Historical Development of Mathematics in Nepal

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Concrete evidences justifying Nepal's claim for rightful place and status in the History of Historical Development of Mathematics in Nepal

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National Workshop on The Historical Development of Mathematics:

National Workshop on The Historical Development of Mathematics July14-15, 2017( Ashad 30-31, 2074 ) Nova International College, Min Bhawan, Kathmandu Organized by Nepal Mathematics Centre

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Historical Development of Mathematics in Nepal Dr. E. R. Acharya, Dr. N. Subedi

Outline:

Outline Mathematics in Nepal Mathematics in Nepal Ancient Medieval Modern 3 rd century BC to 10 th century AD 10 th century AD to 2017 Prehistoric to 3 rd century BC

Slide4:

Arithmetic -Numeration System - Number System -Numeral System -Arithmetic Operations -Measurement System Mathematicians and their contributions. Ethno mathematics-Mathematics that practices on the basis of culturally in different cast, different language, different regions, etc. Geometry and Astronomy point line circle rectangle Astronomy Mathematics Practices in Nepal

Time lime for mathematics practices in Nepal:

Time lime for mathematics practices in Nepal The time line differs region to region, culture to culture, and civilization to civilizations. Prehistoric/Antiquity: Origin to 3 rd century BC Ancient Period: 3 rd Century BC to 10 th century AD Medieval period: 10 th century AD to 17 th century AD Modern period: 18 th century AD and onward. Note: (Purposed by E.R Acharya in his paper History and Recent Trends of Mathematics in (NCHRTM-2017, Nepal Sanskrit University). It is purposed on the basis of International practices of time line of mathematics developments as: Ancient period: 3600BC-500AD Post classical Era: 500 AD-1500AD Modern Era: 1500 AD-Present: Early modern period:1500-1750 Mid modern period:1750- 1914 Contemporary period: 1914-2016 and onward.

Slide6:

In the Yajureveda Saṁbitấ ( Vảjasaneyṥ ) the following list of numeral denominations is given: Eka(1), daṡa (10), sata (100), sahasra (1000), ayuta (10,000), niyuta (100,000), Prayuta (1,000,000), arbuda (10,000,000), nyarbuda (100,000,000), samudra (1,000,000,000),Madhya(10,000,000,000),anta(100,000,000,000), Parấrdha (1,000,000,000,000) Prehistoric Numeration System of Nepal

Rock Arts in Himalayan Region of Nepal:

Rock Arts in Himalayan Region of Nepal

Slide9:

Odf d]˜cUg˜Oi6sf w] gjM ; GTj ] sf r bz r bz r ztd \ r ;x;|d rfo't + r lgo'td \ r lgo'td \r k|o'td \ rfaÍ { bd \ r Goa'{b+ r ; d'›ZrM dWo + rfGtZr k/ fw { Zr } tf d] cUg ˜ Oi6sfw] gjM ; GTjd'qfd'lidnf ]s] . - oh'j ]{b !&M@_ In Mahabharat Aadi Parwa : ci6f} nf ] s;x ;|fl0f ci6f} Znf ] sztflg . cx+ j]b\ld z'sf ] ;~ hof ] j] lQ jf g jf .. From Sabha Parwa : co't + k|o't + r}j zª\s' k2d tyfa '{ bd \. va { zªv lgva { r dxfkb \d r sf]6o..$..

Lexical Numeral System in Nepal 3rd century BC :

Lexical Numeral System in Nepal 3 rd century BC Asoka inscription with lexical numeral of Brahmi script from Lumbini

Slide11:

! b] jfglko ]g lkobl;g nflhg jL;lt–j;flel;t ]g @ ctg cfufr dxLlot ] lxb a'w ] hft ] ;So– d'gL lt # l;nf–lju8–eLrf sfnflkt l;nf –ye] r p;kflkt ] $ lxb euj + hft ] lt n'+ldlg–ufd ] palns ] s6] % c7–efluo] r ( Sircar , 1942: 70) Source: Rajvansi , Shyam Sundar (2067 BS).

