Journal articles: 'Ancient Indian mathematics'

1

Dani, S. G. "Ancient Indian mathematics — A conspectus." Resonance 17, no. 3 (March 2012): 236–46. http://dx.doi.org/10.1007/s12045-012-0022-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Ramakalyani, V. "Computations In Ancient Indian Mathematics." Journal of Combinatorics, Information & System Sciences 44, no. 1-4 (December 30, 2020): 103–34. http://dx.doi.org/10.32381/jciss.2019.44.1-4.7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Hridya, S., Dr S. Bhavani, Dr K. G. Dharani, and M. Darani Kumar. "A Multiplier Design based on Ancient Indian Vedic Mathematics Using Reversible Logic: A Review." Journal of Advanced Research in Dynamical and Control Systems 11, no. 10-SPECIAL ISSUE (October 31, 2019): 911–24. http://dx.doi.org/10.5373/jardcs/v11sp10/20192887.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Et. al., Pooja P. Walke. "A Survey on “Machine translation Approaches for Indian Languages”." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (April 10, 2021): 4792–94. http://dx.doi.org/10.17762/turcomat.v12i3.1941.

Full text

Abstract:

Translation has always helped India to knit Indians together with respect to its rich culture and literature. Ideas and concepts like ‘Indian ancient literature’,’Indian rich culture’,’Indian philosophy’ and ‘Indian knowledgeable systems’ would have been impossible in the absence of translations with their natural integrationist mission.Machine Translation assist to translate Information presented in one language to other language. Information can be present in form of text, speech and image translating this information helps for sharing of information and ultimately information gain.Translation process is an extremely complex & challenging process. It requires an in-depth knowledge about grammar of both the languages i.e. Source language and Target language to frame the rules for target language generation. Marathi is a regional Indian language and consists of a lot of literature that could be useful if projected in the universal English language. As manual translation is a tedious task, we propose a literature survey about machine translation systems that translates Indian Languages into English Language using various Machine translation approaches like RBMT, SMT, NMT, Hybrid translation

APA, Harvard, Vancouver, ISO, and other styles

5

David H. Bailey and Jonathan M. Borwein. "Ancient Indian Square Roots: An Exercise in Forensic Paleo-Mathematics." American Mathematical Monthly 119, no. 8 (2012): 646. http://dx.doi.org/10.4169/amer.math.monthly.119.08.646.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

., PiyushRaut. "PERFORMANCE ANALYSIS OF SQUARE ROOT EVALUATOR USING ANCIENT INDIAN MATHEMATICS." International Journal of Research in Engineering and Technology 05, no. 22 (May 25, 2016): 28–30. http://dx.doi.org/10.15623/ijret.2016.0522009.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Banerjee, Arindam, and Debesh Kumar Das. "The Design of Reversible Signed Multiplier Using Ancient Indian Mathematics." Journal of Low Power Electronics 11, no. 4 (December 1, 2015): 467–78. http://dx.doi.org/10.1166/jolpe.2015.1413.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

M., Shahina. "A Review on Implementation of RSA Cryptosystem Using Ancient Indian Vedic Mathematics." International Journal on Recent and Innovation Trends in Computing and Communication 3, no. 1 (2015): 162–64. http://dx.doi.org/10.17762/ijritcc2321-8169.150134.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Duke, Dennis W. "The Second Lunar Anomaly in Ancient Indian Astronomy." Archive for History of Exact Sciences 61, no. 2 (December 14, 2006): 147–57. http://dx.doi.org/10.1007/s00407-006-0119-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Prof. Sharayu Waghmare. "Vedic Multiplier Implementation for High Speed Factorial Computation." International Journal of New Practices in Management and Engineering 1, no. 04 (December 31, 2012): 01–06. http://dx.doi.org/10.17762/ijnpme.v1i04.8.

Full text

Abstract:

Vedic Mathematics arise from the prehistoric classification of Indian mathematics that was recreated by Tirthaji. Ancient mathematical operations are depending on sixteen methods. In this article, a new VLSI architecture to compute factorial of the given number with Vedic based multiplier is proposed. Simulations are performed using Xilinx ISE 14.2. Effective comparative analysis is made with existing multipliers to prove the momentous development in competence and high speed operation. This efficient multiplier is implemented in the proposed factorial architecture which significantly reduces the path delay and provides better optimization.

APA, Harvard, Vancouver, ISO, and other styles

11

Hilgert, Joachim. "George Gheverghese Joseph: Indian Mathematics. Engaging with the World from Ancient to Modern Times." Mathematische Semesterberichte 65, no. 1 (September 18, 2017): 121–23. http://dx.doi.org/10.1007/s00591-017-0205-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Duke, Dennis. "The Equant in India: The Mathematical Basis of Ancient Indian Planetary Models." Archive for History of Exact Sciences 59, no. 6 (April 13, 2005): 563–76. http://dx.doi.org/10.1007/s00407-005-0096-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Rukmini, S. "Indic Science of Consciousness: Chronological Relevance to the Indic Knowledge Traditions and Modern Science." Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies 4, no. 1 (May 30, 2020): 74. http://dx.doi.org/10.25078/ijhsrs.v4i1.1400.

Full text

Abstract:

In the recent years there seems to be a renaissance of Indic knowledge traditions and this is quite evident from the growing interest among the modern researchers and scholars to unearth the great insights and knowledge that made ancient Indian civilization one of the unique in the world. India as a nation of rich spiritual heritage and diverse knowledge systems have become the most sort out nation across the globe in terms of wisdom and insights on the philosophy of mind and consciousness. Further, research findings in different fields of knowledge such as consciousness studies, health and healing, psychology and mental health, mathematics, physics, astronomy, economics, law and governance, archaeology and history are in good agreement and deeply correlated with the information inscribed in the ancient Indian scriptures. Ancient Indians deeply engrossed in understanding the ontological and epistemological basis of knowledge advocated Vedas as the ultimate source of knowledge. Vedas are considered as the oldest repository of spiritual knowledge in the world, where the prime emphasis is on understanding the nature of mind and consciousness, as this forms the fundamental basis to Indic knowledge. So, here, we propose that the science of consciousness seems to be the first and foremost in the chronology in the world of knowledge. An intuitive and analytical framework that resulted from a deeper understanding of the nature of mind and consciousness paved the way for the development of different Indic knowledge systems. Inner insight emerged through this approach is embraced to understand the external world and formulate different theories and principles of Indic knowledge. From a chronological perspective, Indian science and wisdom emerged in the later stages of development of the science of consciousness. So, the aim of the present paper is to throw light on the Indic science of consciousness and examine chronology of the emergence of other fields of Indic knowledge.

