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## Ancient Greek Impact on Mathematics

**Greek influence on Western civilization**

Ancient Greece became the greatest civilization that ever succeeded because of its great influence on Western civilization.

The Greek Common Era (8th century BC – 146 BC) was marked by colonialism and Homer’s Iliad and Odyssey were the greatest works of world literature.

During the Golden Age of Greece in the 5th century BC, great achievements in art, literature, architecture, science, philosophy and sports took place.

Historians, Herodotus and Thucydides, Hippocrates, the Father of Medicine and philosophers, Plato and Socrates all lived and worked in 5th century AD Athens.

Today, we can see the wonders of ancient Greece and understand the wisdom of the Greek philosophers.

The Hellenistic Age (4th to 1st century BC) was Alexander the Great’s legacy to the world when Greek culture dominated the Mediterranean and the Middle East and Greek became the international language.

**Hellenistic Alexandria**

From about 350 BC the center of mathematics moved from Athens to Hellenistic Alexandria, a port city in northern Egypt, founded in 331-BC by Alexander the Great and built by his chief architect, Dinocrates of Rhodes.

The island of Rhodes is famous for the Colossus of Rhodes, a 33-meter-high statue of the Greek sun god Helios that stood in the city’s harbor and was one of the Seven Wonders of the Ancient World.

In Greece, the Ptolemaic dynasty ruled Egypt (from 305 to 30 BC) during the Hellenistic Age.

Cleopatra VII Philopator (69 – 30 BC), was a descendant of its founder Ptolemy I Soter, of Macedonia, the Greek general of Alexander the Great.

The Great Library of Alexandria was one of the great libraries of the ancient world and its Museum had scholars such as Euclid (Greek mathematician and “father of Geometry”) and Eratosthenes (Greek mathematician, geographer and librarian) who worked there.

**The Importance of Mathematics**

**There are two periods in Greek mathematics:**

**1.** Classical Period (600-BC to 300-BC)

**2.** Alexandrian or Hellenistic Period (300-BC to 300-AD)

The word “mathematics” is derived from the ancient Greek word “mathema” meaning “knowledge or study” and is the study of numbers, shapes and patterns.

It deals with the concepts of reason, quantity, organization, order and almost everything we do today.

**Famous Greek Mathematicians and Their Contributions**

**Pythagoras of Samos (570 BC – 495 BC)**

Pythagoras of Samos is the Father of the famous “Pythagoras theorem”, a mathematical formula that states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Samos was famous in ancient times for its navy, wine, and sanctuary of Hera, the goddess of ancient Greek mythology.

Pythagoras taught that the Earth was a sphere at the center of the universe and that the paths of the planets were circular.

**Pythagoreanism**

Pythagoras founded Pythagoreanism which made important developments in mathematics, astronomy, and music theory.

Many of the Greek philosophers of the 6th, 5th and 4th centuries are called Pythagoreans such as Parmenides, Plato and Aristotle.

Plato (428/427 or 424/423 – 348/347-BC) was an Athenian philosopher during the Classical period in Ancient Greece who founded the Platonist school of thought and the Academy, the first institution of higher education in the Western world.

Parmenides of Elea (late 6th or early 5th century BC) was a pre-Socratic Greek philosopher from Elea in Magna Graecia (“Greater Greece,” meaning the Hellenized areas of Southern Italy) who founded metaphysics (the branch of experimental philosophy ). basic nature of reality).

**Euclid of Alexandria (ca. 300-270-BC)**

Euclid is the father of geometry (Euclidean geometry) who worked in Alexandria during the reign of Ptolemy I (323-283 BC).

He made a revolutionary contribution to geometry and introduced the axiomatic method that is still used in mathematics today, which includes definitions, axioms, theorems, and proofs.

His book, Elements, served as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the beginning of the 20th century.

**Archimedes of Syracuse (287 – 212-BC)**

Archimedes is the Father of mathematics and is considered the greatest mathematician of antiquity.