Slide12:

! b] jfg+lko ]g lkobl;g nflhg rf ]b;– j;f [ lel;t ]g ] @ a'w ; sf ] gfsdg ; y'j ] b'lto + al9t] # [ jL;lt –j ] ; flel;t ]g r ctg cfufr dxf ]lot] $ [ l;nf –ye ][ r ][ p; -] kflkt ] ( Sircar , 1942: 71) Source: Regmi,D.C ., 2060 BS

Three Number Words in 3rd Century BC:

Three Number Words in 3 rd Century BC These three lexical numerals are as follows: c7 efluo ] = 1/8 rf ]b; Ö 14 jL;lt Ö 20

Slide14:

Prehistoric Geometry of Nepal

Prehistoric stone weapons found in mustang:

Prehistoric stone weapons found in mustang

Continued,….:

Continued,….

Jhong Kiore Cave :

Jhong Kiore Cave

Slide18:

Ancient Time period:3 rd Century BC to 10 th century AD. Lichhavi period: 576-880 AD.

Slide19:

Numerical Notation (185 AD) ;+ jt !)& > Lk /db]j [ f‹] ] dxf / fh [ :o ] hoj [ Dd0f{M ] ( Regmi , 2060) Jaya Varma Inscription at Mali Guan, Kathmandu ,

Numerical Notation in Lichhavi Era:

Numerical Notation in Lichhavi Era = 100 = 7

Numerical Notation at Changu Narayan:

Numerical Notation at Changu Narayan

Slide22:

In Lichhavi inscriptions, various symbols were used as numerals to record the works. The number 386 is denotes by the following symbols at Changu Narayan Temple at Bhaktapur . In notation system there were one ligature for 100 , two ligatures for 200 and three ligatures for 300. The hexagonal and octagonal constructions of bricks are found in the compound of the Changu Narayan Temple. Brahmi and Lichhavi numerals were developed in 3 rd century BCE which is considered as the number concept and development of numeration system in Nepal. The notation of different numbers are illustrated as below.

Lichhavi Numerals:

Lichhavi Numerals

Slide35:

In practice in ancient period (Lichhavi) people were used different word for measurement system like Manika to denote the quantity of paddy land that covered by the seed of one Manika . In practice the in Tharu community one mani means four pathi (One tin) Mana, Pathi . Similarly in Lichhavi period they used Kharika for the quantity of paddy land having one Muri seed to be used. Drandika means the paddy land which used to be one drona seed of rice. The Sanskrit words rTfl /+ zT~r ]x oq wfg:o dflgsfM jif ]{ jif ]{o If] qGtGtfb [ zGbxf } indicates the land measurement system. The word 1 li= 1/3 miles . 25/11 miles = 1 kosha . These examples indicate the Nepalese own measurement systems.

Slide36:

Bricks have been in use in Kathmandu valley since very ancient times. The Handiguan Satyanarayan Archeological Site, explored by Italian archeologists in 1984-88, has exposed use of bricks in foundation, wall and paving constructions ranging from 1 st century BC to 10th century AD. Both the dates have been established by Radiocarbon dating of trapped carbon and thus are ‘proven’ (Verardi, 1988: p. 181 ). The other ‘proof’ that architecture in brick and timber was standard for religious buildings is provided by the record of reconstruction of Matin Devakula issued by Mahasamanta Amshuverma in year 610 AD. In that inscription, we find use of the term Istaka for brick and the information that construction of brick wall was done in regular courses, or was ‘ P anktita ’. The Bricks of Amshuverma The very first brick with Lichchhavi inscription is the one reported by Thakur Lal Manandhar as found from spot at about fifty meters north of Manamanesvori (in what is now a school compound) and inscribed with the letters ‘ Mahasamant Amshuvermmanah ’. These bricks were of size (14”x 9”x 2.5”). During the replacement of a compound wall of a house adjoining the temple plinth in Dabali of Handiguan , several broken bricks with similar inscriptions.

