حسابان

Because evolution endowed humans with a complement of ten fingers, a grouping size of ten seems natural to us, perhaps even ideal. But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages. Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each. A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician. Because evolution endowed humans with a complement of ten fingers, a grouping size of ten seems natural to us, perhaps even ideal. But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods,__Arithmetic__invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician. Educator Paul Lockhart's Goal Is To Demystify Arithmetic: To Bring The Subject To Life In A Fun And Accessible Way, And To Reveal Its Profound And Simple Beauty, As Seen Through The Eyes Of A Modern Research Mathematician. The Craft Of Arithmetic Arises From Our Natural Desire To Count, Arrange, And Compare Quantities. Over The Centuries, Humans Have Devised A Wide Variety Of Strategies For Representing And Manipulating Numerical Information: Tally Marks, Rocks And Beads, Marked-value And Place-value Systems, As Well As Mechanical And Electronic Calculators. Arithmetic Traces The History And Development Of These Various Number Languages And Calculating Devices And Examines Their Comparative Advantages And Disadvantages, Providing Readers With An Opportunity To Develop Not Only Their Computational Skills But Also Their Own Personal Tastes And Preferences. The Book Is Neither A Training Manual Nor An Authoritative History, But Rather An Entertaining Survey Of Ideas And Methods For The Reader To Enjoy And Appreciate. Written In A Lively Conversational Style, Arithmetic Is A Fun And Engaging Introduction To Both Practical Techniques As Well As The More Abstract Mathematical Aspects Of The Subject.-- Things -- Language -- Repetition -- Tribes -- Egypt -- Rome -- China And Japan -- India -- Europe -- Multiplication -- Division -- Machines -- Fractions -- Negative Numbers -- The Art Of Counting. Paul Lockhart. Includes Index. Educator Paul Lockhart's goal is to demystify arithmetic: to bring the subject to life in a fun and accessible way, and to reveal its profound and simple beauty, as seen through the eyes of a modern research mathematician. The craft of arithmetic arises from our natural desire to count, arrange, and compare quantities. Over the centuries, humans have devised a wide variety of strategies for representing and manipulating numerical information: tally marks, rocks and beads, marked-value and place-value systems, as well as mechanical and electronic calculators. Arithmetic traces the history and development of these various number languages and calculating devices and examines their comparative advantages and disadvantages, providing readers with an opportunity to develop not only their computational skills but also their own personal tastes and preferences. The book is neither a training manual nor an authoritative history, but rather an entertaining survey of ideas and methods for the reader to enjoy and appreciate. Written in a lively conversational style, Arithmetic is a fun and engaging introduction to both practical techniques as well as the more abstract mathematical aspects of the subject.-- Provided by publisher Paul Lockhart reveals arithmetic not as the rote manipulation of numbers but as a set of ideas that exhibit the surprising behaviors usually reserved for higher branches of mathematics. In this entertaining survey, he explores the nature of counting and different number systems—Western and non-Western—and weighs the pluses and minuses of each.