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Welcome To NAMASTE LECTURE SERIES

Welcome To NAMASTE LECTURE SERIES. 2009. gd:]t. NAMASTE. ?. GARUD AT CHANGU NARAYAN TEMPLE. NAMASTE'S NEW NEPAL MATHS CENTRE. Presents . Something Nonmathematical and Something Mathematical. SOMETHING NONMATHEMATICAL. AND. SOMETHING MATHEMATICAL. AFTERNOON. DAY. GOOD.

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Welcome To NAMASTE LECTURE SERIES

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  1. Welcome To NAMASTE LECTURE SERIES 2009

  2. gd:]t NAMASTE ? GARUD AT CHANGU NARAYAN TEMPLE

  3. NAMASTE'S NEW NEPAL MATHS CENTRE Presents Something Nonmathematical and Something Mathematical

  4. SOMETHING NONMATHEMATICAL AND SOMETHING MATHEMATICAL

  5. AFTERNOON DAY GOOD MORNING

  6. PART ZERO

  7. NAMASTE At a Glance NAMASTE National Mathematical Sciences Team A Non-profit Service Team Dedicated to MAM Mathematics Awareness Movement Established: March 22, 2005, at the premise of NAST .

  8. COMMITTEE OF NAMASTE COORDINATORS • 1. Prof. Dr. Bhadra Man Tuladhar • Mathematician (Kathmandu University) • 2. Prof. Dr. Ganga Shrestha • Academician (Nepal Academy of Science and Technology) • 3. Prof. Dr. Hom Nath Bhattarai, • Vice Chancellor (Nepal Academy of Science and Technology) • 4. Prof. Dr. Madan Man Shrestha, • President, (Council for Mathematics Education) • 5. Prof. Dr. Mrigendra Lal Singh • President, Nepal Statistical Society • 6. Prof. Dr. Ram Man Shreshtha • Academician (Nepal Academy of Science and Technology) • Member Secretary (Namaste) • 7. Prof. Dr. Shankar Raj Pant • President (Former), Nepal Mathematical Society, Tribhuvan University • 8. Prof. Dr. Siddhi Prasad Koirala • Chairman , Higher Secondary School Board, Secondary School Board)

  9. NAMASTE's main objectives are To launch a nationwide Mathematics Awareness Movement in order to convince the public in recognizing the need for better mathematics education for all children, To initiate a campaign for the recruitment, preparation, training and retaining teachers with strong background in mathematics, To help promote the development of innovative ideas, methods and materials in the teaching, learning and research in mathematics and mathematics education, To provide a forum for free discussion on all aspects of mathematics education, To facilitate the development of consensus among diverse groups with respect to possible changes, and To work for the implementation of such changes.

  10. NAMASTEDOCUMENTS * Mathematics Awareness Movement (MAM) Advocacy Strategy (A Draft for Preliminary Discussion) * Mathematics Education for Early Childhood Development (A Discussion paper) * The Lichhavian Numerals and The Changu Narayan Inscription

  11. PART ONE

  12. W H E R ED O W EC O M EF R O M ?

  13. AGO NO MAN LONG LONG NO MATHEMATICS AND NO COUNTING

  14. LONG BEFORE MAN CAME The big bang is often explained using the image of a two dimensional universe (surface of a balloon) expanding in three dimensions THEORY OF BIG BANG The universe emerged from a tremendously dense and hot state about 13.7 billion years ago.

  15. SCIENTIFIC NOTATIONS Age of the Universe in Years :

  16. SHAPE OF THE UNIVERSE Angle sum > 180 degree Angle sum < 180 degree, Angle sum = 180 degree,

  17. Closed surface like a sphere, positive curvature, Finite in size but without a boundary, expanding like a balloon, parallel lines eventually convergent Saddle-shaped surface, negative curvature, infinite and unbounded, can expand forever, parallel lines eventually divergent Flat surface, zero curvature, infinite and no boundaries, can expand and contract, parallel lines always parallel

  18. ARE WE ALONE IN THE UNIVERSE? GENERAL BELIEF : NO Finite non-expanding universe ? With about 200 billion stars in our own Milky Way galaxy and some 50 billion other similar galaxies in the universe, it's hardly likely that our 'Sun' star is the only star that supports an Earth-like planet on which an intelligent life form has evolved.