Slide37:

Nepali numeral system (Lichhavi numeral system)based on: Positional system, sign value system, decimal system, unary system, grouping system.

Manuscript of Sumatitantra (written in 505 AD):

Manuscript of Sumatitantra (written in 505 AD)

Halayudha Bhatt(c. 10th Century AD) & his Contributions:

Halayudha Bhatt(c. 10 th Century AD ) & his Contributions Halayudha Bhatta (10 th CE) was a Nepali citizen who lived at Janakpur since 10 th century of A.D . He has been written prosody on Piṅgala's . Combinatory forms an important statistical contents like permutation and combination . The tradition began with the formal theory of Sanskrit meters formulated by Piṅgala in the 2nd century B.C.E. His recursive algorithms are the first example of recursion in South Asian mathematics. Piṅgala’s calculation of the binomial coefficients , use of repeated partial sums of sequences and the formula for summing a geometric series became an integral part of South Asian mathematics. Halayudha attribution of the construction of what is now known as Pascal’s triangle to Piṅgala (Shah, Jayant , 2012).

Binomial theorem, Permutation and combination:

Binomial theorem, Permutation and combination 40 1 1 1 1 1 1 1 1 1 1 1 2 6 3 4 4 3 5 10 10 5 Piṅgala's Meru/Pascal’s triangle

Slide41:

Ṡripati and his contributions: Ṡripati ( c.1019-1066) was the most prominent mathematicians of the 11th Century. He was born in; Rohinikhanda of Nepal ( Rohinikhanda , near Rohini River of Rupandehi / Nawal Parasi district, Lumbini Zone). There was no unanimity on the birth year of Ṡripati . Pant (1973: 9), cited that Mishra (1932:7) Ṡripati was residence in Shakabda 950 (B.S 1085) Bharatvarsa ; Rohinikhanda . Ṡripati's works; Dhikotidakarana written in 1039 was a work of twenty verses on solar and lunar eclipses; Dhruvamanasa in 1056 a work of 105 verses on calculating planetary longitudes, eclipses and planetary transits.

Slide42:

Siddhantasekhara is a major work on astronomy, Ganitatilaka an incomplete arithmetical treatise. Siddhantasekhara  a major work on astronomy in 19 chapters. Ganitatilaka , an incomplete arithmetical treatise in 125 verses based on a work by Sridhar. Siddhanta Sekhara has 19 chapters. It containsArithmetic , Algebra, and the Sphere in chapters 13,14,and 15 respectively. It has rules of signs for addition, subtraction, multiplication, division, square, square root, cube and cube root of positive and negative quantities.

The most peculiar aspects of the Siddhanta-Sekhara :

The most peculiar aspects of the Siddhanta-Sekhara The second correction of the position of the Moon: The calculated position of the Moon may coincide with, or approximately very nearly to the observed position of the Moon. Equation of the time due to the obliquity of the elliptic. The correction applied for the change of declination of the Sun, in connection with the method of determining the East-West line. The position of the Sun in the different quadrants of the Ecliptic Path. Precession of the Equinoxes. Treatise containing arithmetical and algebraic operations and discussion on the sphere, the astronomical instrument and other minor details of astronomy.

Mediaeval Period (10th century AD to 17th century AD) :

Mediaeval Period (10 th century AD to 17 th century AD) The time period after 10 th century AD is propose as the medieval period in context of Nepal for mathematics practices. Here some mathematicians of that period and their contribution in mathematics is illustrated. Dharmapati Bardhane , Balbhadra Joshi, Chakrapani Aryal, Laxmipati Pande , etc., were contributed for developments of mathematics in Nepal. Mostly they contributed in Jyoutisha arithmetic. They calculated calendars and it is based in planetary motion, that is astronomy.

