# You asked: what are the two periods of Greek mathematics?

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The two periods of Greek mathematics are the Hellenistic period and the Classical period.

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Greek mathematics can be divided into two main periods – the Classical period and the Hellenistic period. The Classical period lasted from about 600 BCE to 300 BCE, while the Hellenistic period lasted from about 300 BCE to 600 CE.

During the Classical period, Greek mathematics focused on geometry, particularly the work of Euclid in his Elements, which is considered one of the most influential works in the history of mathematics. Other notable mathematicians from this period include Pythagoras, who developed the famous Pythagorean theorem, and Archimedes, who made significant contributions to geometry, calculus, and physics.

The Hellenistic period saw a shift towards more advanced algebraic techniques, as well as increased interest in mathematical astronomy. Among the most notable mathematicians of this period were Apollonius, who expanded on Euclid’s work in geometry, and Hipparchus, who made significant contributions to trigonometry and mapping the stars.

Famous scientist and mathematician, Archimedes once said, “Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.”

Here are some interesting facts about Greek mathematics:

• The ancient Greeks did not use the concept of zero in their calculations.
• Geometry was a hugely important field of study for the ancient Greeks and was considered a noble pursuit.
• Pythagoras is often credited with the discovery of the Pythagorean theorem, but it was likely known by the ancient Babylonians before him.
• Euclid’s Elements is the oldest known mathematical textbook in the world and is still used as a reference today.
• Archimedes is said to have made many remarkable discoveries, including the law of the lever, the principle of buoyancy, and the Archimedes screw, which is still used in some parts of the world to move water.
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To summarize, Greek mathematics can be divided into two main periods, the Classical period which focused on geometry, and the Hellenistic period which saw a shift towards algebraic techniques and mathematical astronomy. These periods produced some of the most influential mathematicians in history and their work is still studied and used today.

Period Key Mathematicians Key Contributions
Classical period Euclid, Pythagoras, Archimedes Geometry, Pythagorean theorem, calculus, physics
Hellenistic period Apollonius, Hipparchus Advanced algebraic techniques, mathematical astronomy

In “The Greek Legacy: How the Ancient Greeks shaped modern mathematics,” the concept of proof is discussed. Ancient Greek mathematicians developed the idea of proof over 2,500 years ago, which established mathematics as a way of understanding and testing the reality of the world. By creating convincing arguments to demonstrate whether something is true or false, the Greeks laid the foundation for modern mathematics. Euclid’s development of proof with basic assumptions called axioms has led to modern mathematical understandings in fields like cryptography and engineering.

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From the viewpoint of its mathematics, it is best to distinguish between the two periods: the classical period from about 600 B.C. to 300 B.C. and the Alexandrian or Hellenistic period from 300 B.C. to 300 A.D. Indeed, from about 350 B.C. the center of mathematics moved from Athens to Alexandria (in Egypt), the city

From the viewpoint of its mathematics, it is best to distinguishbetween the two periods: theclassicalperiod from about 600 BCE to300 BCE and theAlexandrianorHellenisticperiod from 300 BCEto 300 A.D.

The answer is yes. There was a split. First of all, for the Greek mathematics (and very long after them)
“numbers” were integers. “Rational numbers” were called fractions, and no concept of
real number existed. Therefore, mathematics was essentially split into two independent areas: arithmetic and geometry. Diophantus wrote on arithmetic, he never mentions geometric interpretation of his problems, and it is not known whether he was aware of any such interpretation. (By modern nomenclature his research subject belongs to algebraic geometry). Apollonius wrote on geometry, and never mentions numbers. (From the modern point of view, he is another founder of algebraic geometry).
Euclid wrote on both subjects, but his arithmetic books are separate from his geometric books, and there is little interaction.

People like Euclid and Archimedes had of course a good intuitive grasp of the concept of real number, and they had a theory of proportions when discussing such thing as lengths and areas, …

## These topics will undoubtedly pique your attention

### What are the two Greek word of mathematics?

The response is: The word máthēma is derived from μανθάνω (manthano), while the modern Greek equivalent is μαθαίνω (mathaino), both of which mean “to learn”. In Greece, the word for “mathematics” came to have the narrower and more technical meaning “mathematical study”, even in Classical times.