  19. WE COME FROM MILKY WAY Our Galaxy 200000000000 STARS Age 13,600 ± 800 million years Hundreds of Thousands of Stars

  20. B L A C K H O L E

  21. T H E S O L A R S Y S T E M SunMercury Venus Ea rthMars Jupiter Saturn Uranus Neptune Pluto (?) Distance between the Earth and the Sun 149598000 km Age 4.560 millionyears

  22. SOLAR SYSTEM Distance between the Earth and the Sun 149598000 km Born 4,560 million years ago

  23. SOLAR SYSTEM Rotation and Revolution of the Earth

  24. Born 4.5 billion years ago Rotating Earth EARTH

  25. TECHTONIC MOVEMENT LAURASIA GONDAWANALAND

  26. TECHTONIC MOVEMENT OR CONTINENTS FORMATION

  27. THE WORLD

  28. ANCIENT CIVILIZATIONS

  29. WORLD CIVILIZATIONS

  30. INDUS CIVILIZATION NEPAL

  31. Nepal The land where a well developed number system existed as early as the beginning of the first millennium CE. WE COME FROM 107 AD NEPAL Maligaon Inscription

  32. PART TWO

  33. What Do We Know About Our Ancient Numbers ? ?

  34. BRAMHI SCRIPTINASHOKA STAMBHA INSCRIPTION (249 BCE)LUMBINI, NEPAL THE BEST KNOWN AND THE EARLIEST OF THE KIND

  35. Number Words In The Brahmi Script InscriptionOfAshoka Stambha (249 BCE),Lumbini Brahmi Script Devanagari Script jL; c7-efluo]_ No Numerals read as read as

  36. Brahmi Numerals The best known Brahmi numerals used around 1st Century CE.

  37. Some Numerals In Some Other Ancient Inscriptions First Phase : Numerals for 4, 6, 50 and 200 No numeral for 5 but for 50 Second Phase : Numerals for 1, 2, 4, 6, 7, 9, 10, 20, 80, 100, 200, 300, 400, 700; 1,000; 4,000; 6,000; 10,000; 20,000. No Numeral for 3 but for 300 Third Phase: Numerals for 3, 5, 8, 40, 70, …, 70,000.

  38. Hypotheses About The Origin of Brahmi Numerals • The Brahmi numerals came from the Indus valley culture of around 2000 BC. • The Brahmi numerals came from Aramaean numerals. • The Brahmi numerals came from the Karoshthi alphabet. • The Brahmi numerals came from the Brahmi alphabet. • The Brahmi numerals came from an earlier alphabetic numeral system, possibly due to Panini. • The Brahmi numerals came from Egypt.

  39. Something MoreAbout Brahmi Numerals • The symbols for numerals from the Central Asia region of the Arabian Empire are virtually identical to those in Brahmi. • Brahmi is also known as Asoka, the script in which the famous Asokan edicts were incised in the second century BC. • The Brahmi script is the progenitor of all or most of the scripts of India, as well as most scripts of Southeast Asia. • The Brahmi numeral system is the ancestor of the Hindu-Arabic numerals, which are now used world-wide.

  40. EPIGRAPHY VERSUS VEDIC MATHEMATICS • Total lack of Brahmi and Kharoshthi inscriptions of the time before 500 BCE • Much of the mathematics contained within the Vedas is said to be contained in works called Vedangas. • Vedic Period : Time before 8000 /1900/ BCE etc. Vedangas period: 1900 – 1000 BCE. • Sulvasutras Period : 800 - 200 BCE. • Origin of Brahmi script : Around 3rd century BCE • No knowledge of existence of any written script during the Ved- Vedangas period. • Numerical calculation based on numerals(?) during the so-called early Vedic period highly unlikely.