Slide45:

Dharmapati Bardhane & his contributions: Daivagya Dharmapati Bardhane (1409) had wrote Sumati Siddhanta. It was the time of 266 years before the appointment of Royal Astrologer in Greenwich Royal Observatory. He was a great astrologer. He constructed the ‘ Sumati Siddhanta ’, with the historical scenario of Mathematics. This treatise was used in calculation of calendars in Malla Dynasty.

Eclipse counted by Dharma Bardhane:

Eclipse counted by Dharma Bardhane

Slide47:

Balbhadra Joshi & his contributions: Balbhadra Joshi (1494) was a residence of Jumla district who had written as the commentary of Bhaswati i.e. Balbodhini . It was very popular in India also. He had prepared a teaching manuals for Mathematics . It is the third commentary in the world on Bhaswati . This Bhashwati book as a text book of Mathematics. Since Bhashwati had helped a lot of count calendars ( Panchanga ) and also to help teaching addition, subtraction, multiplication and division, etc. as basic Mathematics books, so Bhashwati had been as the first book of supplement Mathematics.

Slide48:

There is a strong relationship between Mathematics and Astrology. So in old ages, people used to go to Jyoutisha teachers to learn Mathematics. Assignments from Bhashwati had helped them for complete calculation in Panchanga . For more Mathematics knowledge, people used to read Lilavati . Bhashwati was so popular in different part of country that many of hand written Shlokas (Tikkas) are found from Bhashwati at different places .

Slide49:

Chakrapani Aryal & his contributions: Astrologer Chakrapani Aryal of Gorkha ’(1733) had written Uttana Ganita in 1771. It described the calculation of calendar. He had published his Jyoutisha manual Uttana Ganita for calculation of calendrical data like calculation of Solar and Lunar eclipse . It was 48 years ago than the establishment of Royal observatory at Greenwich and appointment of Royal Astrologer at that observatory.

Slide50:

Laxmipati Pande & his contributions: Laxmipati Pande ( 1758–1831 ) was a famous astrologer and mathematician who advised King Prithvi Narayan Shah (1723–1775) & Bahadur Shah (1757 – 1797 ). He was known to be a great theologian in Nepal. He was honored as a royal astrologer. He was not only the mathematician but he had a nice idea about the timings of stars–planets counting . He had written solar watch [ Dhupa Ghadi (Sundial )].   He had written the commentary of Bhashwati and started his mathematics and Jyoutisha study. He was as the first Nepali astrologer that has written the Nepali meaning of his shlokas.

Slide51:

His contribution has shown that Bhashwati was the initial textbook of mathematics in Nepal then after only students of high level used to read Lilavati for more knowledge in mathematics. Astrologers had calculated planets-stars calendar and eclipses on the basis of this Bhashwati . They taught their students making commentary of this book. He wrote about 40 books.  Some of the notable books are: Ratnadeep, Lilavati , Bhashwati Tika , and Griha Laghava Kalarnav Dipika. Lila Nath Pandey was the son of Laxmipati, who was also mathematician and astrologer. Lila Nath wrote a book in Siddhanta Jyoutisha. Mathematics and Jyoutisha was the Pandey family's’ tradition for many years. 

Sun Dial prepared by Laxmipati Pande:

Sun Dial prepared by Laxmipati Pande

Slide53:

Mohar of king Prithvi Narayan Shah dated Saka Era1685 (1763 CE )

Modern Period (18th century AD and onward):

Modern Period ( 18 th century AD and onward) In context of Nepal we can consider after unification of Nepal as the modern period. Thus here we consider 18 th and onward as the modern time line for mathematics practices in Nepal. F ormal mathematics education was influenced by mathematics practices in neighboring countries' scholars. So as mathematics teachers were hired from India. But indigenous mathematics ( ; gftgL ul0ft _ were practices each and every communities as local mathematics . Later Nepali scholars wrote mathematics books. The writers and their books and matters are described as below.

