By Heinrich Dorrie
Difficulties that beset Archimedes, Newton, Euler, Cauchy, Gauss, Monge and different greats, able to problem today's would-be challenge solvers. between them: How is a sundial built? how are you going to calculate the logarithm of a given quantity with no using logarithm desk? No complicated math is needed. comprises a hundred issues of proofs.
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Extra resources for 100 Great Problems of Elementary Mathematics (Dover Books on Mathematics)
Parallel to this, however, there was another tradition, usually called “logistics,” that arose mainly in the framework of commerce and day-to-day life. Incidentally, the extant direct evidence of written texts is mostly of this latter kind of mathematics. It appears in relatively extensive, but always fragmentary, papyrus texts. They were written by the Greco-Roman administration in Egypt from the fourth century BCE onwards. So, very little of this kind of more practical mathematics appears in Byzantine manuscripts, whereas, at the same time, very little of the scholarly mathematics has remained in original papyrus texts.
We ﬁnd one nowadays in the world of digital computers, where numbers are internally stored and processed in binary representation, namely, with the help of only two symbols: 0 and 1. More precisely, in electronic computers, numbers are presented and processed as strings of tiny electric charges on some kind of medium, and the presence or absence of a charge is taken to represent either 1 or 0, respectively. This is the same positional principle used in our decimal system, but with base two, and any such string of 0’s and 1’s can be easily translated into decimal representation.
Since Ptolemy adopted the Babylonian sexagesimal system as the main way for presenting astronomical data and computations, this has remained the accepted one in the discipline to this day. He modiﬁed the Babylonian system, though, in a crucial respect, namely, by introducing the symbol O to indicate an empty place in the power representation of the numbers. It is remarkable, however, that in spite of the enormous impact and inﬂuence of his book, only a few astronomers that followed him adopted this particular aspect of his work.
100 Great Problems of Elementary Mathematics (Dover Books on Mathematics) by Heinrich Dorrie