APA, Harvard, Vancouver, ISO, and other styles

14

Kumar, Manoj, and Ankur Kumar. "Some Techniques of Ancient Indian Vedic Mathematics for Elliptic Curve Cryptography over the Ring A4." International Journal of Computer Sciences and Engineering 7, no. 5 (May 31, 2019): 1330–37. http://dx.doi.org/10.26438/ijcse/v7i5.13301337.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Banerjee, Arindam, Aniruddha Ghosh, and Mainuck Das. "High Performance Novel Square Root Architecture Using Ancient Indian Mathematics for High Speed Signal Processing." Advances in Pure Mathematics 05, no. 08 (2015): 428–41. http://dx.doi.org/10.4236/apm.2015.58042.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

G.Deshpande, Nishant, and Rashmi Mahajan. "Ancient Indian Vedic Mathematics based 32-Bit Multiplier Design for High Speed and Low Power Processors." International Journal of Computer Applications 95, no. 24 (June 18, 2014): 19–22. http://dx.doi.org/10.5120/16742-6956.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Høyrup, Jens. "On a Collection of Geometrical Riddles and their Role in the Shaping of Four to Six “Algebras”." Science in Context 14, no. 1-2 (June 2001): 85–131. http://dx.doi.org/10.1017/s0269889701000047.

Full text

Abstract:

For more than a century, there has been some discussion about whether medieval Arabic al-jabr (and hence also later European algebra) has its roots in Indian or Greek mathematics. Since the 1930s, the possibility of Babylonian ultimate roots has entered the debate. This article presents a new approach to the problem, pointing to a set of quasi-algebraic riddles that appear to have circulated among Near Eastern practical geometers since c. 2000 BCE, and which inspired first the so-called “algebra” of the Old Babylonian scribal school and later the geometry of Elements II (where the techniques are submitted to theoretical investigation). The riddles also turn up in ancient Greek practical geometry and Jaina mathematics. Eventually they reached European (Latin and abbaco) mathematics via the Islamic world. However, no evidence supports a derivation of medieval Indian algebra or the original core of al-jabr from the riddles.

APA, Harvard, Vancouver, ISO, and other styles

18

N, Shylashree, D. Venkata Narayana Reddy, and V. Sridhar. "Efficient Implementation of Scalar Multiplication for Elliptic Curve Cryptography using Ancient Indian Vedic Mathematics over GF(p)." International Journal of Computer Applications 49, no. 7 (July 28, 2012): 46–50. http://dx.doi.org/10.5120/7643-0730.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Hussain, S. M. Alfarid, and Neelatphal Chanda. "Integrating Classical Language to Modern Media Platforms: A Multimodal Approach towards Mainstreaming Sanskrit." International Journal of Social Sciences and Management 4, no. 1 (January 23, 2017): 5–8. http://dx.doi.org/10.3126/ijssm.v4i1.16337.

Full text

Abstract:

This ancient language, considered to be the mother language of a majority of Indian languages, today appears to be fighting a losing battle with only about 14,000 people in India claiming Sanskrit as their mother tongue in a country of over 1.2 billion people, as the 2011 census data reveal. In an era increasingly engulfed by the forces of globalization amidst the debates surrounding linguistic homogenization and cultural neo-imperialism, mass media as well as various digital media platforms, including social media can contribute towards restoring the rich literary tradition of the Sanskrit language that defines the very essence of what we understand as ‘Indian culture.’ This paper argues that state-run public service broadcasters like Doordarshan and All India Radio, are obligated to create and transmit content that generate awareness about Sanskrit and its significance to modern Indian knowledge like Ayurveda, yoga, music, grammar, philosophy, Vedic mathematics etc. Yet, this paper argues that the public broadcasters should be careful not to create an arcane and pedantic programming structure meant exclusively for a select oligarchy of Sanskrit specialists, but should rather embark on creative programming formats that would actually attract the young people towards learning the language and understanding its relevance. The social media ecosystem reflects the continued dominance of English as a mode of communication, which implies the complex hegemonic processes that are at work. Yet, there is a growing population of people engaging in social media in their own respective languages. This paper argues that the egalitarian nature of social media coupled with the horizontal type of user-generated content flow architecture provides the perfect spawning ground for the preservation and promotion of Sanskrit in the 21st century society.Int. J. Soc. Sc. Manage. Vol. 4, Issue-1: 5-8

APA, Harvard, Vancouver, ISO, and other styles

20

Et. al., Dr Priyanka Rai,. "Consumers Buying Behaviour and Challenges Faced by Consumers During COVID-19 Pandemic Regarding FMCG Products ( During Indian Lockdown)." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 10 (May 30, 2021): 3403–12. http://dx.doi.org/10.17762/turcomat.v12i10.5015.

Full text

Abstract:

Pandemics are the imminent health challenges for consumers whereby fear and panic are integral human responses historically. Panic behavior during pandemic is an expected response consumer threatens the ability to cope and destroy the existing balance in life. Consumers develop much-unexplained behavior which differs from region to region, culture to culture. Panic buying / increased buying behavior has been observed during public health emergencies since the ancient period. However, the exact psychological explanation responsible for it has not sought systematically. Therefore, the study is to intend a thrust to identify the possible psychological explanations behind the consumer buying behavior during pandemics. A perception of scarcity is strongly linked with the consumer buying behavior during pandemics, and collecting & saving behaviors increases if the scarcity develops for the immediate necessaries. It also creates a feeling of insecurity which in turn activates another mechanism to collect things. Panic buying also has been linked with perceived feeling of insecurity and instability of certain situations. Furthermore, supply disruption, a condition where normal product supply in supply chain interrupted, has been frequently observed during a disaster or other unwanted calamities. This also led to a feeling of insecurity. The objective of study is to analyze how pandemic affect consumer buying pattern and sentiments.