Slide55:

Gopal Pande & his contributions: Gopal Pande (1847–1920) wrote the first book of mathematics in Nepali language, called Vyatka Chandrika. In this book he had shown method for cube root by rule of three or Trizoidiacle method. He wrote Lokanu Smiriti , explains about democracy. He had knowledge about architecture and engineering, and helped Nepal Government develop a huge area, called Tundikhel and he revised of calendars and awarded by the government.

Slide56:

Brahmalal Shrestha & his contributions: Brahmalal Shrestha (Marubicche tole) was born and he had written Vichitra Ganita in 1918 which is as a practice book . ' Vichitra Ganita ' mainly dealt with what we describe as 'Arithmetic' in today's mathematical parlance. It consisted of 400 mathematical problems written in Nepali. In the actual work, the Algebra section was quite mixed with Arithmetic. In fact, ' Vichitra Ganita ’ did not contains much of algebra, at least not explicitly. He added certain elements of algebra such as finding an unknown quantity subject to certain constraints using the method of supposition.

Slide58:

Pahal Man Singh Swar & his contributions: Pahal Man Singh Swar (1878-1934) had written Ankendushekhara which influenced Nepali mathematics. It contains the elementary concept of mathematics based on four fundamental operations of mathematics .

Slide59:

Jayaprithvi Bahadur Singh (1877-1940) had written Aksharanka Shiksha in 1901. It was a very remarkable works in Nepali mathematics.

Slide60:

Chandra Shamsher (1883) was the first student of matriculation. He passed (S.L.C.) with mathematics majoring. Chakravarti Arithmetic, Lilavati, SiddhantaSiromani were as the text books at that time. The Square roots, Cube roots, Rule of three, L.C.M., etc. were taught at Shresta Pathashala school . Narendramani Aadhi translated the arithmetic used for teaching in 1834 in Shresta Pathashala.

Slide61:

Noor Dutta Pandey was the second son of Gopal Pandey , who wrote Gorkha Bijaganita (1925) (part one to four), a book about algebra, and Saral Bija Ganita .

Slide63:

Tika Ram (Marasini) Dhananjaya & his contributions: Tika Ram (Marasini) Dhananjaya (born 1909) and Chandrakala Dhananjaya had written Shishubodha Tarangini part I (1931). Shishubodha Tarangini part II (1931), Shishubodha Tarangini part II (1931/1932). This is one of the very rare books for today. He had also written Laghu Kaumudi and other so many books on mathematics and literatures. The presentation is in prosody style. This book contains elementary mathematics and sum of the series.

Slide64:

Naya Raj Pant & his contributions: Naya Raj Pant (1913-2002)worked as a researcher in Balmiki Vidyapitha from 2033 B.S to 2035 B.S. He was as a Scholar member of Institute of Royal Nepal Academy from 2036 B.S.to 2050 B.S. and he was the life member of Institute of Royal Nepal Academy since 2051 B.S. He was recognized as a great scholar of mathematics in Asia. He was a self-learner and seen very much inquisitive in mathematics and Jyoutisha Ganita. He was praised as a great astronomer and mathematician by foreign scholars. He was awarded so many times due to his pioneer works in the field of research and publications with teaching Jyoutisha Ganita. He revised the Gopal Pandey's rule of calculation of cube roots by applied the rule of three. He used the rule of three to calculate the square root.

Slide65:

He explored the contributions of Gopal Pande and Laxmipati Pande. He wrote the commentary and modifications on some mathematics developed by Bhaskaracharya. He gives the connection between ancient and modern mathematics. He revised the calculation of calendars. He wrote the following books: Jyoutisha, Pandit Gopal Pande and his rule of calculation of cube roots, Comparisons of ancient and new (modern) mathematics, Comparisons of Hindu Siddhanta Jyoutisha and Greek Siddhanta Jyoutisha, Declaration of Lichhavi Era, Laxmipati Pandey's Sundial, Sumati Tantrum, Ratna Dip part one and two, Golbodha, Kalachakra and its analysis (part I and II), Trigonometry, etc. and he has written hundreds papers of mathematics and commentaries.

