A Mersenne prime is written in the form of 2p-1. So far, the largest known Mersenne prime is 225,964,951-1, which is the 42nd Mersenne prime. This prime number has 7,816,230 digits! Many number theorists, who study certain properties of integers, have been trying to find formulas to generate primes. They believed that 2p-1 would always generate primes whenever p is prime.
This theorem combined the sides of a right triangle, and this led to the development of irrational numbers by Pythagoras later on. Pythagoras discovered that the square root of 2 was an irrational number. Plato, another great mind of Greece, did more than just develop theorems for geometry, he stressed that geometry was essential. Plato believed that everyone should be well educated in mathematics as well as geometry.
Fermat’s Little Theorem: Fermat’s little theorem says that for a *prime number p and some natural number a, a p – a is divisible by p and will have a *remainder of 0. *Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 3 is a prime number because only 1 and 3 evenly divide it. *Remainder: The remainder is the number that is left over in a division in which one quantity does not exactly divide another. If we divide 23 by 3 the answer will be 7 and the remainder 2.
Sometimes a theorem is so important that it becomes known as a fundamental theorem in mathematics. This is the case for the Fundamental Theorem of Algebra. The Fundamental Theorem of Algebra states that every polynomial equation of degree n, greater than or equal to one, has exactly n complex zeros. In fact, there are many equivalent formulations: for example that every real polynomial can be expressed as the product of real linear and real quadratic factors. The Fundamental Theorem of Algebra can also tell us when we have factored a polynomial completely but does not tell us how to factor a polynomial completely.
In fact the ancient Greeks were one of the first to deal with recurring decimals. The Greek mathematician Zeno had a paradox in which the answer was a finite number that was a sum of an infinite sequence. The answer to his problem was a recurring decimal, and it definitely would not be the last time recurring decimals played a role in mathematics. Famous mathematicians such as Euler, Gauss, and Fermat all have contributed their own discoveries about the nature of these numbers. Fittingly, recurring decimals fall under the elegant category of number theory in mathematics, called the “queen of mathematical studies” by Gauss.
The Ancient Indians had some mathematical achievements. One of their mathematical achievements, which was shown in the Vedic texts, is that they had names for every number up to one billion. The Vedic texts also show that they managed to calculate irrational numbers, such as√3, very accurately (Whitfield, Traditions 42).... ... middle of paper ... ...affect us in numerous ways, such as in architecture, modern mathematics, modern science, the medical world, technology, and much more. Ancient India, China, and Greece all contributed to math and science, however, the Greek achievements influenced us the most. They invented Pythagorean Theorem, calculated the value of pi, discovered atoms, accurately found the size of the Earth, and had much more accomplishments than India or China.
A prime number is an integer with only positive divisors one and itself. The ancient Greeks proved that there where infinitely many primes and that they where irregularly spaced. Mersenne examined prime numbers and wanted to discover a formula that would represent all primes. The formula is (2p-1) where p is a known prime number. Mersenne claimed that if a number n=(2p-1) is prime then p=2,3,5,7,13,17,31,67,127, and 257, but composite for the other forty-four primes smaller than or equal to 257.
Obviously Euclid’s The Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Very little information is known about the author, beyond knowing the fact he lived in Alexandria around 300 BCE. Subjects of works includes geometry, proportion and number theory. Euclid proved his concepts logically, using definitions, axioms, and postulates. Proclus Diadochus wrote a commentary on Euclid's Elements that kept Euclid's works in circulation.
Quadratic equations were also studied and these examples led to a type of numerical algebra. Geometric problems relating to similar figures, area and volume were also studied and values obtained for p.The Babylonian basis of mathematics was inherited by the Greeks and independent development by the Greeks began from around 450 BC. Zeno of Elea's paradoxes led to the atomic theory of Democritus. A more precise formulation of concepts led to the realisation that the rational numbers did not suffice to measure all lengths. A geometric formulation of irrational numbers arose.
The Greeks brought a variety of great minds to life, including Thales of Miletus, Archimedes, Apollonius, Euclid, and Democritus. They began using logic to explore new mathematical concepts. Pythagoras of Samos was one of the foremost logical minds of this age. He is the inventor of abstract mathematics, and the founder of the “Pythagoras Theorem”. This theorem is still used today, in modern geometric equations The Hindu / Arabian Period (500A.D.