The Indian Gift

2016 ◽  
Author(s):  
Joseph Mazur
Keyword(s):  
Number System ◽  
Decimal Place ◽  
Place Value ◽  
Ancient India ◽  
Finger Counting ◽  
History Of ◽  
Indian Mathematics

This chapter discusses the legacy of Indian mathematics. With very few archaeological clues, the origins of the Indian numbers must rely on a small wealth of writing that survives almost exclusively in the form of stone inscriptions. Some of those stone epigraphs used decimal place-value numerals, providing some evidence that ancient India was familiar with a kind of place-value numerical system. Some letter combinations of the Sanskrit words for numbers probably contributed suggestive shapes early in the morphographic history of our current script. The chapter first considers the Brahmi number system before turning to modern Hindu-Arabic numerals. It also examines how the Western system of numerals with zero came to be by focusing on finger counting, the dust boards, and the abacus.

The Egyptian Number System

2016 ◽  
Author(s):  
Annette Imhausen
Keyword(s):  
Number System ◽  
Decimal Place ◽  
Place Value ◽  
Decimal System ◽  
Absolute Value ◽  
Ancient Egyptian ◽  
System P ◽  
The Absolute ◽  
The Individual

This chapter describes the ancient Egyptian number system. The system can be described in modern terminology as a decimal system without positional (place-value) notation. The basis of the number system was 10 (hence decimal system), but unlike our decimal place-value notation using the ten numerics 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, in which the absolute value is determined by its position within the number (e.g., in the number 125, the absolute value of 1 is 1 × 102, the absolute value of 2 is 2 × 101, and the absolute value of 5 is 5 × 100), the Egyptian system used individual symbols for each power of 10. Although there is no information about the choice of the individual signs for the respective values, some of them seem plausible choices. The most basic, the simple stroke to represent a unit, is used not only in Egypt but also in a variety of other cultures, possibly originating from marks on a tally stick.

From Middle Horizon cord-keeping to the rise of Inka khipus in the central Andes

Antiquity ◽  
2014 ◽  
Vol 88 (339) ◽  
pp. 205-221 ◽  
Author(s):  
Gary Urton
Keyword(s):  
Number System ◽  
Central Andes ◽  
Decimal Place ◽  
Place Value ◽  
Middle Horizon ◽  
Value System ◽  
Intermediate Period ◽  
Andean South America ◽  
Ams Dating ◽  
Descendant Communities

Recording devices formed of knotted cords, known askhipus, are a well-known feature of imperial administration among the Inka of Andean South America. The origins and antecedents of this recording system are, however, much less clearly documented. Important insights into that ancestry are offered by a group of eight khipus dating from the later part of the Middle Horizon period (AD 600–1000), probably used by the pre-Inka Wari culture of the central Andes. This article reports the AMS dating of four of these early khipus. A feature of the Middle Horizon khipus is the clustering of knots in groups of five, suggesting that they were produced by a people with a base five number system. Later, Inka khipus were organised instead around a decimal place-value system. Hence the Inka appear to have encountered the base five khipus among Wari descendant communities late in the Middle Horizon or early in the Late Intermediate period (AD 1000–1450), subsequently adapting them to a decimal system.

scholarly journals The Date and Nature of Sphujidhvaja’s Yavanajātaka Reconsidered in the Light of Some Newly Discovered Materials

2013 ◽  
Vol 1 ◽  
pp. 1 ◽  
Author(s):  
Bill M. Mak
Keyword(s):  
Present Author ◽  
History Of Mathematics ◽  
Decimal Place ◽  
Historical Documents ◽  
Place Value ◽  
The Past ◽  
Mathematical Astronomy ◽  
History Of

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.

Miscellanea—Mathematical, Historical, Pedagogical

1950 ◽  
Vol 43 (3) ◽  
pp. 120-122
Author(s):  
Phillip S. Jones
Keyword(s):  
Decimal Place ◽  
Place Value ◽  
History Of

In January of 1948 a new footnote, if not a new chapter, was added to the history of π.1 At this time John W. Wrench, Jr., of Washington, D. C., and D. F. Ferguson of Manchester, England, published jointly the corrected and checked value of π computed to 808 decimal places.2 This concludes a project begun by Dr. Ferguson in 1945 when he became interested in the • correctness of the unchecked 707 decimal place value first given by the Englishman William Shanks in 1873 and revised by Shanks himself in 1874.3

HIGHER EDUCATION IN ANCIENT INDIA

2018 ◽  
Vol 6 (26) ◽  
Author(s):  
Satyendra Singh Chahar ◽  
Nirmal Singh
Keyword(s):  
Cultural History ◽  
Early Stage ◽  
University Education ◽  
Educational Institutions ◽  
Educational Method ◽  
Men And Women ◽  
Ancient India ◽  
Herbert Spencer ◽  
History Of ◽  
The Ideal

University education -on almost modern lines existed in India as early as 800 B.C. or even earlier. The learning or culture of ancient India was chiefly the product of her hermitages in the solitude of the forests. It was not of the cities. The learning of the forests was embodied in the books specially designated as Aranyakas "belonging to the forests." The ideal of education has been very grand, noble and high in ancient India. Its aimaccording to Herbert Spencer is the 'training for completeness of life' and ‘the molding o character of men and women for the battle of life’. The history of the educational institutions in ancient India shows a glorious dateline of her cultural history. It points to a long history altogether. In the early stage it was rural, not urban. British Sanskrit scholar Arthur Anthony Macdonell says "Some hundreds of years must have been needed for all that is found" in her culture. The aim of education was at the manifestation of the divinity in men, it touches the highest point of knowledge. In order to attain the goal the whole educational method is based on plain living and high thinking pursued through eternity.

scholarly journals Art. II.—Samudra Gupta (A specimen chapter of the projected Ancient History of Northern India from the Monuments.)

1897 ◽  
Vol 29 (1) ◽  
pp. 19-33
Author(s):  
Vincent A. Smith
Keyword(s):  
Fourth Century ◽  
Ancient History ◽  
The South ◽  
Ancient India ◽  
Northern India ◽  
History Of

The following history of the reign of the great conqueror, Samudra Gupta, who was emperor of Northern India, and made extensive, though temporary, conquests in the south, about the middle of the fourth century of the Christian era, is offered as a specimen of the author's projected “Ancient History of Northern India from the Monuments.” Though that projected history may never be completed, I venture to think that fragments of it may not be altogether valueless, and that they may suffice to prove that even now the materials exist for the construction of an authentic and fairly readable “History of Ancient India.”

Multiplication by 10 base-5: Making Sense of Place Value Structure Through an Alternate Base

2015 ◽  
Vol 3 (2) ◽  
pp. 83-98
Author(s):  
Jodi Fasteen ◽  
Kathleen Melhuish ◽  
Eva Thanheiser
Keyword(s):  
Preservice Teachers ◽  
Conceptual Understanding ◽  
Sense Of Place ◽  
Number System ◽  
Place Value ◽  
Mathematical Activity ◽  
Making Sense ◽  
Procedural Fluency ◽  
Whole Number

Prior research has shown that preservice teachers (PSTs) are able to demonstrate procedural fluency with whole number rules and operations, but struggle to explain why these procedures work. Alternate bases provide a context for building conceptual understanding for overly routine rules. In this study, we analyze how PSTs are able to make sense of multiplication by 10five in base five. PSTs' mathematical activity shifted from a procedurally based concatenated digits approach to an explanation based on the structure of the place value number system.

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