Slide66:

He identified Lichhavi numerals used these symbols in representation of pages of a book. He identified the birth place of Ṡripati and highlights his work Siddhantasekhara. He presented 62 talks at Nepal Academy and he has nearly 200 mathematical papers and books. He is as the mathematician and historian of mathematics. He planned the observatory for observing solar systems.

Slide68:

Chandrakala Devi Dhananjaya (1915-2002) & her contributions: She is as a first women scholar and writer of mathematics books. She has written Shishubodha Tarangini. She express a prosody of mathematics as given below: Vyaparile pachisko dara gari Ridima Panch sau Dushala Yeksau tettis sattaish dara gari gharma bechihalechha kala Dwosau pachchas dar gari hariya , banki tettis darle Seta bechechha napha bhana timi ahile katti payechha tesle ?

Slide70:

There she has given answer as Rs.2,202 , which can be determining any way. But this poetic form of expression increased interests in mathematics . For simplification we can express as, Solution: C.P= Rs . 25ⅹ500 = 12,500 S.P=133ⅹ27+250ⅹ29+117ⅹ33 =3591+7250+3861=14,702 ∴Profit = 14702-12500= Rs . 2,202 . Her book contains elementary mathematics to advanced contents of series.

As far as we are concerned, the name “Mathematical Sciences” appeared for the first time some 40 years ago in the title “The Nepali Mathematical Sciences Report” of the bi-annual mathematical publication published in the 7th Falgun, 2032 (20th February, 1975) published by Institute of Education, Tribhuvan University. Its basic objective was to publish and promote everything that is purely mathematical, partially mathematical and those with potentiality of being mathematical. :

As far as we are concerned, the name “Mathematical Sciences” appeared for the first time some 40 years ago in the title “The Nepali Mathematical Sciences Report” of the bi-annual mathematical publication published in the 7 th Falgun , 2032 (20 th February, 1975) published by Institute of Education, Tribhuvan University. Its basic objective was to publish and promote everything that is purely mathematical, partially mathematical and those with potentiality of being mathematical .

Activities of Mathematics as time line:

Activities of Mathematics as time line ( 1847–1920): Gopal Pande wrote the first book (Vyatka Chandrika) of mathematics in Nepali language . 1853: Durbar High School was established and it is the main source of education and it introduced courses of mathematics . 1877: First Sanskrit School was established by Ranodip Singh. (1877-1940): Jayaprithvi Bahadur Shah had written Aksharanka Shiksha in 1901. It was a very remarkable works in Nepali mathematics. (1878-1934): Pahal Man Singh Swar had written Ankendushekhara which influenced Nepali mathematics .

Slide74:

1884: Publication of first Nepali Calendar. Himnath Pant (son of Toya Nath Pant) was the first Masters Degree in Jyoutisha in Nepal. He had works in preparation of calendar. 1903 (born) Harinath Pokharel wrote Brahmanda Darpan (1922) and Miti Darpan and Panchnga (1928) books in Nepali language in Kashi . (1909-1936):Tika Ram Dhananjaya had contribution in Nepali mathematics through Sishubodhatarangini in 1933 . ( 1915-2002): (1915-2002): Chandrakaladevi Dhananjya , first woman mathematician/writer of mathematics in Nepal. She had written Shishubodhatarangini part one and part two.

Slide75:

(1913-2002): Naya Raj Pant occupies a central position in history of mathematics in South Asia. He had written more than 200 mathematical treaties based on number theory, trigonometry, Jyoutisha, spherical trigonometry, planetary motion and calendar, sun dial, calculus, chhanda , etc. Meru Nath Pane, Kabi Raj Pande are also the popular writer of algebra in Nepali language at that time. (1913-2007): Prof. Keshav Dev Bhattarai was a Matriculation from Patna University was as the second M.A.Degree holder in whole of the Nepal. He conducted a memorable quiz contest for school level Mathematics in Olympiad mode. He taught at Trichandra College.

