(Zero, One, Infinity)

Greeks were the first to acknowledge the existence of infinity as a central issue in mathematics.

(Zero, One, Infinity)

Philosopher who lived in Elea. His paradoxes deal with motion and continuity, he showed that motion is impossible. In order for a runner to move from one point to another, he would first have to cover half the distance, then half the distance remaining, and so on as infinitum. The runner would never reach the desination because it requires infinite steps. But he still knew well that the runner would reach his enpoint after a finite lapse of time. He left his paradox unsolved for future generations, and humbly admitted that infinity is too intellectually challenging for his generation.

MY OPINION: He is wrong, because as seen in class, 1/2 + 1/8 + ... = 1 (think of the square) which is a finite value!

(Zero, One, Infinity)

The great scientist who achieved immortal fame as the discoverer of the laws of floating bodies and of the mechanical lever. His method was based on a simple observation. Put circles inside/outside polygons, and increase the number of sides of the polygon: it will get closer and closer to the circumference of the circle. If we can find the perimeters of these polygons and divide it by the diameter of the circle, we get close to pi.

(Towards Legitimation)

The french mathematician discovered the infinite product: (2/pi)=(root(2)/2)x(root(2+root(2)))+... It shows that pi can be calculated solely from the number 2 by a sucession of additions, multiplications, divisions, and square root extractions. The most important part though is that the formula goes on and on: infinity. This was the first time an infinite process was explicitily expressed as a mathematical formula, which began a new era. "No longer woud the infinite be ominous, but it would be the contrary, to be accepted into the math kingdom."(10)

(Towards Legitimitation)

Published a book . He was the driving force in promoting the method of indivisibles which he did in the book.

(Towards Legitimation)

invented differential and integral calculus all revolving around the infintely small, the infinitessimal. Controvery existed about this, for Example Bishop George Berkeley (1685-1753) who published a work in which he attacked this.(Page 13)

(Towards Legitimation)

(1616-1703) once again involved pi, had a formula like vietes. (pi/2)=(2x2x4x4x6x6...)/(1x3x3x5x5x7...).

(Zero, One, Infinity)

(1616-1703) English mathematician who was the first to use the current infinity symbol. He was also a classical scholar and probably took it from the Roman numeral for 100 million.

(Towards Legitimation)

Scottish man found another infinite formula with pi, an infinite series: (pi/4)=(1/1)-(1/3)+(1/5)-(1/7)+-... This was discovered independently in 1674 by Gottfried Wilhelm Leibniz, co-inventor with Newton of the calculus, and is sometimes referred to as the Gregory-Leibniz series.

Was the first to find the area of a segment of the parabola. "Method of Exhaustion": He used figures that almost made of the parabola, then smaller ones to fill in the empty spaces, and so on.

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