The Historical Roots of Elementary Mathematics
eBook - ePub

The Historical Roots of Elementary Mathematics

Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient

Condividi libro
  1. 336 pagine
  2. English
  3. ePUB (disponibile sull'app)
  4. Disponibile su iOS e Android
eBook - ePub

The Historical Roots of Elementary Mathematics

Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient

Dettagli del libro
Anteprima del libro
Indice dei contenuti

Informazioni sul libro

`Will delight a broad spectrum of readers.` — American Mathematical Monthly.
Do long division as the ancient Egyptians did! Solve quadratic equations like the Babylonians! Study geometry just as students did in Euclid's day! This unique text offers students of mathematics an exciting and enjoyable approach to geometry and number systems. Written in a fresh and thoroughly diverting style, the text — while designed chiefly for classroom use — will appeal to anyone curious about mathematical inscriptions on Egyptian papyri, Babylonian cuneiform tablets, and other ancient records.
The authors have produced an illuminated volume that traces the history of mathematics — beginning with the Egyptians and ending with abstract foundations laid at the end of the nineteenth century. By focusing on the actual operations and processes outlined in the text, students become involved in the same problems and situations that once confronted the ancient pioneers of mathematics. The text encourages readers to carry out fundamental algebraic and geometric operations used by the Egyptians and Babylonians, to examine the roots of Greek mathematics and philosophy, and to tackle still-famous problems such as squaring the circle and various trisectorizations.
Unique in its detailed discussion of these topics, this book is sure to be welcomed by a broad range of interested readers. The subject matter is suitable for prospective elementary and secondary school teachers, as enrichment material for high school students, and for enlightening the general reader. No specialized or advanced background beyond high school mathematics is required.

Domande frequenti

Come faccio ad annullare l'abbonamento?
È semplicissimo: basta accedere alla sezione Account nelle Impostazioni e cliccare su "Annulla abbonamento". Dopo la cancellazione, l'abbonamento rimarrà attivo per il periodo rimanente già pagato. Per maggiori informazioni, clicca qui
È possibile scaricare libri? Se sì, come?
Al momento è possibile scaricare tramite l'app tutti i nostri libri ePub mobile-friendly. Anche la maggior parte dei nostri PDF è scaricabile e stiamo lavorando per rendere disponibile quanto prima il download di tutti gli altri file. Per maggiori informazioni, clicca qui
Che differenza c'è tra i piani?
Entrambi i piani ti danno accesso illimitato alla libreria e a tutte le funzionalità di Perlego. Le uniche differenze sono il prezzo e il periodo di abbonamento: con il piano annuale risparmierai circa il 30% rispetto a 12 rate con quello mensile.
Cos'è Perlego?
Perlego è un servizio di abbonamento a testi accademici, che ti permette di accedere a un'intera libreria online a un prezzo inferiore rispetto a quello che pagheresti per acquistare un singolo libro al mese. Con oltre 1 milione di testi suddivisi in più di 1.000 categorie, troverai sicuramente ciò che fa per te! Per maggiori informazioni, clicca qui.
Perlego supporta la sintesi vocale?
Cerca l'icona Sintesi vocale nel prossimo libro che leggerai per verificare se è possibile riprodurre l'audio. Questo strumento permette di leggere il testo a voce alta, evidenziandolo man mano che la lettura procede. Puoi aumentare o diminuire la velocità della sintesi vocale, oppure sospendere la riproduzione. Per maggiori informazioni, clicca qui.
The Historical Roots of Elementary Mathematics è disponibile online in formato PDF/ePub?
Sì, puoi accedere a The Historical Roots of Elementary Mathematics di Lucas N. H. Bunt, Phillip S. Jones, Jack D. Bedient in formato PDF e/o ePub, così come ad altri libri molto apprezzati nelle sezioni relative a Mathematics e History & Philosophy of Mathematics. Scopri oltre 1 milione di libri disponibili nel nostro catalogo.






The earliest written mathematics in existence today is engraved on the stone head of the ceremonial mace of the Egyptian king Menes, the founder of the first Pharaonic dynasty. He lived in about 3000 B.C. The hieroglyphics on the mace record the result of some of Menes’ conquests. The inscriptions record a plunder of 400,000 oxen, 1,422,000 goats, and 120,000 prisoners. These numbers appear in Figure 1-1, together with the pictures of the ox, the goat, and the prisoner with his hands behind his back. Whether Menes exaggerated his conquests is interesting historically but does not matter mathematically. The point is that even at this early date, man was recording very large numbers. This suggests that some mathematics was used in the centuries before 3000 B.C., that is, before the invention of writing (the prehistoric period).
Figure 1-1 From a drawing (Plate 26B) in J. E. Quibell, Hierakonopolis, London, 1900.
There are two ways of learning about the mind and culture of prehistoric humans. We have learned about them through the discovery of ancient artifacts, which were found and interpreted by archaeologists. We have also learned about prehistoric civilization by observing primitive cultures in the modern world and by making inferences as to how prehistoric thought and customs developed. In our study of the development of ideas and understandings, both approaches are useful.
One of the most exciting archaeological discoveries was reported in 1937 by Karl Absolom as a result of excavations in central Czechoslovakia. Absolom found a prehistoric wolf bone dating back 30,000 years. Several views are shown in Figure 1-2. Fifty-five notches, in groups of five, are cut into the bone. 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.
Figure 1-2 Prehistoric Wolf Bone. (From London Illustrated News, October 2, 1937.)
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. C. Haddon in 1889, describes a tribe that had no written language which counted as follows: 1, urapun; 2, okosa; 3, okosa-urapun; 4, okosa-okosa; 5, okosa-okosa-urapun; 6, okosa-okosa-okosa . 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...

Indice dei contenuti