APA, Harvard, Vancouver, ISO, and other styles

21

Raj, Sadhana. "CURRENT SOCIAL NEEDS MUSIC THERAPY." International Journal of Research -GRANTHAALAYAH 3, no. 1SE (January 31, 2015): 1–4. http://dx.doi.org/10.29121/granthaalayah.v3.i1se.2015.3411.

Full text

Abstract:

There is also a rich tradition of music in India. Few countries have found such an old and rich tradition of music. Indian music has an inspiring Siva and Saraswati which means that human beings cannot develop such high art without any divine inspiration, only on their own strength. Music existed in India since Vedic period. The Yajurveda mentions several instrumental choirs in the 19th and 20th mantras of the 30th scandal. Which makes the existence of music clear. The history of Indian music is at least 4000 years old. The most ancient music mentioned in the world is found in the Samaveda, the artistic atmosphere of various instruments and vocals developed here. Pythagoras became the first person in Europe to determine the place of vowels by the laws of mathematics. भारत में भी संगीत की समृद्ध परम्परा रही है। कुछ ही देशों में संगीत की इतनी पुरानी एवं समृद्ध परम्परा पायी गई है। भारतीय संगीत के प्रेरक षिव और सरस्वती है इसका तात्पर्य है कि मानव इतनी उच्च कला को बिना किसी दैवी प्रेरणा के, केवल स्वयं के बल पर विकसित नहीं कर सकता। वैदिककाल से ही संगीत भारत में विद्यमान था। यजुर्वेद में 30वें कांड के 19वें और 20वें मंत्र में कई वाद्य बजानेवालों का उल्लेख है। जिससे संगीत का अस्तित्व स्पष्ट होता है। भारतीय संगीत का इतिहास कम से कम 4000 वर्ष पुराना है। संसारभर में सबसे प्राचीन संगीत का उल्लेख सामवेद में मिलता है यहाँ विभिन्न प्रकार के वाद्य यंत्रों और स्वरों के कलात्मक वातावरण का विकास हुआ। यूरोप में पाइथागोरस पहला व्यक्ति हुआ है जिसमें गणित के नियमों द्वारा स्वरों के स्थान को निर्धारित किया।

APA, Harvard, Vancouver, ISO, and other styles

22

Rasheed, Shebina P., and Murugesh Shivashankar. "Preparation and Characterization of Calcium Based Indian Traditional Drug: Varatika Bhasma-Herbomineral." Advanced Science Letters 24, no. 8 (August 1, 2018): 5931–35. http://dx.doi.org/10.1166/asl.2018.12222.

Full text

Abstract:

Herbomineral is effective for a number of ailments from ancient times. Bhasma an effective herbomineral are highly potent, non-toxic and therapeutically beneficent medicines due to their unique method of preparation known as Samskara. Thereby by the metal particles are reduced to finer and finer sizes. Bhasma prepared by herbs, mineral, and metals are incinerated to ash under supervised conditions Prepared bhasma are subjected to physiochemical characterization using modern technical like elementary analysis with EDAX, SEM.TEM, TGA, XRD, AAS, etc. These studies reveal that Bhasma particles are in oxygen defective state and clearly noticeable particles fractions are in nanometre size range. These properties like oxygen defiant and nanoparticles in bhasma might disseminate therapeutic property.

APA, Harvard, Vancouver, ISO, and other styles

23

Vadiraj, G., K. Shivanand, B. Sampat, and G. Subramanya Nayak. "Implementation of High Speed Vedic Multiplier Using Vertical and Crosswise Algorithm." International Journal of Reconfigurable and Embedded Systems (IJRES) 6, no. 1 (May 28, 2018): 36. http://dx.doi.org/10.11591/ijres.v6.i1.pp36-40.

Full text

Abstract:

Multiplication is an important fundamental function in arithmetic operations. Multiplication-based operations such as Multiply and Accumulate (MAC) and inner product are some of the frequently used operations in many Digital Signal Processing (DSP) applications such as convolution, Fast Fourier Transform(FFT), filtering and in microprocessors in its arithmetic and logic unit. Since multiplication dominates the execution time of most DSP algorithms, so there is a need of high speed multiplier. Higher throughput arithmetic operations are important to achieve the desired performance in many real-time signal and image processing applications. In this project, the comparative study of Vedic multiplier and Sequential multiplier is done for low power requirement and high speed. The proposed architecture is based on the Vertical and Crosswise algorithm of ancient Indian Vedic Mathematics, which increases the speed of multiplier by reducing the number of clock cycles thus achieving the greater speed of the processor or system.

APA, Harvard, Vancouver, ISO, and other styles

24

Ruane, P. N. "Reviews - Ancient Indian leaps into mathematics, B. S. Yadav and Man Mohan (eds). Pp. 217. £66.99 (Hardback). 2011 ISBN: 978-0-8176-4694-3 (Birkhäuser)." Mathematical Gazette 97, no. 539 (July 2013): 362–63. http://dx.doi.org/10.1017/s0025557200006252.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Safoev, Nuriddin, and Jun-Cheol Jeon. "Design and Evaluation of Cell Interaction Based Vedic Multiplier Using Quantum-Dot Cellular Automata." Electronics 9, no. 6 (June 23, 2020): 1036. http://dx.doi.org/10.3390/electronics9061036.

Full text

Abstract:

A multiplier is one of the main units for digital signal processing and communication systems. In this paper, a high speed and low complexity multiplier is designed on the basis of quantum-dot cellular automata (QCA), which is considered promising nanotechnology. We focus on Vedic multiplier architectures according to Vedic mathematics from ancient Indian sculptures. In fact, an adder is an important block in the design of almost all types of multipliers and a ripple carry adder is used to design simple multiplier implementations. However, a high-speed multi-bit multiplier requires high-speed adder owing to carry propagation. Cell-interaction-based QCA adders have better improvements over conventional majority-gate-based adders. Therefore, a two-bit Vedic multiplier is proposed in QCA and it is used to implement a four-bit form of the multiplier. The proposed architecture has a lower cell count and area compared to other existing structures. Moreover, simulation results demonstrate that the proposed design is sustainable and can be used to realize complex circuit designs for QCA communication networks.

APA, Harvard, Vancouver, ISO, and other styles

26

Mak, Bill M. "The Date and Nature of Sphujidhvaja’s Yavanajātaka Reconsidered in the Light of Some Newly Discovered Materials." History of Science in South Asia 1 (May 1, 2013): 1. http://dx.doi.org/10.18732/h2rp4t.

