... earth's circumference; he was able to measure the angle between the sun's rays and a perpendicular line at the same time in Alexandria (Mahoney 541). Eratosthenes also worked on prime numbers, and is remembered for his prime number sieve, the "Sieve of Eratosthenes," which, in modified form, is still an important tool in number theory research (O"Conner 2). It ultimately eliminates all multiples of the ... successive prime numbers beginning with 2 (Mahoney 543). The sieve can help solve math problems such as this one: "What are all the prime numbers up to 100?" (Stanton 13). Using the s...

• Word Count: 664
• Approx Pages: 3
• Has Bibliography

... chief work, Elements, is a comprehensive treatise on mathematics in thirteen volumes on such subjects as plane geometry, proportion in general, the properties of numbers, incommensurable magnitudes, and solid geometry. He was probably educated at Athens by pupils of Plato. He taught geometry in Alexandria and founded a school ... of previous mathematicians such as those of Eudoxus, but Euclid himself is thought to have made several original discoveries in the theory of numbers. Euclid laid down some of the conventions central to modern mathematical proofs. His book The Elements, written...

• Word Count: 533
• Approx Pages: 2
• Grade Level: High School

... ). They explained the arrangement of things as bodies in a single sphere of reality, moving according to a numerical scheme. THEORY OF NUMBERS:- Among the mathematical investigations carried on by the Pythagoreans were their studies of odd and even numbers and of prime and square numbers, all essential in number theory. From this standpoint they produced the concept of number, which became for them the ultimate ... ...

• Word Count: 379
• Approx Pages: 2
• Grade Level: Undergraduate

... would examine the values of the results as he or she got closer to that number from the positive side of the number line. So approaching 1 from the right the numbers 3, 2, and 1 would be examined. The process of finding the derivative of a function is called differentiation. A function is called differentiable at x if its derivative exists at x. Thus when mathematicians differentiate a problem ... terms play a part within the process of differentiating or finding the derivative of a function. The derivative of a function f at C is given by the equation f"(C) = limit x C, [f(x) - f(C)]/(...

• Word Count: 991
• Approx Pages: 4
• Has Bibliography
• Grade Level: High School