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Realm of Numbers Hardcover – 1 Jun 1959

4.5 out of 5 stars 2 customer reviews

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Product details

  • Hardcover
  • Publisher: Houghton Mifflin (T) (Jun. 1959)
  • Language: English
  • ISBN-10: 0395065666
  • ISBN-13: 978-0395065662
  • Product Dimensions: 21.6 x 14.2 x 2.3 cm
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Bestsellers Rank: 349,907 in Books (See Top 100 in Books)

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Format: Hardcover
In this book, Asimov takes you through the development of numbers, from the initial set of positive integers through the transfinite alephs. The progression is logical, he first establishes the infinitude of the positive integers and then explains the reasons why negative numbers are needed. Along with the negative integers, he explains the basic rules of addition, subtraction, multiplication and division as applied to integers. Subtraction is used to justify the need for negative integers and then division to explain the need for fractions. Asimov uses the applications for commerce to describe how negative numbers and fractions came to be accepted.
At one point, he argues that the most powerful force driving the development of early mathematics was the need for the rulers of civilization to assess the values of land and collect the appropriate taxes. Interesting thought, and quite likely true. Negative numbers no doubt have their origin in the computation of back taxes and plane geometry and fractions arose from the need to measure and subdivide land. The more complicated computations of the areas of non-rectangular regions also led to the development of a great deal of geometry.
After fractions are covered, he then goes on to explain infinite decimals, starting with those that repeat and then to the ones that do not. Complex numbers are next, although here, he is somewhat limited in the explanation of the details in how arithmetic is done on complex numbers.
Written at the level of the middle school student, Asimov is once again at his best, explaining the various categories of numbers and showing why they are needed in the modern world. This book is very suitable reading for students at that level.
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Format: Mass Market Paperback Verified Purchase
Clear explanations and well written.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 4.5 out of 5 stars 11 reviews
33 of 33 people found the following review helpful
4.0 out of 5 stars What comes after one? 17 Oct. 2008
By Judy K. Polhemus - Published on Amazon.com
"The number sense is not confined to the human race." This is the first sentence in "Realm of Numbers," written by Isaac Asimov.

He goes on to explain that animals can recognize the differences in numbers (I think as a kind of encouragement to those humans who have problems dealing with numbers and mathematics or are clearly math phobes like me.)

Even a math phobe is able to recognize patterns of numbers on the faces of playing cards. As another example of pattern recognition, he gives the situation of Mr. Caveman peering into the cave to check on his two children. However, as the pattern increases, he needs some way to communicate this and so creates names for numbers.

Mr. Caveman has a rack of stone axes--four to be exact, but the pattern shows one is missing. He goes to his neighbor and asks if he borrowed one. Just this simple mathematical problem shows us the necessity of naming numbers.

Now Mr. Caveman must move beyond counting on his fingers to creating and using an abacus. However, Mr. Caveman has Dr. Isaac Asimov to explain the maneuvers to him.

Here are some of the chapter titles to give an idea of Asimov's Big Brain in action:
*Nothing--and Less than Nothing
*By-Passing Addition (make sure you read this line correctly!!)
*Broken Numbers
*The Shape of Numbers (why is he including erotica?--just kidding to see if you are paying attention!)
*Digging for Roots
*The Very Large and Very Small
*Endlessness (what math seems to have to me!)

In the 1950's this book must have been a best seller because my copy is from the 8th printing. Wow!

Honestly, anyone who opens this book to get some help will enter the "Realm of Numbers" where "a clear, imaginative approach to mathematics" can be as easy as 1-2-3. If anything is unclear in this review, blame it on math, not the reviewer.

Note: Any biographical sketch about Dr. Asimov will state that he was a prolific writer who wrote in nine of the ten Dewey Decimal categories. This is my third Asimov review. The first book belonged to the world of science (Dewey 500s) in that it was a book of science terms. The second book is about the meanings of map names and places and their etymologies (Dewey 400s or 900s). This book is about making the use of numbers easier--another 500s category.
5.0 out of 5 stars Five Stars 14 July 2016
By Amazon Customer - Published on Amazon.com
Format: Hardcover Verified Purchase
0 of 8 people found the following review helpful
5.0 out of 5 stars Great 29 May 2009
By Drago - Published on Amazon.com
Format: Hardcover Verified Purchase
I received the book well packed, in due time and according to the description, a satisfactory purchase.
3 of 3 people found the following review helpful
4.0 out of 5 stars Great math book for laymen 7 Sept. 2013
By Robert W. Bly - Published on Amazon.com
Format: Mass Market Paperback
If you like math but are not a mathematician, you will most likely enjoy this book as I did. In numerous essays, Asimov has mentioned that while he loved math, his abilities in mathematics were modest, not equal to his mastery of the sciences. But he wanted to write engagingly on math just as he wrote engagingly on chemistry, biology, and physics, and he succeeded. How? By not going above his head but treating more elementary math topics in a novel, entertaining, and clear way. I loved this book. My younger son, a math minor in college, would find it too elementary and unchallenging.
2 of 2 people found the following review helpful
5.0 out of 5 stars Should never go out of print 26 Sept. 2012
By Peter Formiller - Published on Amazon.com
Format: Mass Market Paperback
This is the first of a series of four basic math books written by Isaac Asimov in the early days of the Space Race. The ten chapters of "Realm of Numbers" (1959) cover basic math topics, starting with what numbers are and how our number system developed through history. Other topics include negative numbers, multiplication, fractions, decimals, squares, cubes, factorials, logarithms, infinity, and the Pythagorean Theorem. This book should be available in a 3-in-1 edition with its two siblings, "Realm of Measure" (1960) and "Realm of Algebra." (1961) Dr. Asimov's fourth basic math book, "An Easy Introduction to the Slide Rule" (1965), is also excellent but would be of interest mostly to collectors and historians.
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