Full text

Abstract:

Since Pingree's 1978 publication of his work on the Yavanajātaka, the text had established itself as one of the most important historical documents in various fields of Indology, from the history of mathematics and astral science, to Indian chronology and historical contacts among ancient cultures. A number of Pingree's discoveries concerning the text were widely quoted by scholars in the past decades. These discoveries may be summarized as follows: The Yavanajātaka was an astrological/astronomical work composed in 269/270 CE. by Sphujidhvaja, an "Indianized Greek" who lived in the realm of the Western Kṣatrapas. The work was a versification of a prose original in Greek composed by Yavaneśvara in Alexandria in 149/150 CE. The work, though highly corrupted and clumsily expressed, contains algorithms of "ultimately Babylonian origin" and the earliest reference to the decimal place-value with a symbol for zero (bindu). Pingree's discoveries were based largely on readings from the last section of the Yavanajātaka, described by him as "Chapter 79 - Horāvidhiḥ", an exposition of mathematical astronomy. In the recent years, scholars including Shukla (1989) and Falk (2001) pointed out some major flaws in some of Pingree's interpretations and reconstitution of the text. However, further progress of a proper reevaluation of the controversial contents of this chapter has so far been hampered by the lack of a better manuscript. In 2011-2012, additional materials including a hitherto unreported copy of the Yavanajātaka became available to the present author. This paper will therefore be the first attempt to reexamine Pingree's key interpretations of the Yavanajātaka, focusing on this last chapter, in the light of the new textual evidences.

APA, Harvard, Vancouver, ISO, and other styles

27

Amirbekian, Raisa. "Les Sujets Soufis Dans la Miniature Medievale Orientale (Collection du Maténadaran, Erevan)." Iran and the Caucasus 11, no. 1 (2007): 61–87. http://dx.doi.org/10.1163/157338407x224914.

Full text

Abstract:

AbstractThe Matenadaran, Mashtots Institute of Ancient Manuscripts, is a unique repository of Armenian and Oriental manuscripts. The Oriental Collection of the Matenadaran (known usually as Arabo-Persian Collection), including manuscripts in Persian, Arabic, Turkish, Hebrew, Indian and other languages (total ca. 2,500), is formed over a long time and is regularly augmented by purchases and gifts. This collection covers nearly all subjects of human and natural sciences and culture, including theology, jurisprudence, Qur'ānic sciences, Tafsīrs, Hadīthes, lexicography, literature, poetry, history, politics, philosophy, logic, astronomy, magic, mathematics, medicine, veterinary, and agriculture. Among them there are some Sufi codices from the period of the 15th to the 19th century, illustrated and illuminated in the various ateliers in Iran and the region. The article presents the analysis of some Oriental medieval miniatures from the Matenadaran Collection connected with the Sufi motifs in their compositions. The most important are illustrative cycles of a copy dating back to 1848-1849 of the Commentaries of the Seven Qasidas by Husayn Ibn Ahmad al-Zuzani (Ms. no. 1610); of the Afghan manuscript of the 18th century Gulshan-i Afghan by 'Ali Akbar Oraqzay (Ms. no. 538); of a manuscript (no. 599) dated from 1841-1842 and containing the poem Yusuf va Zuleykha by 'Abd ul-Rahman Djami; and of a manuscript of 1629 (no.1036), the travel diary of the Iranian diplomat Muhammad 'Ali Bek Isfahani; as well a number of single miniature compositions from the collection of Louise Aslanian (Paris) (no.1999).

APA, Harvard, Vancouver, ISO, and other styles

28

Abdul Rasheed, Mohammed Aref, Murtaza M. Junaid Farooque, Haridas S. Acharya, and Mohammed Sharique A. Quadri. "Mathematical Modelling of the Relationship between Two Different Temperament Classifications: During the Covid-19 Pandemic." Emerging Science Journal 5, no. 1 (February 1, 2021): 67–76. http://dx.doi.org/10.28991/esj-2021-01258.

Full text

Abstract:

In medicine, it is well known that healthy individuals have different physical and mental characteristics. Ancient Indian medicine, Ayurveda and the Persian-Arabic traditional Unani medicine has two distinct approaches for the classification of human subjects according to their temperaments. The individual temperament is an important foundation for personalized medicine, which can help in the prevention and treatment of many diseases including COVID-19. This paper attempts to explore the relationship of the utmost important concepts of these systems called individual temperament named as Prakruti in Ayurveda and Mizaj in Unani practice using mathematical modelling. The results of mathematical modelling can be adopted expediently for the development of algorithms that can be applied in medical informatics. For this, a significant literature review has been carried out. Based on the previous researchers' reviews the essential parameters have been identified for making the relationship and hypothesis were framed. The mathematical modelling was adopted to propose the existence of the relationship between the parameters of such an ancient and rich medicine systems. The hypotheses are validated through the mathematic driven model. Doi: 10.28991/esj-2021-01258 Full Text: PDF

APA, Harvard, Vancouver, ISO, and other styles

29

Lee-Chua, Queena N. "Mathematics in Tribal Philippines and Other Societies in the South Pacific." Mathematics Teacher 94, no. 1 (January 2001): 50–55. http://dx.doi.org/10.5951/mt.94.1.0050.

Full text

Abstract:

Many history-of-mathematics textbooks begin with the four ancient centers of civilization: Egypt, with its pyramids and Rhind papyri; Babylon, with its cuneiform blocks and sexagesimal system; China, with its magic squares and arithmetic classics; and India, with its Sanskrit manuscripts and numeral system. The focus then shifts chronologically to Greek geometry, Arab algebra, Renaissance calculus, nineteenth-century specializations, and finally, the technologically aided wonders of our present age.

APA, Harvard, Vancouver, ISO, and other styles

30

Chandel, Ekta, and Vivek Vijay. "Yagya Kunds of one-hast (24 angul) with different shapes have equal volume." Interdisciplinary Journal of Yagya Research 3, no. 2 (January 7, 2021): 01–08. http://dx.doi.org/10.36018/ijyr.v3i2.60.