  41. Numerals in Ancient Nepal MALIGAON INSCRIPTION Read as “sam*vat a7 gri- pa 7 d(i)va pka maha-ra-jasya jaya varm(m)a(n*ah*)” and translated by Kashinath Tamot and Ian Alsop: “(In) the (Shaka) year 107 (AD 185), (on) the 4th (lunar) day of the 7th fortnight of the summer (season), of the great King Jaya Varman

  42. WHY DO WE FOCUS ON THE NUMBERS ? in the Maligaon inscription in the Changu Narayan inscription • Earliest of the available number-symbols. • Concrete evidences of the knowledge of the concept of number and the existence of numerals and a well-developed number system in Nepal at a time (around 2nd century CE) when a civilization like Greek civilization worked with very primitive or alphabetic numerals • Beginning of the recorded history of ancient Nepal

  43. Lichhavian Number 1 to 99

  44. Lichhavian NumbersandMajor Number Systems

  45. Table I(A) Table I(B)

  46. Something About Lichhavian Number System • Lichhavian numerals for 1, 2 and 3 consist of vertically placed 1, 2 and 3 horizontal strokes like the Chinese 14th century BCE numerals, Brahmi numerals of the 1st century CE and Tocharian numerals of the 5th century CE. • The Lichhavian numerals for 1, 2, 3, 40, 80 and 90 look somewhat similar to the corresponding Brahmi numerals. • There is a striking resemblance between the Lichhavian and Tocharian numerals for, 1, 2, 3, 20, 30, 80 and 90; just like many Tocharian albhabet. • Several other Tocharian numbers appear to be some kind of variants of the Lichhavian numbers. • Each of the three systems uses separate symbols for the numbers, 1, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 1000, … .

  47. Something About Lichhavian Number System • Compound numbers like 11, 12, …, 21, 22, …, 91, 92, … are represented by juxtaposing unit symbols without ligature. • Hundred symbol is represented by different symbols and is often used with and without ligature . • Non-uniformity in the process of forming hundreds using hundred symbol and other unit symbols. • Several variants of numerals are found during a period of several centuries.

  48. Something About Lichhavian Number System • Each of the three systems uses separate symbols for the numbers, 1, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 1000, … • Compound numbers like 11, 12, …, 21, 22, …, 91, 92, … are represented by juxtaposing unit symbols without ligature. • Hundred symbol is represented by different symbols and is often used with and without ligature . • Non-uniformity in the process of forming hundreds using hundred symbol and other unit symbols. • Several variants of numerals are found during a period of several centuries. • Available Lichhavian numbers are lesser than 1000. • No reported number lies between 100 and 109, 201 and 209, …, 900 and 909. Numbers for 101, 102, …, 109, 201, 202, …, 209, …, 901, 902, …, 909 are missing .

  49. Something About Lichhavian Number System • Arithmetic of Lichhavian is not known • Formation of two and three indicate vertical addition, while formation of 11, 12, …, indicate horizontal addition in the expanded form – a kind of horizontal addition. • Lichhavian system is additive • Lichhavian system is a decimal system. • Liichhavian system is multiplicative: numeral for 4 attached to symbol for 100 by a ligature stands for 400 to be read as 4 times 1 hundred numeral for 5 attached to symbol for 100 by a ligature stands for 500 to be read as 5 times 1 hundred numeral for 6 attached to symbol for 100 by a ligature stands for 600 to be read as 6 times 1 hundred, Existence of some kind of arithmetic in Tocharian number system may provide some clue in this direction.

  50. Something About Lichhavian Number System • Lichhavian numbers like 462 is to be read as 4 times hundred or 4 hundreds and 1 sixty and 2 ones or, 4(100) 1(60) 2(1) = 4100 + 1  60 + 2  1 and 469 is to be read as 4 times hundred or 4 hundreds and 1 sixty and 1 nine or, 4(100) 1(60) 1(9) = 4100 + 1  60 + 1  9.

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