Slide76:

(1922-1997): Prof. Gobinda Dev Pant was appointed as a professor of mathematics in Tri-Chandra College. 1918 : Mmathematics was teaching at Trichandra College at proficiency level (I.A.). 1922: Indra Nath Arjyal was born and now he is as the living legend of Nepali mathematics, he can expressed mathematics in classical way in practical base. 1924: The study of mathematics in B.A. level was started in Trichandra College. 1925/26: Noor Datta Pande, second son ( mahila chhora ) of Gopal Pande had written Gorakha Bijaganita part one to four.

Slide77:

1926: Narayan Bahadur Manandhar (born 1906) was the first Nepali person who received first Masters Degree in mathematics major from Calcutta University and he taught at Trichandra College. 1930: Prof. Dhupa Ratna Bajracharya was the founder President of Nepal Mathematical Society and Head of Central Department of Mathematics in Tribhuvan University. (1941-1951): Nepali Arithmetic book was published by Khadga Man Malla for fulfii the mathematics need to service holder in the Government Office. Unward 1959: Asutosh Ganguli (1961) was the first Department Head of Mathematics for Masters Degree class in Trichandra College. Prof. T. P. Chaudhary, Prof. V.D. Thawani also tought mathematics.

Slide78:

1953: Date for training (5 months then 10 months) at Min Bhawan for mathematics teacher in Nepal. In 1956 Proficiency Certificate Level Class (I. Ed.) at Chetbhawan . 1956: I. Ed. class of mathematics education was started at Chetbhawan . 1963: Date for first mathematics curriculum in lower secondary. 1967: Year that college of education the mathematics of education was started in Kirtipur. 1971: New Educational System Plan (NESP) is as the milestone for development of education which also supports mathematics education. From that date Mathematics Education and Statistics were taught in Masters Degree Level in T.U at Kirtipur. Department of Mathematics shift Kirtipur. 1973: First Semester class in Mathematics Department of T.U. in Masters Degree class.

Slide79:

The end of the tenth years of 1900: the Three Pass and Four Pass degree also allowed for service holder in Government Office with mathematics major. 1979: Establishment of Nepal Mathematical Society. Prof. Dhupa Ratna Bajracharya , Ram Man Shreshtha and Shankar Raj Pant, etc. are as the founder members of NMS. 1991: Establishment of Council for Mathematics Education. Prof. Madan Man Shrestha as the founder President. 2004: Ministry of Science and Technology published a famous historical paper Mathematics in Nepal: a Historical Analysis written by Prof. Shankar Raj Pant was published in the scientific journal Scientific World . Perhaps this is the first paper which gives the brief history of Nepali Mathematics and it is as the milestone for search the historical Development of Nepali Mathematics and Mathematics Education.

Slide80:

2008: Nepal Academy of Science and Technology (NAST) announced a mathematical report for Mathematics Education for the 21 st Century New Nepal prepared by Prof. R.M.Shreshtha . It is as a base stone for review of Nepali Mathematics with comparing mathematics in different civilizations of the world. It is also a milestone for research in mathematics and mathematics education in Nepal. After these two works, dozens of papers are published nationally and internationally including biography of mathematicians. 2009: Establishment of Nepal Mathematics Centre. Prof. Ram Man Shreshtha as the founder President. 2010 and onward: Awareness in history of mathematics and classical developments and research in this fields which focused mainly mathematics in Nepal. Searching of mathematical treaties written in Nepal. Introduce of mathematics in Nepal in curriculum (Masters and Bachelors Degree). It is as the achievement in mathematics curriculum reformation.