Full text

Abstract:

Yagya kund construction is the outcome of great research of ancient India. Indian scripture has given very sophisticated Vedic mathematical formulations for construction of Yagya kund. There are different types of shapes described for Yagya kund; Circular & Lotus, Semi-circular, Vulvar, Trigonal, Square, Pentagonal, Hexagonal, Heptagonal, Octagonal. Irrespective of shapes,all these Yagya kunds have same surface area. Based on the fact given in the literature, 1000 offerings (ahutis) require construction of BhuHastatmakaKund (1 hand or 24 angul long). In addition, height of the all one-hand long kunds are same. Hence, the present research tests the hypothesis that the volume should be same for all different shaped kunds. In the present study, the volume of 1 hast Yagya kund (24 angul) for all these shapes is calculated using the dimensions given in the scripture using available simple available mathematical formulas. Volume of all these kunds is compared with circular shape kund. The difference in the volume of different shapes is foundbelow 0.3% in all the kunds except for vulvar, pentagonal and octagonal shapes which is observed to be 7.48%, 1.76% and 2.83% respectively. The difference isdueto inappropriate mathematical formula for these complex structures having different angles in the slants and multiple sides of the bases.

APA, Harvard, Vancouver, ISO, and other styles

31

Denisov, D. V., and Kh D. Lamazhapov. "THE INTEGER MODELING OF MACROPROCESSES: ANCIENT AND MODERN APPROACHES." Izvestiya of the Samara Science Centre of the Russian Academy of Sciences. Social, Humanitarian, Medicobiological Sciences 22, no. 74 (2020): 85–92. http://dx.doi.org/10.37313/2413-9645-2020-22-74-85-92.

Full text

Abstract:

This paper aims rehabilitation of the ancient ideas about the world, which have an integer expression in the eyes of the scientific community, and their return to the conceptual apparatus of modern science. Integer modeling, apart from mathematical programming, can be found in the systems of microelements of activity, as well as in ancient myths of creation and numerical models of being. Different ways of structuring 10-element integrity reflect the levels of its system arrangement in the Pythagorean tetractys, the Sephiroth tree of the Jewish Kabbalah, in the Old Indian Saankhya. The structure of the Pythagorean tetraktis is found in the fractal-cluster model, but the relative units of value, that make it up, have the traditional decimal or percentage expression.

APA, Harvard, Vancouver, ISO, and other styles

32

Abshire, Corey, Anthony Durham, Dmitri A. Gusev, and Sergey K. Stafeyev. "Ptolemy's Britain and Ireland: A New Digital Reconstruction." Proceedings of the ICA 1 (May 9, 2018): 1–6. http://dx.doi.org/10.5194/ica-proc-1-1-2018.

Full text

Abstract:

In this paper, we expand application of our mathematical methods for translating ancient coordinates from the classical Geography by Claudius Ptolemy into modern coordinates from India and Arabia to Britain and Ireland, historically important islands on the periphery of the ancient Roman Empire. The methods include triangulation and flocking with subsequent Bayesian correction. The results of our work can be conveniently visualized in modern GIS tools, such as ArcGIS, QGIS, and Google Earth. The enhancements we have made include a novel technique for handling tentatively identified points. We compare the precision of reconstruction achieved for Ptolemy's Britain and Ireland with the precisions that we had computed earlier for his India before the Ganges and three provinces of Arabia. We also provide improved validation and comparison amongst the methods applied. We compare our results with the prior work, while utilizing knowledge from such important ancient sources as the Antonine Itinerary, Tabula Peutingeriana, and the Ravenna Cosmography. The new digital reconstruction of Claudius Ptolemy's Britain and Ireland presented in this paper, along with the accompanying linguistic analysis of ancient toponyms, contributes to improvement of understanding of our cultural cartographic heritage by making it easier to study the ancient world using the popular and accessible GIS programs.

APA, Harvard, Vancouver, ISO, and other styles

33

Gager, Philip C., and Mark B. Shackleton. "A snakes and ladders representation of stock prices and returns." Mathematical Gazette 95, no. 533 (July 2011): 177–85. http://dx.doi.org/10.1017/s0025557200002874.

Full text

Abstract:

Snakes and ladders is an ancient Indian game of chance that offers amusement as well as a metaphor for life's many ups and downs. Games offer useful and fun ways of conveying ideas as well as solution techniques and this game has considerable mathematical tractability.This note shows how snakes and ladders can be used to represent the ups and downs of share ownership and determine fair values of a multistage project that pays fixed dividends at uncertain completion times and has random returns

APA, Harvard, Vancouver, ISO, and other styles

34

Gurm, H. S. "Teaching of Astronomy in India." International Astronomical Union Colloquium 105 (1990): 389–93. http://dx.doi.org/10.1017/s0252921100087340.

Full text

Abstract:

Studies of the skies have dominated intellectual activities since ancient man. In this respect, India has a very long tradition of such recorded activity, covering the observations of celestial bodies both as a science and as mythology (Gurm, 1980). The first half of the Christian era witnessed the evolution of spherical astronomy as a part of the study of mathematics (algebra and trigonometry) and its application to astrology. The evolution of spherical astronomy culminated in the concrete manifestation in the northern parts of India in the form of Jantar-Mantars by Raja Jai Singh (Mayer, 1979) in the early eighteenth century. Interestingly, spherical astronomy remained one of the most important activities in the study of astronomy during the British period too. Some of the older treatises on this subject during the nineteenth century were written in the Offices of the Survey of India.

APA, Harvard, Vancouver, ISO, and other styles

35

Lloyd, Geoffrey. "After Joseph Needham: The legacy reviewed, the agenda revised – some personal reflections." Cultures of Science 3, no. 1 (March 2020): 11–20. http://dx.doi.org/10.1177/2096608320917579.

Full text

Abstract:

We all owe Joseph Needham an immense debt for discovering Chinese science and technology for Western scholars. But his famous question (Why did the Chinese, who had been so far in advance of Europe until the 17th century, fail to produce modern science independently?) is simplistic. Needham’s discussion relied on categories (‘physics’, ‘engineering’, even ‘mathematics’) that are largely anachronistic. He was preoccupied by questions of priorities (who did what first). We should recognise that the historical record brings to light many breakthroughs in the development of science, in Egypt, Mesopotamia, India, ancient Greece and ancient China, as well as in Europe in the 17th century and beyond; they all call for detailed analysis of the different social, political, economic, institutional and intellectual factors at work. One topic of particular importance and current interest concerns the factors that enable innovation to flourish, where the differing experience of ancient societies can provide lessons that may still be relevant today. The new agenda for the history of science should have a global remit.

