI GADATI GANITAM KAALKRIYAAM
GOLAM
 1. 2: vargAkshrANi varge avarge avargAkshrANi kAt mau YaH
khadvinavake swarA nav varge avarge navAntyavarge Va
 1. 3: IN ONE MAHAYUGA SUN REVOLUTION ARE 43,20,000; OF
MOON 57,753,336;EARTH 1,582,237,500;SATURN 146,564;JUPITER
364,224;MARS 2,296,824; OF MERCURY & VENUS ARE SAME AS
SUN
 1. 4: LISTS PERIGEE & APOGEE MOON,DISCUSSES RAHU &
KETU; CALCULATION OF REVOLUTION PERIOD OF 5 VISIBLE
PLANETS

12. DASHAGITIKA……..
 1.6: ORBIT CIRCUMFERENCE OF 5 PLANETS & SUN ; 1.7:
DIAMETERS OF PLANETS,SUN,MOON
 1. 8: DEALS WITH ANGLES WHICH PLANETS AND MOON MAKES
WITH ECLIPTIC. A TABLE IS THERE AT THE END TO
UNDERSTAND THIS
 1.12: CALCULATION OF SINE VALUES
1.13: MERITS OF STUDYING DASHAGITIKA

13. GANITAPAAD
 2.2: PLACE VALUES; 2.3: SQAURE & CUBE ;
2.4:SQAURE; &2. 5: CUBE ROOT; 2.6: AREA OF
TRIANGLE ;2. 7: AREA OF CIRCLE
 2.10: BY MULTIPLYING 8 TO 104 AND ADDING IT IS
62000, AND BY DIVIDING BY 20000 WE GET VALUE OF
PI
 2.11: SINE CALCULATION WITH HELP OF GEOMETRY;
2.12 THEIR DIFFERENCE; 2.13 CIRCLE DRAWING
 2.19: ARITHEMATIC PROGRESSION :- AVERAGE OF ALL
DIGITS=a+(n-1)/2*d SUM OF ALL DIGITS=a+(n-1/2*d)*n or
sum=(first+last)*n/2

14. GANITAPAAD………
 2.23: SUBSTRACT ADDITION OF SQAURES OF 2 DIGITS
AND SQAURE OF THE ADDITION OF 2 NUMBERS,DIVIDE
IT BY 2, WE GET MULTIPLICATION OF 2 DIGITS
 2.25: INTEREST,CAPITAL
 2.31: DIVIDE THE DISTANCE BETWEEN 2 BODIES BY
ADDITION OF THEIR VELOCITIES;FOR THE BODIES
ACCELERATED IN ONE DIRECTION DIVIDE DISTANCE
BETWEEN THEM BY SUBSTRACTION VELOCITIES OF
BOTH, TWO ANSWERS THAT WE GET GIVES THE
PERIOD AFTER COMING AT A POINT OR THE TIME IN
WHICH THEY WILL COME AT ON POINT

15. KAALKRIYAAPAAD
 3.3: CONJUNCTION OF PLANETS
 3. 4: ANOMALISTIC MONTH, 3.5: SOLAR AND LUNAR
MONTHS,3.6: INTERCALARY MONTH & KSHAYA TITHI
 3.9: FIRST HALF IS CALLED UTSARPINI,LATTER HALF IS
AVSARPINI. MIDDLE OF YUGA IS SUSHMA,END IS DUSHMA
 3.12; VELOCITY OF PLANETS; 3.13&14: ORBITAL
CIRCUMFERENCE & DAILY MOTION, 3.15: ORDER OF EACH
ORBIT

16. GOLPAAD
 4.4: DEALS WITH HELIACAL RISE AND SETTING OF
PLANETS. FOR
MOON(48),VENUS(36),JUPITER(52),SATURN(60),MARS(68
) MINUTES EACH IS TIME DIFFERENCE RISE AND SET
OF EACH PLANET WITH RESPECT TO SUN
 4.9; A MAN SEATING IN BOAT EXPERIENCES THAT STILL
THINGS ON THE BANK ARE RECEDDING,LIKE THIS FOR
ANY MAN STANDING IN LANKA HE IS ABLE TO SEE
MOVEMENT OF STARS,NAKSHATRA,PLANETS FROM
EAST TO WEST
 4.13: WHEN THERE IS SUNRISE IN LANKA,SUNSET IS IN
SIDDHAPURA,MID NOON IN YAVAKOTI,AND MIDNIGHT IN
ROMAKA ; 4.14: POSITION OF UJJAIN & LANKA

