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Man and Number (Dover Science Books) Paperback – October 17, 2003

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Product Details

  • Series: Dover Science Books
  • Paperback: 128 pages
  • Publisher: Dover Publications (October 17, 2003)
  • Language: English
  • ISBN-10: 0486432769
  • ISBN-13: 978-0486432762
  • Product Dimensions: 8.7 x 5.4 x 0.3 inches
  • Shipping Weight: 5.3 ounces
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #4,492,303 in Books (See Top 100 in Books)

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3 of 3 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on December 22, 2005
Format: Paperback
Counting is the point of origin of all mathematics, and it can be done in many ways. There are the trivial differences in the names of the numbers, and the more significant ones concerning the base and the notation used to abbreviate the names of the numbers. For example, the words "twenty one" are but one name for 21, which means two tens and one one. In base twenty, this would be one twenty and one one. We tend to think of the base ten as a mathematical law, but that is largely an anatomical accident. Humans have ten fingers and that is the origin of the base 10.

Depending on the circumstances, other bases are more natural than 10. For example, base 2 is more natural for computers, base 12 is more natural for some areas of commerce due to the larger number of factors and base 360 works very well for astronomical computations. Smeltzer takes us through the historical and cultural records of the different bases used by humans and when bases other than ten make more sense. It is an excellent demonstration of how humans have tightened up the notation used for numbers and the abstractions that have developed over centuries.

We use the representation of numbers and the symbols for arithmetic operations routinely and rarely realize that they developed over centuries. I believe all students of mathematics, especially those who are on track to teach elementary and middle school mathematics, should know the history of the development of these notations. This readable book is an excellent way to learn the fundamentals of number representation and how those notations developed over time.
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