APA, Harvard, Vancouver, ISO, and other styles

36

Dorner, Bryan C. "More Meaning From the Geometric Mean." Mathematics Teacher 96, no. 2 (February 2003): 142–46. http://dx.doi.org/10.5951/mt.96.2.0142.

Full text

Abstract:

We are all familiar with the average, or arithmetic mean, of two numbers. Less frequently used is the notion of the geometric mean. In “Geometric Meaning in the Geometric Mean Means More Meaningful Mathematics” in the March 2001 issue of the Mathematics Teacher, Matt E. Fluster shows how the geometric mean, s = _ab, of two positive numbers, a and b, can be used in a first-year algebra course to tie together geometric, algebraic, and computational investigations. In this article, I add a bit of history and an example suitable for more advanced courses. The example uses the geometric mean to compute square roots with Newton's method and does not require calculus. The history surrounding these concepts provides an opportunity to point out the universal nature of mathematics as a human activity. The basic ideas in this article were alive in the minds of ancient peoples who lived in what are now India, Pakistan, Iraq, and Egypt.

APA, Harvard, Vancouver, ISO, and other styles

37

Sharma, S. D. "Periodic Nature of Cometary Motions as Known to Indian Astronomers Before Eleventh Century A.D." International Astronomical Union Colloquium 91 (1987): 109–12. http://dx.doi.org/10.1017/s0252921100105925.

Full text

Abstract:

AbstractApparitions of comets were thought to be a bad omen in earlier times in almost all the old civilizations. This led to correlating these apparitions with some particular events which took place simultaneously. Although the information was collected and recorded merely for astrological purposes, yet these records are in no way less important from astronomical points of view. Ancient Indian astronomers like Garga, Marīci, Asita, Devala and others made cometary studies and recorded their trajectories(Bṛhat-saṃhitā, Chapter on Ketucārādhyāya).In earlier times there was a notion that the comets were heavenly bodies and their apparitions, paths, rising and setting in the sky, could not be found out by mathematical calculations as is clear from the following śloka(Bṛhat-saṃhitā, Chapter on Ketucārā dhyāya).

APA, Harvard, Vancouver, ISO, and other styles

38

Pinchback, C. L., and Damber S. Tomer. "A Multiplication Algorithm for Two Integers." Mathematics Teacher 95, no. 1 (January 2002): 37–39. http://dx.doi.org/10.5951/mt.95.1.0037.

Full text

Abstract:

The term Vedic mathematics usually refers to a set of sixteen word formulas, or sutras, along with their corollaries, that have origin in the Vedas. The Vedas are ancient holy texts from India that can be characterized as the allencompassing repository of Hindu knowledge from eons past. The Urdhva-tiryagbhyam sutra, or algorithm, has similarities to the FOIL (first, outer, inner, last) method that is used in algebra to multiply two binomials. We first illustrate this sutra with examples. Then we focus on similarities between Urdhva-tiryagbhyam and the standard multiplication algorithm, justifications for it, and student projects that relate to this algorithm.

APA, Harvard, Vancouver, ISO, and other styles

39

Warnaby, John. "James Wood's ‘Stoicheia’ and ‘Oreion’." Tempo, no. 172 (March 1990): 20–25. http://dx.doi.org/10.1017/s004029820006109x.

Full text

Abstract:

Although James Wood has been in the forefront of contemporary music as both choral conductor and percussionist, directing the New London Chamber Choir in many new works, and organizing the Darmstadt Summer School Percussion Course for several years, his own compositions have little in common with the mainstream of postwar European music. It might be assumed that his interest in ancient Greek rhythms, together with their Indian and Chinese equivalents, stems from his association with the music of Xenakis; but he has never shown any inclination to use complex mathematical formulae, and has probably been less concerned than almost any other contemporary composer with the organization of pitch.

APA, Harvard, Vancouver, ISO, and other styles

40

Saraswathi, N., Lokesh Modi, and Aatish Nair. "Complex Number Vedic Multiplier and its Implementation in a Filter." International Journal of Engineering & Technology 7, no. 2.24 (April 25, 2018): 336. http://dx.doi.org/10.14419/ijet.v7i2.24.12078.

Full text

Abstract:

Complex numbers multiplication is a fundamental mathematical process in systems like digital signal processors (DSP). The main objective of complex number multiplication is to perform operations at lightning fast speed with less intake of power. In this paper, the best possible architecture is designed for a Real vedic multiplier based on the ancient Indian mathematical procedure known as URDHVA TIRYAKBHYAM SUTRA i.e. the structure of a MxM Vedic real multiplier architecture is developed. Then, a Vedic real multiplier solution of a complex multiplier is presented and its simulation results are obtained. The MxM Vedic real multiplier architecture, architecture of the Real Vedic multiplier solution for 32 x 32 bit complex numbers multiplication of complex multiplier and the architecture of a FIR filter has been code in Verilog and implementation is done through Modelsim 5.6 and Xilinx ISE 7.1 navigator.

APA, Harvard, Vancouver, ISO, and other styles

41

Melo, Helena de Fátima Sousa, and Maria do Carmo Carvalho Sousa da Cunha Martins. "Estratégias e Metodologias para o Ensino-Aprendizagem da Operação Aritmética da Multiplicação utilizando Tópicos da História da Matemática." História da Ciência e Ensino: construindo interfaces 20 (December 29, 2019): 381–94. http://dx.doi.org/10.23925/2178-2911.2019v20espp381-394.

