History of Mathematics. Chapter 3: The Greeks

THE GREEKS AND THE MATHEMATICS

1. THALES OF MILETUS (C. 624 – C. 546 BCE) Thales is considered one of the first Greek mathematicians and philosophers. He is credited with the concept of mathematical proof and applying geometry to practical problems.

PYTHAGORAS (C. 570 – C. 495 BCE)

Pythagoras founded the Pythagorean school of thought, which emphasized mathematics and philosophy. He is best known for the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Anaxagoras (c. 510 – c.

428 BCE)

ANAXAGORAS IS KNOWN FOR HIS WORK ON IRRATIONAL NUMBERS AND THE IDEA THAT THE UNIVERSE CAN BE UNDERSTOOD THROUGH MATHEMATICAL PRINCIPLES.

What is an irrational number?

An irrational number is a real number that cannot be expressed as a simple fraction (or a ratio) of two integers, where the denominator is non-zero.

In other words, irrational numbers cannot be represented exactly as a fraction a/b, where a and b are integers.

The square root of 2 (√2) – The first known irrational number, which was discovered by the ancient Greek mathematician Hippasus. It is the positive solution of the equation x^2 = 2.

Zeno of Elea (c. 490 – c.

430 BCE)

ZENO IS FAMOUS FOR HIS PARADOXES, WHICH USED MATHEMATICAL CONCEPTS TO CHALLENGE ASSUMPTIONS ABOUT MOTION, SPACE, AND TIME.

Space

Motion

"ACHILLES AND THE TORTOISE."

ACHILLES, A SWIFT RUNNER FROM GREEK MYTHOLOGY, IS RACING AGAINST A TORTOISE. ACHILLES IS MUCH FASTER THAN THE TORTOISE, SO HE GIVES THE TORTOISE A HEAD START OF, SAY, 100 METERS.

Who's going to win?

When the race begins, Achilles quickly reaches the point where the tortoise started. However, during the time it took Achilles to reach that point, the tortoise has moved forward, albeit by a much smaller distance.

Now, Achilles must reach the new position of the tortoise. But while he is doing so, the tortoise moves a bit further again.

Every time Achilles reaches the tortoise's previous position, the tortoise has advanced a small distance

This pattern continues indefinitely, with Achilles always having to reach a new, albeit smaller, distance

According to the paradox, Achilles can never actually catch the tortoise because he must first cover an infinite number of progressively smaller distances, which seems impossible

Hippocrates of Chios (c. 470 – c. 410 BCE)

Hippocrates was a pioneer in the field of geometric analysis and is credited with developing the first systematic study of geometry.

Democritus (c. 460 – c. 370 BCE) Democritus is known for his work on atomic theory, which postulated that the universe is composed of indivisible, discrete particles called atoms. He also studied geometry and number theory.

Plato (c. 428 – c. 348 BCE)

Plato, a student of Socrates, founded the Academy in Athens, where mathematics was a central subject. He contributed to the development of number theory and geometry, and his work influenced later mathematicians like Euclid.

Eudoxus of Cnidus (c. 408 – c. 355 BCE) Eudoxus made significant contributions to geometry, including the method of exhaustion, a precursor to the concept of limits in calculus.

Aristotle (384 – 322 BCE)

Aristotle, a student of Plato, made contributions to logic and the philosophy of mathematics, which would later influence the development of mathematical thought.

Euclid (c. 300 BCE)

Euclid's "Elements" is a collection of 13 books that systematized much of the existing knowledge of geometry and number theory. His work laid the foundation for axiomatic geometry and has been influential for over 2,000 years.

Archimedes (c. 287 – c. 212 BCE)

Archimedes is considered one of the greatest mathematicians of all time. He made significant contributions to geometry, calculus, and the understanding of the properties of solids, liquids, and gases. He also developed methods for calculating areas, volumes, and the value of π (pi).

Apollonius of Perga (c. 262 – c. 190 BCE)

Apollonius is known for his work on conic sections, which laid the groundwork for the study of ellipses, parabolas, and hyperbolas.

Diophantus (c. 201 – c. 285 CE)

Diophantus is known as the "father of algebra." His work, "Arithmetica," provided the foundation for the study of algebraic equations and number theory.