By Yoshihide Igarashi
Exploring an unlimited array of subject matters concerning computation, Computing: A old and Technical Perspective covers the historic and technical starting place of historic and modern day computing. The ebook begins with the earliest references to counting by way of people, introduces a variety of quantity structures, and discusses arithmetic in early civilizations. It courses readers all through the most recent advances in desktop technological know-how, akin to the layout and research of laptop algorithms.
Through ancient bills, short technical factors, and examples, the publication solutions a number of questions, including:
- Why do people count number in a different way from the way in which present digital desktops do?
- Why are there 24 hours in an afternoon, 60 mins in an hour, etc.?
- Who invented numbers, while have been they invented, and why are there diversified kinds?
- How do mystery writings and cryptography date again to historic civilizations?
Innumerable contributors from many cultures have contributed their abilities and creativity to formulate what has develop into our mathematical and computing historical past. through bringing jointly the old and technical features of computing, this ebook allows readers to realize a deep appreciation of the lengthy evolutionary procedures of the sector built over hundreds of thousands of years. appropriate as a complement in undergraduate classes, it offers a self-contained historic reference resource for someone attracted to this significant and evolving field.
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Additional resources for Computing: A Historical and Technical Perspective
Diophantus of Alexandria and Arithmetica ◾ 45 (Note that given two numbers a and b, ((a + b)/2)2 – ab = ((a – b)/2)2. ) Problem II-6 Find two numbers having a given difference and a number such that the difference of their squares exceeds their difference by a given number. Necessary condition: The square of their difference must be less than the sum of the said difference and the given excess of the difference of the squares over the difference of the numbers. Let the two numbers be x and y. Suppose that the given difference is x – y = 2 and the given excess x2 – y2 – (x – y) = 20.
The Pythagoreans again enter history when Nicomachus (c. 60–c. 120 AD) reported a technique from the third century BC by a scholar named Eratosthenes (276–194 BC). The technique is called (appropriately enough) the sieve of Eratosthenes. , withoutthinking too much). Eratosthenes is perhaps best known for calculating the circumference of the earth, its tilt (relative to the sun), and its distance from the moon. He was also a noteworthy playwright and a poet, and furthered (if not founded the modern form of) the subject of geography.
Simply put, a prime number has only 1 as its natural divisor, without a remainder. If a number is a product of two numbers and has a factor of a prime, then one of the two numbers has a factor of the prime. Any nonprime number has a prime number as its factor. Any number is either prime or divisible by a prime. Summarized, these statements become: “any integer can be expressed as a unique ordered product of primes,” which is typically known and understood to be the fundamental theorem of arithmetic.