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.

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.

Mathematics in Egypt

2018 ◽  
pp. 48-60
Author(s):  
Annette Imhausen
Keyword(s):  
Number System ◽  
Place Value ◽  
High Status ◽  
Decimal System ◽  
Unit Fractions ◽  
Essential Tool ◽  
Mathematical Texts

This chapter studies Egyptian mathematics, an essential tool to administer resources, from the invention of the script and number system, ca 3000 bce. Egyptian writing was a tool restricted to the elites. Their number system was a decimal system without positional (place-value) notation. Their concept of unit fractions, as the inverses of integers, was fundamentally different from ours; other fractional values were expressed as a sum of unit fractions. The few surviving mathematical texts contain a collection of problems or tables to aid in calculations, or actual worked calculations, or a mixture of these. Some scribes had high status, based explicitly on the numerate activity of calculating taxes owed and work produced. Later Egyptian mathematics displays Mesopotamian influences.

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.

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

scholarly journals Incentive Function of Audit Opinion for the Increase of Regional Operational Expenditure and Own-Source Revenues Through Sensitivity Analysis in Indonesia

2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Muhammad Ikbal Abdullah ◽  
Andi Chairil Furqan ◽  
Nina Yusnita Yamin ◽  
Fahri Eka Oktora
Keyword(s):  
Sensitivity Analysis ◽  
Significant Influence ◽  
Provincial Government ◽  
Sensitivity Testing ◽  
Audit Opinion ◽  
Absolute Value ◽  
Operating Expenditure ◽  
The Absolute ◽  
Operational Expenditure

This study aims to analyze the sensitivity testing using measurements of realization of regional own-source revenues and operating expenditure and to analyze the extent of the effect of sample differences between Java and non-Java provinces by using samples outside of Java. By using sensitivity analysis, the results found the influence of audit opinion on the performance of the provincial government mediated by the realization of regional operating expenditure. More specifically, when using the measurement of the absolute value of the realization of regional operating expenditure it was found that there was a direct positive and significant influence of audit opinion on the performance of the Provincial Government. However, no significant effect of audit opinion was found on the realization value of regional operating expenditure and the effect of the realization value of regional operating expenditure on the performance of the Provincial Government. This result implies that an increase in audit opinion will be more likely to be used as an incentive for the Provincial Government to increase the realization of regional operating expenditure.

Die Bedeutung der Homogenisationsart und -intensität für die Größe und Konstanz der Sauerstoffaufnahme von Meerschweinchen-Leberhomogenat / The Influence of Mode and Intensity of Homogenization on the Absolute Value and Stability of Oxygen Consumption of Guinea Pig Liver Homogenates

1977 ◽  
Vol 32 (11-12) ◽  
pp. 908-912 ◽  
Author(s):  
H. J. Schmidt ◽  
U. Schaum ◽  
J. P. Pichotka
Keyword(s):  
Oxygen Uptake ◽  
Guinea Pig ◽  
Measuring Time ◽  
Pig Liver ◽  
Absolute Value ◽  
Modified Method ◽  
Simultaneous Measurements ◽  
Liver Homogenates ◽  
The Absolute ◽  
Guinea Pig Liver

Abstract The influence of five different methods of homogenisation (1. The method according to Potter and Elvehjem, 2. A modification of this method called Potter S, 3. The method of Dounce, 4. Homogenisation by hypersonic waves and 5. Coarce-grained homogenisation with the “Mikro-fleischwolf”) on the absolute value and stability of oxygen uptake of guinea pig liver homogenates has been investigated in simultaneous measurements. All homogenates showed a characteristic fall of oxygen uptake during measuring time (3 hours). The modified method according to Potter and Elvehjem called Potter S showed reproducible results without any influence by homogenisation intensity.

Thue equations that simultaneously fail the Hasse principle

2021 ◽  
pp. 1-10
Author(s):  
PALOMA BENGOECHEA
Keyword(s):  
Positive Integer ◽  
Hasse Principle ◽  
Fixed Degree ◽  
Binary Forms ◽  
Absolute Value ◽  
Positive Proportion ◽  
The Absolute

Abstract We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x, y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree ≥ 3 and are ordered by the absolute value of the maximum of the coefficients.

Comparison of the acceleration due to gravity at the National Physical Laboratory, Teddington, the Bureau International des Poids et Mesures, Sèvres, the Physikalisch-Technische Bundesanstalt, Brunswick, and the Geodetic Institute, Potsdam

1952 ◽  
Vol 213 (1114) ◽  
pp. 408-424 ◽  
Keyword(s):  
National Physical Laboratory ◽  
Absolute Value ◽  
Geodetic Institute ◽  
Physical Laboratory ◽  
The Absolute

The values of gravity at these stations have been compared by means of pendulum observations with Invar invariable pendulums. The observed differences of gravity from the National Physical Laboratory are: B. I. P. M. -256·73 ± 0·49 mgal P. T. B. + 68·68 ± 0·49 mgal Bad Harzburg - 15·68 ± 0·49 mgal The accuracy of the measurements is not so great as has been achieved once or twice previously with the same apparatus, mainly because the changes in the lengths of the pendulums were greater than usual. These differences have been combined with German pendulum observations and with gravimeter comparisons with the following results: Value of gravity at N. P. L. on the Potsdam system: 981196·29 ± 0·3 mgal. Differences between sites of absolute determinations of gravity: N. P. L. - B. I. P. M. +256·45 ± 0·3 mgal N. P. L. - P. T. B. - 68·98 ± 0·3 mgal P. T. B. - Potsdam - 8·95 ± 0·4 mgal ( g at Potsdam = 981274 mgal.) The effects of these results on gravity surveys based on Cambridge and on the absolute value of gravity are indicated.

Sign in / Sign up

Export Citation Format

Share Document