Eratosthenes of Cyrene was a Greek mathematician, geographer and astronomer. He was chief librarian at the Library of Alexandria. He invented the discipline of geography, including the terminology used today. He is best known for being the first person to calculate the circumference of the earth. The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter.
Seventeen hundred years after Eratosthenes' death, while Christopher Columbus studied what Eratosthenes had written about the size of the Earth, he chose to believe that the Earth's circumference was much smaller. Had Columbus set sail knowing that Eratosthenes' larger circumference value was more accurate, he would have known that the place where he made landfall was not Asia, but rather a New World.
The Sieve of Eratosthenes
The Sieve of Eratosthenes is a simple method that can be used to find prime numbers. It is an excellent exercise for students because it helps them recognize the characteristics of prime numbers.
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements. The Pythagorean Theorem was known long before Pythagoras, but he may well have been the first to prove it
The Pythagorean theorem states:
The square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The theorem has numerous proofs, possibly the most of any mathematical theorem. These are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The proof attributed to Pythagoreus is very simple, and is called a proof by rearrangement.
The two large squares shown in the figure each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently.
Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean Theorem.
The Fibonacci sequence is named after Leonardo Fibonacci, an Italian Mathematician. However the sequence is first found in Indian Mathematics, where it was discovered many years earlier.
The next number is found by adding up the two numbers before it.
The 2 is found by adding the two numbers before it (1+1)
Similarly, the 3 is found by adding the two numbers before it (1+2),
And the 5 is (2+3),
and so on...
A Fibonacci prime is a Fibonacci number that is prime. The first few are:
- 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, …