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## Ancient Greek Impact on Mathematics

**Greek influence on western civilization**

Ancient Greece is one of the greatest civilizations that had a great influence on Western Civilization.

The Classical Age of Greece (8th century BC – 146 BC) was marked by colonization and Homer’s Iliad and Odyssey were the first two great epics in world literature.

During the Golden Age of Greece in the 5th century BC, the greatest 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 Athens in the 5th century BC.

Today, we can look at the architectural wonders of ancient Greece and gain insight into the wisdom of ancient Greek philosophers.

The Hellenistic period (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**

Around 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, which stood in the city’s harbor and was one of the seven wonders of the ancient world.

The Greek Ptolemaic dynasty ruled Egypt during the Hellenistic period (from 305 to 30 BC).

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

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

**Importance of Mathematics**

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

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

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

The word “mathematics” comes from the ancient Greek word “mathema” which means “knowledge or learning” and the study of numbers, shapes and patterns.

It is related to the logic of reason, number, order, sequence 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 on the other two sides.

In ancient times, Samos was famous for its sea, wine and temple of Hera, a goddess in ancient Greek mythology.

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

**Pythagoreanism**

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

Many of the most famous Greek thinkers 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 Greek regions of southern Italy) who studied metaphysics (the branch of philosophy that studies does) built. the fundamental nature of reality).

**Euclid of Alexandria (around 300 – 270 BC)**

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

He made revolutionary contributions to geometry and introduced the axiomatic method that is still used in mathematics today, consisting of definitions, axioms, theorems and proofs.

His book called Elements was 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 was born in the Greek city of Syracuse, Sicily.

His father, Phidias, was a mathematician and astronomer.

Archimedes revolutionized geometry and his methods predicted integral calculus (its applications include calculations of area, volume, arc length, center of mass, work and pressure).

He is also known for the inventions of compound pumps and the Archimidean screw pump device (a machine used to transfer water from a low-lying body of water through irrigation ditches).

**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 astrologer, known as one of the legendary Seven Sages, or Sophoi, of antiquity.

He is best known for his work in 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 east coast of the Chalkidice peninsula of Central Macedonia.

Aristotle was a student of Plato and participated in Platonism.

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

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

Aristotle tutored Alexander the Great and built a library that helped produce hundreds of books.

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

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

Greek mathematician, known as the father of algebra and 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 music theorist who became the librarian at the Library of Alexandria.

His work was related to the study of geography and he introduced some terminology that is still used today.

Eratosthenes accurately calculated the circumference of the earth and even the shape of the earth.

**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 mathematical contributions.

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

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

**Heron of Alexandria (10 – 70-AD)**

Heron is considered the greatest experimenter of antiquity and is remembered for Heron’s formula, a way to calculate 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 one who invented many machines including a steam turbine.

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

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

The Great Treatise is one of his most famous works, now known as the Almagest on astronomy.

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

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

Hypatia, the daughter of mathematicians, was the first woman known to have taught mathematics and made valuable contributions to mathematics.

He was also a philosopher who taught Plato and Aristotle as a school principal.

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

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

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

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

He was the first to inscribe and then draw a polygon around a circle and finally began to calculate the areas of polygons, giving an upper and lower bound for Pi values. The method was applied to squaring the circle.

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