The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)


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Bunt Paperback February 1, Prices and offers may vary in store. Kobo ebook. Exciting, hands-on approach to understanding fundamental underpinnings of modern arithmetic, algebra, geometry and number systems, by examining their origins in early Egyptian, Babylonian and Greek sources. Students can do division like the ancient Egyptians, solve quadratic equations like the Babylonians, and more. Lists with This Book. This book is not yet featured on Listopia.

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Community Reviews. Showing Rating details. More filters. Sort order. May 07, Akos Hochrein rated it really liked it. Quite a good read to learn about how people perceived math in the past. Sometimes the text can get a bit too heavy for people who are not used to math lingo, though. Oct 31, Hannah rated it really liked it Shelves: books-i-read-in-college. Of the three texts we read in my history of math class, this one was my favorite. It read like a textbook, but it was pretty straightforward although some of the math was challenging.

Each section had practice problems which was a nice way to check if we were learning the material. It was fun learning how to do math the way the Egyptians and Babylonians did, and the explanations of all the propositions from Euclid's Elements were very thorough.

Steven Teasdale rated it liked it Nov 03, Fiona K rated it liked it May 15, Leah rated it really liked it Jun 08, Reid rated it it was amazing Feb 27, Joshua Meigs rated it it was amazing Jun 18, Meredith rated it liked it Jun 10, Norana Cantrell rated it it was amazing Feb 14, Jim rated it liked it Nov 17, Farras Abdelnour rated it liked it Jul 11, Jim rated it liked it Oct 15, Jesse Taylor rated it really liked it Apr 20, Carlowen rated it liked it Nov 25, Michael Lloyd-Billington rated it really liked it Dec 26, Adam marked it as to-read Sep 07, Rageofanath marked it as to-read Jan 09, C added it Jun 04, Ryan Coons marked it as to-read Aug 15, The first 25 are separated from the remaining notches by one of double length.

Although we do not know how this bone was notched, the most plausible explanation is that some prehistoric man deliberately cut it. Perhaps he was recording the number of a collection, possibly of skins, of relatives, or of days since an event. It is reasonable to assume that he made a notch for each object in the collection that he was counting. If this interpretation is correct, then we can recognize in this prehistoric record rudimentary versions of two important mathematical concepts. One is the idea of a one-to-one correspondence between the elements of two different sets of objects, in this case between the set of notches on the bone and the set of whatever the prehistoric man was counting.

The other is the idea of a base for a system of numeration. The arrangement of the notches in groups of 5 and of 25 indicates a rudimentary understanding of a base 5 system of numeration. Anthropological studies reinforce our belief in the existence of prehistoric number ideas. A study of the western tribes of the Torres Straits, reported by A. Haddon in , describes a tribe that had no written language which counted as follows: 1, urapun; 2, okosa; 3, okosaurapun; 4, okosa-okosa; 5, okosa-okosa-urapun; 6, okosaokosa-okosa.


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Everything greater than 6 they called ras. A student of modern mathematics would recognize in this system of counting the beginnings of a base 2 numeration system. If a Torres Strait native had recognized this idea, however, he would have used a different word for 4 and would not have said ras for numbers greater than 6. Seidenberg has recently published a theory of the origin of counting see reference 12 at the end of the chapter.

The Historical Roots of Elementary Mathematics

He believes that counting was invented for use in early religious rituals. Many studies of primitive tribes as well as early Babylonian religious writings are cited which indicate that participants in religious rituals were called into the ritual in a definite order and that counting developed in connection with specifying this order.

A Book of Abstract Algebra Second Edition Dover Books on Mathematics

In his studies, Seidenberg found 2- counting to be the earliest counting that he could detect. This seems to indicate that the counting of the Torres Straits natives is consistent with a method of counting that was in use thousands of years earlier.

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These two types of prehistoric number ideas, matching and counting, correspond to two different approaches to number which are common both in modern life and in modern education. One of these is the approach through the ideas of set and one-to-one correspondence between sets that have developed since the work of Georg Cantor in the latter part of the nineteenth century.

This treatment is sometimes referred to as a cardinal approach to number. At about the time that Cantor was developing the beginnings of modern set theory, Giuseppe Peano was attempting to axiomatize the natural numbers and their arithmetic. To do this, he stated a set of five axioms. One of these axioms is that every natural number has a successor.

Such a treatment is called an ordinal approach to number. It emphasizes the counting idea, in contrast to the matching idea stressed in the cardinal approach to number. These two approaches can be shown to be equivalent to each other, but our purpose here is merely to point out the antiquity of the underlying ideas which have recently been organized into important modern mathematical systems. Evidences of other prehistoric mathematical ideas are not hard to find. One can read into primitive cave paintings some ideas of proportion and symmetry as skilled artists produced remarkably realistic drawings of animals and hunters.

Ideas of number and one-to-one correspondence appear in connection with stickmen and four-legged animals. Elaborate geometric designs can be found on prehistoric pottery. Prehistoric drawings showing different views of a wagon and horses have been found in Europe.

Sketches from the time of ancient Babylonia that might be plans of a building, perhaps a temple, have been unearthed. What appears to be a decimally divided ruler has been unearthed at Mohenjo-Daro in Pakistan. Interesting as these archeological findings are, from a mathematical point of view we shall find a study of the historic period to be more profitable. Let us therefore turn our attention to the earliest written mathematics, that of the Egyptians and the Babylonians.

Although monuments, inscriptions, and Menes' mace record the earliest written numbers, most of our knowledge of Egyptian mathematics comes from writings on papyrus. Papyrus is a paperlike substance made from the papyrus plant, which grows along the Nile River. From these writings we learn that mathematics was studied in Egypt as early as years before Christ. Why in Egypt? Herodotus about B. For that purpose surveyors were needed with some practical knowledge of simple arithmetic and geometry.

Many of their computations remain.

The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)
The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)
The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)
The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)
The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)
The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)
The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)
The Historical Roots of Elementary Mathematics (Dover Books on Mathematics) The Historical Roots of Elementary Mathematics (Dover Books on Mathematics)

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