Full text

Abstract:

Resumo As dificuldades no ensino-aprendizagem das operações aritméticas podem interferir na aquisição de algumas competências matemáticas básicas e, de certo modo, influenciar futuros processos de cálculo. Uma abordagem diferente, como a utilização de tópicos de História da Matemática, pode revelar-se uma boa estratégia para motivar os alunos e encaminhá-los para um conhecimento eficaz das referidas operações. Muitos foram os povos que aplicaram técnicas, processos, métodos e algoritmos na resolução de problemas do quotidiano ao longo da história. A Matemática de então tinha um cunho mais prático do que teórico, que decorria diretamente das necessidades diárias. Abordando estes meios ancestrais podemos cativar e estimular os alunos para as operações aritméticas, nomeadamente, a operação de multiplicação.Neste trabalho descrevemos o modo como alguns povos procediam à operação de multiplicação, bem como os métodos usados para tal, nomeadamente: a duplicação no Antigo Egito; a gelosia e o zigzag na India medieval; os bastões de Napier; a multiplicação com as mãos no Renascimento; e o processo de multiplicação do povo Yoruba.A utilização de diversos ábacos e o uso de outros materiais de efeito similar, como os bastões de Napier, podem ser um excelente complemento às estratégias para a aprendizagem da operação de multiplicação. Palavras-chave: operação de multiplicação; história da matemática Abstract The difficulties in teaching-learning of arithmetic operations can interfere with the acquisition of some basic mathematical skills and, in a way, influence future computation processes. A different approach, such as the use of topics in the History of Mathematics, may prove to be a good strategy to motivate students and direct them to an effective knowledge of such operations. Many people have applied techniques, processes, methods, and algorithms to solve everyday problems throughout history. The Mathematics of that time had a more practical rather than a theoretical character, which came directly from the daily necessities. Approaching these ancestral techniques, we can call attention for and stimulate students for arithmetic operations, namely, the multiplication operation. In this presentation we present the way in which some people performed the multiplication operation, as well as the methods used for such: duplication in Ancient Egypt; “gelosia” and zigzag in medieval India; Napier's bones; multiplication with hands in the Renaissance; and the multiplication process of the Yoruba people. The use of several abacuses and of other materials of similar effect, such as the Napier rods, can be an excellent complement to the strategies for learning the multiplication operation. Keywords: multiplication operation; History of Mathematics

APA, Harvard, Vancouver, ISO, and other styles

42

Bhadwal, Neha, Prateek Agrawal, and Vishu Madaan. "A Machine Translation System from Hindi to Sanskrit Language using Rule based Approach." Scalable Computing: Practice and Experience 21, no. 3 (August 1, 2020): 543–54. http://dx.doi.org/10.12694/scpe.v21i3.1783.

Full text

Abstract:

Machine Translation is an area of Natural Language Processing which can replace the laborious task of manual translation. Sanskrit language is among the ancient Indo-Aryan languages. There are numerous works of art and literature in Sanskrit. It has also been a medium for creating treatise of philosophical work as well as works on logic, astronomy and mathematics. On the other hand, Hindi is the most prominent language of India. Moreover,it is among the most widely spoken languages across the world. This paper is an effort to bridge the language barrier between Hindi and Sanskrit language such that any text in Hindi can be translated to Sanskrit. The technique used for achieving the aforesaid objective is rule-based machine translation. The salient linguistic features of the two languages are used to perform the translation. The results are produced in the form of two confusion matrices wherein a total of 50 random sentences and 100 tokens (Hindi words or phrases) were taken for system evaluation. The semantic evaluation of 100 tokens produce an accuracy of 94% while the pragmatic analysis of 50 sentences produce an accuracy of around 86%. Hence, the proposed system can be used to understand the whole translation process and can further be employed as a tool for learning as well as teaching. Further, this application can be embedded in local communication based assisting Internet of Things (IoT) devices like Alexa or Google Assistant.

APA, Harvard, Vancouver, ISO, and other styles

43

Seyidbeyli, Maryam. "Life and activity of Nasir al-Din al-Tusi." History of science and technology 10, no. 2 (December 12, 2020): 353–67. http://dx.doi.org/10.32703/2415-7422-2020-10-2-353-367.

Full text

Abstract:

At the beginning of the VII century in the political life of the Near and Middle East, fundamental changes have taken place. The Arabs conquered a colossal territory, which included the lands of Iran, North Africa, North-West India, the Asian provinces of Byzantium, most of the former Roman Empire. In the conquered cities of the caliphate, observatories, madaris, libraries were built. At the end of VII century, the first scientific center, an academy, the House of Wisdom, was founded in Baghdad, in which scholars who spoke different languages were assembled. Here the translation and commentary activity were very developed, the main works of ancient thought, such as the writings of Aristotle, Ptolemy were published in the 9th century in the Arabic-speaking world. For two centuries from 750 to 950 years, the works of ancient authors on philosophy, mathematics, medicine, alchemy, and astronomy were translated into Arabic, which indicates the high scientific potential of that time in the East. At the same time, in the XII century, Ibn Rushd composed 38 commentaries on the works of Aristotle, the “Republic” of Plato, the treatise “On the Mind” of Alexander of Aphrodisias, which subsequently had an important influence on the work of Nasir al-Din al-Tusi. Thus, this period in the history of Eastern scientific thought is marked by high intellectual potential. To this day, historians of medieval Arabic literature face a sufficient number of difficulties, since the vast majority of manuscripts remain inaccessible to them. The works of many renowned Arab authors of the middle Ages are more than 1000 years old, so it seems obvious that the manuscripts of the vast majority of authors have not survived to this day. The researchers of the history of Azerbaijan and neighboring countries in the middle Ages, with all the variety of available sources on which they rely, still attract little factual material related to the Arabic-language works of the historical and scientific genre. Undoubtedly, a comprehensive study of the entire complex of information of Nasir al-Din al-Tusi on the history of science in Azerbaijan is of great importance.

APA, Harvard, Vancouver, ISO, and other styles

44

Chornaya, O. A., and T. P. Yegorova. "Gravity field of Sarmatia according to satellite data (model EIGEN-6S2) and its interpretation." Geofizicheskiy Zhurnal 43, no. 3 (July 28, 2021): 47–63. http://dx.doi.org/10.24028/gzh.v43i3.236380.

Full text

Abstract:

The paper presents a brief overview of satellite observations of the CHAMP, GRACE and GOCE missions to study the Earth’s global gravity field, and the used mathematical apparatus in the form of an expansion of the geopotential in spherical harmonics. The application of satellite data in various fields of Earth Sciences is considered. As a basic global model of the Earth’s gravity field based on satellite data we used the EIGEN-6S2 model [Rudenko et al, 2014] that combines satellite mission data GRACE and GOCE, and also uses satellite data of LAGEOUS laser ranging. On its basis, the gravity field of Sarmatia was analyzed using the Free Air anomalies, Bouguer anomalies, the second radial derivative of the geopotential and the geoid heights. The geological units of Sarmatia and its surroundings are most clearly manifested in the Free Air anomalies and in the distribution of the second derivative of the geopotential, showing differences in the gravity field pattern of the Ukrainian Shield, the Voronezh Massif, and the Pripyat-Dnieper-Donets basin (PDDB) with characteristic anomalies of the general northwest strike. The continuation of the PDDB in a southeastern direction through the Karpinsky Swell to the northern part of the Caspian Sea confirms the existence of an extended ancient tectonic zone of the Sarmato-Turanian lineament. The geoid within Sarmatia shows in general a regional west-east gradient change from +40 m in the west to -10 m in the east. Such large-scale geoid changes are determined by the Sarmatia position between two global geoid anomalies — the maximum of the North Atlantic and the minimum of the Indian Ocean.