Slide81:

A research team of Research Centre for Innovation and Development (CERID, 1990) conducted a study of Elementary Process of Learning Mathematical Concepts in Nepal as a study on Mathematics concepts and process of Rasuwa of Tamang Community concluded that, The Tamangs of Rasuwa have their own system of measurement and counting and their own mathematics process. The mathematical process is all based on traditional practice and practical utility value. The counting and mathematics processes are essentially based on the use of physical objects in the environment and on practical situations. Counting and mathematical processes are manifest mostly in money-accounting.

Slide82:

Trade, farming and employment from the main bases of social interactions between the Tamangs and the people of other ethnics groups. The mathematics that the student has learned from their communities comes to interfere in their learning modern mathematical concepts in school. Tamangs have their own distinct concept for calculation, measurement and other mathematical treatments . Tamangs in Rasuwa , measured length of an object with hand and fingers and volumes with wooden pots.

Slide83:

The area of tract of lands is measured in terms of the volume of seed grains. Quantities of meat, wool, ghee, etc , are weighed out on ‘ TSANG ’ and ‘ OMALI ’ the popular local weight measurement devices. Most Tamangs of Rasuwa use a simple time measurement system. The Tamangs used the Lama calendar based on the phases of the moon. Geometrical concepts are based on the shapes and structure patterns of the objects existing around. The Tamang system of numeration and mathematics in Rasuwa is influenced by the Devanagari- Nepali based system, i.e. base 20

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References: Acharya, E. R. ( 2012), Prof. Naya Raj Pant As an Institution of Mathematics , J . of Ramanujan Society of Math. and Math. Sc. vol.1 No. 4 (2012). pp. 83-89 Acharya, E. R. (2015), Mathematics Hundred Years Before and Now, History Research: Science Publishing Group. Acharya , E.R.(2015). Naya Raj Pantka Ganitiya Kritiharuko Adhyayan (Study of Mathematics Treatise of Naya Raj Pant) (unpublished PhD dissertation), Nepal Sanskrit University, Dang . Acharya, E. R. (2016), Antiquity of Nepali Mathematics, American Research journal of History and Culture. Acharya, E.R. and Chhetri, D.B. (2016/17). Historical Development of Mathematics : Sunlight Publication, Kirtipur. Adhikari, B.(2015). Mathematical Contribution of First Nepali Women Mathematician Chandrakala Devi Dhananjaya (unpublished Masters’ thesis), Tribhuvan University. Basyal, D.(2015). A 1933 Nepali Mathematics And Astrology Book Shishubodha Tarangini II: Translation And Commentary on Mathematics Chapters .(Unpublished PhD dissertation), New Mexico State University Las Cruces, New Mexico. Chhetri D. B.(2006). Mathematical idea of Sawyers (unpublished Masters thesis), Tribhuvan University, Kirtipur. Dhananjaya, C. (1934), Shishubodha Tarangini , Ramghat Vanaras City. Kandel, K.P.(2015). Biography of Brahmalal Shrestha and His Contribution In Nepalese Mathematics. (unpublished Masters’ thesis), Tribhuvan University. Maskey, S.M. (2013). Mathematics developments in Nepal (A paper presented at South Asian University, New Delhi. Pande, G. (1914), Vyaktachandrika, Nirnnaya Chhapakhana , Mumbay . Pant, N. R. (1978), Sumatitantra, Tribhuvan University , Kathmandu. Pant, S.R.(2004). Mathematics in Nepal: a Historical Analysis: Ministry of Science and Technology, Kathmandu. Shreshtha, R.M.(2008). Mathematics Education for the 21 st Century New Nepal, NAST. Subedi, N.(2010). Study of Numeral System in Nepal . Upadhya , Maheshwor (2069 ). Nepali Ganitaka sata Prabhanda , Biplawa Paudel,Kathmandu , p. 3 Yadav, L N., et all (2015). History of Mathematics : Sunlight Publication, Kirtipur . https://www.researchgate.net/

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