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## Ancient Greek Impact on Mathematics

**Greek Influence on Western Civilization**

Ancient Greece is the greatest civilization that flourished due to its great influence on Western civilization.

The colonization of Greece during the classical era (8th century BC – 146 BC) and Homer’s Iliad and Odyssey were the first two epics in world literature.

During the Golden Age of Greece in the 5th century BC, the greatest artistic, literary, architectural, scientific, philosophical and sporting achievements took place.

Historians, Herodotus and Thucydides, Hippocrates, father of medicine and philosophers, Plato and Socrates all lived and worked in 5th century BC Athens.

Today, we can look at the architectural marvels of ancient Greece and gain an insight into the wisdom of the ancient 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 the Hellenistic Alexandria, a port city in northern Egypt, founded by Alexander the Great in 331-BC and built by his chief architect, Dinocrates of Rhodes.

The island of Rhodes is famous for the Colossus of Rhodes, a 33-meter-tall 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.

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, the 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 (Greek mathematician and “father of geometry”) and Eratosthenes (Greek mathematician, geographer and chief librarian) who worked there.

**Importance of Mathematics**

**Greek mathematics has two periods:**

**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” meaning “knowledge or learning” and is the study of numbers, shapes and patterns.

It deals with logic, quantity, order, order and the logic of 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 “Pythagorean 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 antiquity for its navy, wine and sanctuary to the goddess Hera in 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 led to important developments in mathematics, astronomy and music theory.

Many prominent Greek thinkers of the sixth, fifth, and fourth centuries were 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 of ancient Greece who founded the Platonist school of thought and the academy, the first institution of higher learning in the Western world.

Parmenides of Ilia (late 6th or early-5th century BCE) was a pre-Socratic Greek philosopher of Magna Graecia (“Greater Greece,” i.e., Greek-populated areas in southern Italy) who founded metaphysics (the branch of philosophy that examines it). fundamental nature of reality).

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

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

He made revolutionary contributions to geometry and introduced the axiomatic method that is still used in mathematics today, including 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 early 20th century.

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

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

He lived in the Greek city of Syracuse in his native Sicily.

His father, Phidias, was a mathematician and astronomer.

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

He is also known for inventing compound pulleys and the Archimedean screw pump device (a machine used to move water from aquifers to 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 astronomer, best known as the legendary Seven Wise Men, or Sophoi, of antiquity.

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

**Aristotle (384-322-BC)**

Aristotle was born in the ancient Greek city of Stegira, near the east coast of the Chalkidiki Peninsula in central Macedonia.

Aristotle was a student of Plato and contributed to Platonism.

He was a polymath (knowledge spanning many disciplines) that included mathematics, geology, physics, metaphysics, biology, medicine and psychology during the classical period of ancient Greece.

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

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

From his teachings, Western civilization inherited its intellectual vocabulary in almost all forms of knowledge.

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

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

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 chief librarian at the Library of Alexandria.

His work included the study of geography and he introduced some terminology that is still 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 mathematical contributions.

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

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

**Heron of Alexandria (10-70-AD)**

Heron is considered the greatest mathematician 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 who specializes in the study of geometry) and who invented many machines, including the steam turbine.

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

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

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

His world map, published as part of his Geography treatise in the second 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 woman to teach mathematics and make valuable contributions to the field of mathematics.

She was also a philosopher who taught Plato and Aristotle as head of the Enlightenment School.

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

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

The historic area of Athens is the ancient Greek city of Rhamnus in Attica, located on the coast overlooking the Euboean Strait.

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

He was the first to inscribe the upper and lower limits for the values of Pi and then proceed to calculate polygonal areas by circumscribing the polygon around the circle and finally. The method was applied to square the circle.

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