He lived in the Greek city of Syracuse, Sicily, where he was born.

His father, Phidias was a mathematician and astronomer.

Archimedes revolutionized geometry and his methods were expected to calculate integrals (its applications include calculations involving area, volume, arc length, center of mass, work and pressure).

He is also known for the invention of combined pulleys and the device of the Archimedean screw pump (a machine used to move water from an underground body of water to irrigation canals).

**Thales of Miletus (624-620 – 548-545-BC)**

Miletus was an ancient Greek city in Ionia, Asia Minor (now modern Turkey).

Thales was a pre-Socratic philosopher, mathematician and astronomer, known as one of the seven wise men, or Sophoi, of antiquity.

He is best known for his work calculating the height of the pyramids and the distance of ships from shore using geometry.

**Aristotle (384 – 322-BC)**

Aristotle was born in Stagira, an ancient Greek city near the eastern coast of the Chalkidice peninsula in Central Macedonia.

Aristotle was a student of Plato and contributed to Plato’s teaching.

He was a polymath (knowledge covering many subjects) during the Classical period of Ancient Greece which included mathematics, geology, physics, metaphysics, biology, medicine and psychology.

He was the founder of the Lyceum, the Peripatetic school of philosophy, and the tradition of Aristotle.

Aristotle taught Alexander the Great and established a library that helped produce hundreds of books.

From his teachings, Western Civilization inherited its intellectual vocabulary for almost every form of knowledge.

**Diophantus of Alexandria (circa 200 – 214-AD – 284 and 298-AD)**

Greek mathematician, known as the father of algebra and the author of a series of books called Arithmetica dealing with solving algebraic equations.

He was the first Greek mathematician to recognize fractions as numbers.

**Eratosthenes of Cyrene (276 – 194-BC)**

Cyrene was an ancient Greek city in Libya and was founded in 631-BC.

Eratosthenes was a Greek mathematician, geographer, poet, astronomer, and musicologist who became the chief secretary of the Library of Alexandria.

His work included the study of geography and introduced the vocabulary used today.

Eratosthenes accurately calculated the circumference of the earth and the tilt of the Earth’s axis.

**Hipparchus of Nicaea (190 – 120-BC)**

Nicaea was an ancient Greek city in Anatolia, Asia Minor (now modern Turkey).

Hipparchus was a Greek astronomer, geographer, and mathematician who made many contributions to mathematics.

He was the founder of trigonometry and the first mathematical trigonometric table.

Hipparchus was also the first to develop a reliable method of predicting eclipses.

**Heron of Alexandria (10 – 70-AD)**

Heron is considered the greatest experiment of antiquity and is remembered for Heron’s formula, a method of calculating the area of a triangle using only the lengths of its sides.

He was also an important geometer (mathematician specializing in the study of geometry) and designed many machines including the steam engine.

**Ptolemy of Alexandria (100 – 170-AD)**

Ptolemy was a Greek mathematician, astronomer and geographer who wrote many scientific studies.

The Great Book is one of his most famous works now known as the Almagest of Astrology.

His map of the world, published as part of his book Geography in the 2nd century, was the first to use lines of longitude and latitude.

**Hypatia of Alexandria (355 – 415-BC)**

Hypatia, the daughter of a mathematician, was the first known woman to teach mathematics and made a significant contribution to the study of mathematics.

He was also a philosopher who taught as the head of the school, the knowledge of Plato and Aristotle.

Hypatia was the first woman to follow her dreams and became an inspiration to many young women.

**Antiphon of Rhamnus (480 – 411-BC)**

Rhamnus, an ancient Greek city in Attica, the historical region of Athens, is located on the coast, facing the Euboean Strait.

Antiphon was the first of the ten Attic orators, and an important figure in 5th century Athenian political and intellectual life.

He was the first to give upper and lower bounds to the values of Pi by writing and circumscribing a polygon around a circle and finally proceeding to calculate the areas of polygons. The method was used for squaring the circle.

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