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About 10,000 papers for “Arithmetic”

Arithmetic Sequences without Arithmetic Operations

Md. Shouvik Iqbal · Preprints.org · 2024

The generation of arithmetic sequences involves arithmetic operations. However, is it possible to generate such sequences without being subject to any arithmetic or related operations, all by just hand? The answer may be negative, as the very rule defining these sequences itself relies on arithmetic operations. Nonetheless, this paper presents a few results demonstrating that the exact sequences of $an$, where, $a \in \{ 2,3,\cdots,9,10\}$ and $n \in \mathbb N \cup \{0\}$, can indeed be generated up to any desired number of terms without relying on any arithmetic operations and others derived from such. This is done by the formation of a specialized table that leverages numerical patterns and the notion of concatenation.

Cited by 0Open access

Arithmetic and pseudo-arithmetic billiards

P. A. Braun · arXiv (Cornell University) · 2015

The arithmetic triangular billiards are classically chaotic but have Poissonian energy level statistics, in ostensible violation of the BGS conjecture. We show that the length spectra of their periodic orbits divides into subspectra differing by the parity of the number of reflections from the triangle sides; in the quantum treatment that parity defines the reflection phase of the orbit contribution to the Gutzwiller formula for the energy level density. We apply these results to all 85 arithmetic triangles and establish the boundary conditions under which the quantum billiard is \textquotedblleft genuinely arithmetic\textquotedblright, i. e., has Poissonian level statistics; otherwise the billiard is "pseudo-arithmetic" and belongs to the GOE universality class

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Ordinal arithmetic and natural arithmetic

Q.T. Dijkstra · Utrecht University Repository (Utrecht University) · 2020

Starting with the definition of an ordinal number, we develop some of the elementary theory of ordinals, with a focus on ordinal arithmetic. We investigate some of the algebraic and order-theoretic properties of ordinal addition, multiplication, and exponentiation. We then make use of these properties to prove the basis representation theorem for ordinals. This in turn allows us to define first the Cantor normal form and then the operations of natural addition and natural multiplication for ordinals. We briefly compare the algebraic properties of conventional ordinal arithmetic to those of natural arithmetic. In the appendices we briefly discuss the construction of the least infinite ordinal as well as a proof of the transfinite recursion theorem for ordinals.

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Arithmetic

American Mathematical Monthly · 1894

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Arithmetic

Geoff Renshaw · Oxford University Press eBooks · 2021

This chapter revises the basic concepts of numbers and operations with them. It looks at positive and negative numbers, fractions, decimals, and percentages. It also reviews powers, such as squares and cubes, and square roots and cube roots. Basic operations of addition, subtraction, multiplication, and division, as well as finding powers and roots are reviewed and how these operations are performed with pen and ink only, and with the aid of a calculator.

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Arithmetic

Jean-Baptiste le Rond d'Alembert (biography), David Fleming · The Journal of the Abraham Lincoln Association

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Arithmetic.

Daniel Starch · MacMillan Co eBooks · 1921

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Arithmetic

Lawrence M. Leemis · W&M Publish (College of William & Mary) · 2012

Transitioning to Calculus is a comprehensive compilation of the mathematical concepts and formulas that are required of students entering their first class in calculus. The essentials of arithmetic, algebra, geometry, analytic geometry, trigonometry, and complex variables are organized into separate chapters. The purpose of this book is to provide a succinct but comprehensive list of the topics required of students entering calculus. Over 100 figures highlight the intuitive and geometric aspects of the formulas and concepts. Each chapter ends with a series of exercises (with space provided for working out a solution) that are designed to reinforce the application of the concepts and formulas. Complete solutions to the problems are included.

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Arithmetic

eVols (University of Hawaii) · 2023

Wise buying -- Storage -- Handicrafts -- Selling things from the farm -- General problems -- Trochus (yogyog) -- Copra production -- Postage

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Arithmetic

MUELER, FRANCIS J. · Andalas University Repository (Andalas University) · 1964

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Arithmetic

Eugene Herz, Mary G . Brants, George Gailey Chambers · Bulletin of Miscellaneous Information (Royal Gardens Kew) · 1920

Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

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