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### What 2 periods is the Greek civilization split in to?

Response: During the Archaic Period the Greek government began to form with the rise of the city-states such as Athens and Sparta. This was also when the Greeks began to explore philosophy and theatre. The Classical Period began with the introduction of democracy in Athens.

### What are two contributions the ancient Greeks made in mathematics and who were the people credited with those contributions?

In reply to that: Pythagoras (c. 570 – c. 495 BC) was credited with many mathematical and scientific discoveries, including the Pythagorean theorem, Pythagorean tuning, the five regular solids, the Theory of Proportions, the sphericity of the Earth, and the identity of the morning and evening stars as the planet Venus. Theaetetus (c.

### What type of math was created in ancient Greece?

Answer: The period between 250 and 350 AD is the Silver Age of Ancient Greek Mathematics. During this period Diophantus made significant advances in algebra, particularly indeterminate analysis. It is known as Diophantine Analysis. A Diophantine equation and a polynomial are one and the same.

### When did mathematicians start in ancient Greece?

The answer is: This is a timeline of mathematicians in ancient Greece. Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus (cca. 624–548 BC), which is indicated by the green line at 600 BC. The orange line at 300 BC indicates the approximate year in which Euclid ‘s Elements was first published.

### What numbers were used in Ancient Greek mathematics?

Response will be: Incommensurability and Pythagoras’ TheoremAs with other ancient cultures, the only numbers in Greek mathematics were positive integers. These were used to compare lengths/sizes of objects. Definition. Lengths are in the ratio m:n if somesub-lengthdivides exactly m times into the first andn times into the second.

### What did the Greeks understand about mathematical rigour?

Answer to this: The Greeks understood something that somehow eluded the Egyptians: the importance of mathematical rigour. Ancient Egyptians, for example, equated the area of a circle to the area of a square whose sides were 8/9 of the circle’s diameter.

### Why did the Greeks look into geometry?

After many unsuccessful attempts in finding the value of the square root of 2, the Greeks had no choice but to accept that arithmetic could not be the basis of mathematics. They had to look somewhere else, so they looked into geometry. Euclid (c.325- c. 265 BCE) was an ancient Greek mathematician who lived in Alexandria.

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### When did mathematicians start in ancient Greece?

This is a timeline of mathematicians in ancient Greece. Historians traditionally place the beginning of Greek mathematics proper to the age of Thales of Miletus (cca. 624–548 BC), which is indicated by the green line at 600 BC. The orange line at 300 BC indicates the approximate year in which Euclid ‘s Elements was first published.

### What were some ancient Greek mathematical works?

The response is: The names of ancient Greek mathematical works run to pages. A few may be mentioned. Elements written by Euclid at around 300 BC was the most comprehensive work from history on geometry. Pappus had written the Mathematical Collection which was an account of classical mathematics from Euclid to Ptolemy. Treasury of Analysis was his work.

### What numbers were used in Ancient Greek mathematics?

Response will be: Incommensurability and Pythagoras’ TheoremAs with other ancient cultures, the only numbers in Greek mathematics were positive integers. These were used to compare lengths/sizes of objects. Definition. Lengths are in the ratio m:n if somesub-lengthdivides exactly m times into the first andn times into the second.

### Why did the Greeks look into geometry?

In reply to that: After many unsuccessful attempts in finding the value of the square root of 2, the Greeks had no choice but to accept that arithmetic could not be the basis of mathematics. They had to look somewhere else, so they looked into geometry. Euclid (c.325- c. 265 BCE) was an ancient Greek mathematician who lived in Alexandria.

## Relevant information

And did you know: The names of ancient Greek mathematical works run to pages. A few may be mentioned. Elements written by Euclid at around 300 BC was the most comprehensive work from history on geometry. Pappus had written the Mathematical Collection which was an account of classical mathematics from Euclid to Ptolemy. Treasury of Analysis was his work.
Did you know: The basic of mathematics was inherited by the Greeks and independent by the Greeks beg the major Greek progress in mathematics was from 300 BC to 200 AD. After this time progress continued in Islamic countries Unlike the Babylonians, the Egyptians did not develop fully their understanding of mathematics.
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