17. CONTINUE……..
 4.17: ON NORTH POLE WHEN SUN RISES IT SHINES FOR
6 MONTHS,GOD ARE ABLE TO SEE IT,SIMILAR IS FOR
RAKSHAS IN SOUTH POLE. PITAR LIVING ON MOON
SEES SUN FOR 15 DAYS AND PEOPLES LIVING ON
EARTH SEES SUN FOR 12 HRS
 4.18: DEFINITION OF PRIME VERTICAL,MERIDIAN &
HORIZON
 4.19: CIRCLE INTERSECTING EAST AND WEST POINT
AND INCLINED TO LINE FROM NORTH TO SOUTH AT
LATITUDE OF OBSERVER IS CALLED UNMANDALA ( SIX
O’CLOCK CIRCLE)

18. CONTINUE……..
 4.20 : DEFINITION OF ZENITH & NADIR
 4. 21: A CIRCLE PASSING THROUGH
ZENITH,PLANET POSITION,NADIR IS
DRIKMANDALA; A CIRCLE PASSING THROUGH
ZENITH,A POINT AT DISTANCE MORE THAN 3
SIGNS FROM EAST HORIZIN(LAGNA) & NADIR
IS CALLED DRIKSHEPAMANDALA
 4.22: GOLYANTRA(ARMILLARY SPHERE)
 4.37: MOON IS WATERY,SUN IS FULL OF
FIRE,EARTH IS FILLED WITH MUD &
CLAY,SHADOW IS BLACK. MOON COVERS UP
THE SUN AND EARTHS LONG SHADOW
ECLIPSES MOON.

19. CONTINUE……
 4.39 & 40 : MULTIPLY SUN-EARTH DISTANCE BY EARTHS
DIAMETER,DIVIDE IT BY DIIFERENCE OF SIN & EART’S
DIAMETER, WE GET LENGTH OF EARTH’S SHADOW
FROM ITS CENTER. MULTIPLY THE DISTANCE BETWEEN
EARTHS SHADOW TIP & MOON BY EARTH’S DIAMETER,
DIVIDE IT BY EARTH SHADOW LENGTH, WE GET
DIAMETER OF EARTH’S SHADOW AT MOON’S
DISTANCE.
 4. 46: AT BEGINNING & END OF ECLIPSE LUNAR DISC IS
BLACKISH. AT PARTIAL DISC IS BLACK. AT TOTALITY IT
LOOKS COPPERY

20. CONTINUE………
 4.49: BY THE GRACE OF LORD BRAHMA, I UNEARTHED
THIS TRUE KNOWLEDGE( A GEM) WITH THE HELP OF
MY INTELLECT FROM DEPTH OF TIME
 4.50 UPSAMHAAR : THOSE WHO DENIGRATE,DEMEAN
THIS KNOWLEDGE HIS GOOD DEEDS & LIFE WILL
PERISH.

21. MENTIONS
 DAVID DUNCAN IN HIS “ THE CALENDAR” SAYS : IN 476,FAR AWAY IN
TIME AND PLACE FROM CHARLEMAGNES DARK,IMPOSING CASTLE AT
AACHEN,BEYOND EATERN BORDER OF FRANKLAND AND ON ACROSS
THE BALKANS,THE TERRITORIES O FBYZANTIUM,AND THE VASTNESS
OF MESOPOTEMIA AND PERSIA ,A HINDU GENIUS WAS BORN ON THE
RIVER GANGES, A BLEND OF PTOLEMY THE
ASTRONOMER,PYTHAGORAS THE MATHEMATICIAN AND BACON THE
REBEL. AARYABHATA WAS ONE OF A REMARKABLE GROUP OF INDIAN
SCHOLARS, AND A PIVOTAL FIGURE ON ONE OF THE STRANGER
JOURNEYS EVER TAKEN BY AN ASSEMBLAGE OF IDEAS ACROSS
TIME AND GEOGRAPHY. THE ARYABHATIYA IS A SLIM
VOLUMEWRITTEN IN SANSKRIT VERSE, AND WHILE ONLY 123
METRICAL STANZAS LONG,IT PACKS AN ENORMOUS AMOUNT OF
INFORMATION IN WHAT BECAME A HANDY VOLUME OF
MATHEMATICAL AND ASTRONOMICAL CONCEPTS PASSED DOWN AND
COMMENTED ON OVER THE CENTURIES. SOME OF ITS HIGHLY
ACCURATE,SOME NOT. ONE SENSES THAT THE ARYABHATIYA WAS
INTENDED AS MORE OF A SUPPLEMENT OR SUMMARY FOR PEOPLE
ALREADY FAMILIAR WITH THE CONCEPTS THAN A COMPREHENSIVE
ENCYCLOPEDDIA ON THEORY OF MATHEMATICS.”