APA, Harvard, Vancouver, ISO, and other styles

45

Ravi, P., C. Naveena, and Y. H. Sharath Kumar. "Deep Learning in Historical Kannada Document." Journal of Computational and Theoretical Nanoscience 17, no. 9 (July 1, 2020): 4111–15. http://dx.doi.org/10.1166/jctn.2020.9028.

Full text

Abstract:

Kannada is one of the famous ancient languages of the India and the official language of the State of Karnataka, which has a very large heritage. The digital analysis of these historical Kannada documents will provide us information about the culture and traditions that were practiced. Retrieving such information from paper documents, palm leaves or from stone carvings will enhance our knowledge. Investigating Historical document isn’t straight advance procedure because of low quality, differentiation, contrast and covering of characters. In this analysis, the authors propose a novel Scale invariant Feature Transform (SIFT) with deep learning classifier to recognize Historical kannada characters. To begin with, the character is divided utilizing Connected Component Analysis and later the Different SIFT Features are detached. At long last, form a powerful convolutional neural system classifier to recognize the Historical kannada archives. Proposed tale schemes during the preprocessing stage to guarantee strong, precise and constant grouping. They assess their strategy all alone datasets their characterization results surpass 97% on all datasets, which are superior to the cutting edge in this space.

APA, Harvard, Vancouver, ISO, and other styles

46

Vasechko, V. Yu. "Epistemological Discourse in a Politarial Society: Conceptual Opposition “Cognitive” – “Ritual”." Concept: philosophy, religion, culture, no. 3 (November 17, 2019): 18–26. http://dx.doi.org/10.24833/2541-8831-2019-3-11-18-26.

Full text

Abstract:

The article describes the socio-cultural situation in which the individual professionally working on scientific and mathematical problems turns out in politary society (ancient Egypt and Babylon, India and China, medieval Arab-Muslim world, etc.). It focuses on the complex relationship between scientists seeking to uncover the mysteries of nature, and the clergy whose aim is complete control of the process and results of any cognitive activities. Hierocratic estate allows research only to the extent that is necessary for the consolidation of its prerogatives and powers. The conflict of these two cognitive trends largely determines the general character and peculiarities of scientific-cognitive activity in these societies. Existing sacral picture of the world is considered as a firm and perfect one, requiring only minor refinements and specifications. While rituals, committed by clergy, positioned as a necessary condition for the preservation of the natural and social world order. On the contrary, sovereign scientific discourse implies that scientist has a right on free revision of existing views as about the world in general and about specific details of its devices and evolution. The scientist also should not be restricted in finding and applying specific means and methods of cognition of truth. Accordingly, the performance of rituals cannot play a significant role in the picture of the world which is created by scholar’s work. Patterns found in the natural processes are independent from actions committed by various people, including the sacred ceremonies of both ordinary and very senior individuals of spiritual title. Proto-scientific concepts of the universe and particular consequents from them are treated by hierocracyas godless and heretical. In the absence of adequate empirical and theoretical arguments, priests and theologians have to resort in struggle against scholar’s freethinking to force “arguments”. But scientists under favorable conditions can successfully resist this pressure and continue their professional work.

APA, Harvard, Vancouver, ISO, and other styles

47

Banasiak, Jacek. "Foreword to BIOMATH 2017 Proceedings: Some comments on mathematical modelling and biomathematics." Texts in Biomathematics 1 (July 23, 2018). http://dx.doi.org/10.11145/texts.2018.06.107.

Full text

Abstract:

Both biology and mathematics have existed as well established branches of science for hundreds of years and both, maybe not in a well defined way, have been with the humankind for a couple of thousands of years. Though nature was studied by the ancient civilizations of Mesopotamia, Egypt, the Indian subcontinent and China, the origins of modern biology are typically traced back to the ancient Greece, where Aristotle (384-322 BC) contributed most extensively to its development. Similarly, the ancient Babylonians were able to solve quadratic equation over four millennia ago and we can see the development of mathematical methods in all ancient civilisations, notably in China and on the Indian subcontinent. However, possibly again the Greeks were the first who studied mathematics for its own sake, as a collection of abstract objects and relations between them. Nevertheless, despite the fact that the development of such a mathematics has not required any external stimuli, an amazing feature of the human mind is that a large number of abstract mathematical constructs has proved to be very well suited for describing natural phenomena.This prompted Eugene Wigner to write his famous article The Unreasonable Effectiveness of Mathematics in the Natural Sciences, ...

APA, Harvard, Vancouver, ISO, and other styles

48

Awasthi, Jitendra. "The rediscovery of Vedic Ganita." Anusandhaan - Vigyaan Shodh Patrika 4, no. 1 (October 1, 2016). http://dx.doi.org/10.22445/avsp.v4i1.4391.

Full text

Abstract:

From ancient times Mathematics has great importance in India. In the classical period of Indian Mathematics, important contributions were made by scholars like Aryabhatt, Brahmgupta, Mahaveera etc. Later on Shri Bharti Krishna Teert rediscovered the old Mathematics in a new form known as Vedic Ganita.

APA, Harvard, Vancouver, ISO, and other styles

49

Kowalski, Jean-Marie. "Sailing the Indian Ocean in Ancient Times." Angles, no. 9 (November 1, 2019). http://dx.doi.org/10.4000/angles.800.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Bag, AK. "Book Review: A Selected Works of Gurugovinda Chakravarti on Ancient and Medieval Indian Mathematics." Indian Journal of History of Science 50, no. 1 (March 5, 2015). http://dx.doi.org/10.16943/ijhs/2015/v50i1/48118.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Ancient Indian mathematics'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles