Greek Impact on Western Civilization
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Ancient Greece has been one of the greatest civilization's to have ever flourished because of its enormous impact it had on Western Civilization.
The Classical Age of Greece (8th century BC – 146 BC) was characterized by colonization and Homer's Iliad and the Odyssey were the first two greatest 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, the Father of Medicine and the philosophers, Plato and Socrates all lived and worked in 5th-century BC Athens.
Today, we can gaze at the arcthitectural wonders of ancient Greece and gain an insight to the wisdom of 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 Middle East and Greek became the international language.
Hellenistic Alexandria
From about 350 B.C. 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.
Rhodes Island is famous for the Colossus of Rhodes, a 33-metre-high statue of the Greek sun-god Helios which straddled the harbor of the city and was one of the Seven Wonders of the Ancient World.
The Greek, Ptolemaic dynasty ruled Egypt (from 305 to 30 BC) during the Hellenistic Period.
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 of the ancient world and its Museum had scholars such as Euclid (Greek mathematician and "Father of Geometry") and Eratosthenes (Greek mathematician, geographer and chief librarian) who worked there.
Importance of Mathematics
There are two periods of Greek mathematics:
1. The Classical Period (600-B.C. to 300-B.C.)
2. The Alexandrian or Hellenistic Period (300-B.C. to 300-A.D.)
The word "mathematics" is derived from the ancient Greek word "mathema" which means "knowledge or learning" and is the study of numbers, shapes and patterns.
It deals with logic of reason, quantity, arrangement, 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 which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
Samos was famous in antiquity for its navy, wine, and sanctuary to Hera, a goddess in ancient Greek mythology.
Pythagoras taught that Earth was a sphere in 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 the theory of music.
Many 6th, 5th, and 4th-century's most prominent Greek thinkers are labeled 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 learning 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 Greek-populated areas in Southern Italy) who founded metaphysics (branch of philosophy that examines 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 still 中四生物補習 used in mathematics today, consisting of definition, axiom, theorem, and proof.
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 the Father of mathematics and is considered the greatest mathematician of antiquity.
He lived in the Greek city of Syracuse, Sicily, his birthplace.
His father, Phidias was a mathematician and astronomer.
Archimedes revolutionised geometry and his methods anticipated the integral calculus (its applications include computations involving area, volume, arc length, center of mass, work, and pressure).
He is also known for the invention of compound pulleys and the Archimidean screw pump device (machine used for transferring water from a low-lying body of water into 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, renowned as one of the legendary Seven Wise Men, or Sophoi, of antiquity.
He's best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry.
Aristotle (384 – 322-BC)
Aristotle was born in Stagira, an ancient Greek city near the eastern coast of the peninsula of Chalkidice of Central Macedonia.
Aristotle was a pupil of Plato and made contributions towards Platonism.
He was a polymath (knowledge spans 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 Aristotelian tradition.
Aristotle tutored Alexander the Great and established a library which aided in the production of hundreds of books.
From his teachings, Western Civilization inherited its intellectual lexicon on 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 the compilation 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 founded in 631-BC.
Eratosthenes was a Greek mathematician, geographer, poet, astronomer, and music theorist who became the chief librarian at the Library of Alexandria.
His work involved the study of geography and he introduced some of the terminology still used today.
Eratosthenes correctly 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 to predict 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 who specializes in the study of geometry) and who invented many machines including a steam turbine.
Ptolemy of Alexandria (100 – 170-AD)
Ptolemy was a Greek mathematician, astronomer and geographer who wrote several scientific researches.
The Great treatise is one of his renowned works now known as Almagest on astronomy.
His world map, published as part of his treatise Geography in the 2nd century, was the first to use longitudinal and latitudinal lines.
Hypatia of Alexandria (355 – 415-BC)
Hypatia, the daughter of a mathematician, was the first woman known to have taught mathematics and to make valuable contributions in the field of mathematics.
She was also a philosopher who taught as the head at a school, the knowledge of Plato and Aristotle.
Hypatia was the first woman to pursue her dreams and became 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 situated 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 give an upper and lower bound for the values of Pi by inscribing and then circumscribing a polygon around a circle and finally proceeding to calculate the polygons areas. The method was applied to squaring the circle.
The following data was collected by a Toronto-based tutoring academy during the 2005/2006 school year and provides a summary of 169 students and what subjects they were being tutored in. This data provides a good summary of the relative demand for tutoring in different subjects in a large North American city. Although this is not a perfectly representative sample and that demand for different subjects may vary by city, it still provides information that may be useful in determining what subjects and grades to offer.
Students:
The split between male and female students is almost even, with 49% male and 51% female. Students are spread out amongst the different grade levels, with 25% in K-6, 15% in grades 7-8, 57% in grades 9-12, and less than 3% in college/university.
Subjects:
Below is a list of the most popular tutoring subjects and their relative incidence amongst this group.
Math… 77 students (45.6%)
English… 37 students (21.9%)
Math and English… 27 students (16.0%)
Math and Science… 18 students (10.7%)
Science… 7 students (4.1%)
French… 3 students (1.8%)
Results:
Math is by far the most popular subject, with 45.6% of students requiring tutoring in Math only, and another 26.7% requiring tutoring in Math and another subject.
English comes in second place, with almost 30% requiring tutoring in English and another 16% requiring tutoring in Math and English.
Science comes in at a distant third, with only 4.1% requiring tutoring in Science only, and another 10.7% requiring tutoring in Math and Science.
The demand for French tutoring is almost negligible, with less than 2% requiring tutoring in this subject.
What is the significance of this data?
This data may provide a useful example of the relative demand for tutoring subjects in a typical small/medium-sized North American tutoring academy. Anyone considering starting a tutoring academy should research the demand for subjects, as well as the grade level of tutoring students for their relevant market. You should carefully consider this information before deciding upon what subjects and grade levels you will offer with your tutoring service, so you can make the best use of a scarce resource…your tutors.
For example, if you choose to offer tutoring in all subjects and grades, you will need to have a lot more available tutors than if you just offer Math for grades 7-12. And based on the numbers, you could probably attract enough students to run a profitable academy by offering just Math for grades 7-12. On the other hand, an academy specializing in English tutoring for grades K-6 probably would not attract nearly as many students as the previous example.
The decision of what subjects to tutor is therefore a balance between what grades and subjects you can comfortably manage, and what you need to offer to sustain a profitable business.