22. COMPARISON TABLES
SR
NO
CELESTIA
L BODY
REVOLUTIONS IN
MAHAYUGA
AARYABHA
TA(IN
DAYS)
MODERN(IN
DAYS)
1 SUN 43,20,000 365.25868 365025636
2 MOON 5,77 ,53,336 27.32167 27.32166
3 MOON
APOGEE
4,88,219 3231.98708 3232.37543
4 ASC NODE 2,32,226 6794.74951 6793.39108
5 MERCURY 1,79,37,020 87.96988 87.9693
6 VENUS 70,22,388 224.69814 224.7008
7 MARS 22,96,824 686.99974 686.9797
8 JUPITER 3,64,224 4332.27217 4332.5887
9 SATURN 1,46,564 10766.06465 10759.201

23. NO.2
S
R
CELESTIAL
BODIES
AARYABHATI
YA DIAMETER
CONVERTED MODERN
1 EARTH 1050 12,600 12,800
2 SUN 4410 52,900 13,92,000
3 MOON 315 3780 3500

24. NO.3
SR
NO
CELESTIAL
BODY
ORBIT INCLINATION
TO ECLIPTIC(AS
PER TEXTS)
MODERN
1 MOON 4.5 4.95-5.33
2 MARS 1.5 1.84983
3 MERCURY 2 7.00427
4 JUPITER 1 1.30450
5 VENUS 2 3.39438
6 SATURN 2 2.48933

25. NO.4
DEG
REE
MINUTES BHUJAJYA
A
DIFFERENC
E
BHUJAJYA
A
BHUJAJY
AA/3438
MODER
N VALUE
3.75 225 225 225 0.0654 0.0654
15 900 219 890 0.2589 0.2588
30 1800 199 1719 0.5 0.5
45 2700 164 2431 0.7071 0.7071
60 3600 119 2978 0.8662 0.8660
75 4500 65 3321 0.9660 0.9659
90 5400 7 3438 1 1

26. NO.5
SR
NO
CELESTIAL
BODY
MODERN
PERIOD
AARYABHATIY
A
YUTIKAAL(DAY
S)
MODERN
VALUE
1 MARS 1.88089 779.92102 779.89546
2 MERCURY 0.24085 115.87833 115.9773
3 JUPITER 11.86 398.8895 398.889586
4 VENUS 0.61521 583.89746 583.979287
5 SUN-MOON 29.530582 29.53
6 SATURN 29.46 378.08595 378.090426

27. NO.6
SR
NO
CELESTIAL
BODY
AVG DAILY
MOTION(FROM
TEXT)
MODERN VALUE
1 MOON 13.176333 13.178029
2 MERCURY 4.092029 4.0953717
3 VENUS 1.6019858 1.6013164
4 SUN 0.9856377 0.9861002
5 MARS 0.524014 0.5234908
6 JUPITER 0.0830973 0.0833221
7 SATURN 0.0334383 0.03330

28. NO.7 FROM A SITE1
PERIOD ROTATIONS
PER SOLAR
ORBIT
DAYS PER
SOLAR ORBIT
ROTATION
PER MOON
ORBIT
DAYS PER
MOON
ORBIT
2000 CE 366.25636031 365.25636031 27.32166120 27.39646289
500 CE 366.2563589 365.2563589 27.3216638 27.39646514
1604
BCE
366.25635656 365.25635656 27.32166801 27.39646936

29. NO.8 FROM SAME SITE
PERIOD ONE NAKSHATRA
MONTH OF MOON
ONE LUNAR MONTH
2000 CE 27.32166156 29.53058888
498 CE 27.3216638 29.530591
AARYABH
ATA
27.321668 29.530582
PAULISHA 27.321673 29.530587
1604 BCE 27.321668 29.530595

30. HONOURED BY WORLD…
 BHARAT LAUNCHED ITS FIRST SATELLITE AARYABHATA, MADE BY ISRO,
WITH THE HELP OF SOVIET UNION ON 19/4/1975 USING COSMOS-3M
LAUNCH VEHICLE FROM KAPUTSIN YAR
 RSA CONFERENCE OF 2006 CHOSE THEIR THEME TO BE “ ANCIENT VEDIC
MATHEMATICS AND AARYABHATA

31. REFERENCES…
 AARYABHATA THE ELDER (AARYABHATA 1)- ARUN KUMAR
UPADHYAY
 BHARATIYA VIGYAN KE MAHAN UNNAYAK “AARYABHATA”- DR
PARAMESHWAR JHA, PUB: MANDAVI
PRAKASHAN,SUPAUL,BIHAR (1999)
 BHARATIYA KHAGOLSHASTRACHA ADYAGRANTHA
“ARYABHATIYA”- MOHAN APTE,;RAJHANS PRAKASHAN,
PUNE(2009)

32. EXPRESSIONS
DHANYAWAAD!!!!!!
THANK YOU VERY MUCH!!!!
MIKAVUM NANDRI!!!
GRAZIE MILLE!!!
SHUBHAM BHAVATU!!!