The Ancient Greeks used whole numbers, fractions, and irrational numbers such as the square root of 2 and pi in their mathematics.
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Ancient Greek Mathematics: Numbers Used
The ancient Greeks made significant contributions to the field of mathematics and used various types of numbers in their calculations. As mentioned, the Greeks used whole numbers, fractions, and irrational numbers such as the square root of 2 and pi in their mathematics.
According to historian Carl B. Boyer, “The Greeks made the first attempt to establish a logical system that would enable them to deduce mathematical truths by using axioms and theorems based on deductive reasoning.” This method of deductive reasoning led to the development of geometry, which was heavily influenced by the Greeks’ use of numbers.
One interesting fact is that the Greeks had two different systems for numbering. The first was the Attic system, which used symbols for the first nine numbers and then symbols for every tenth number (10, 20, 30, etc.). The second system was the Ionian system, which used symbols for the first four numbers and then symbols for every fifth number (5, 10, 15, etc.).
Another fascinating fact is that the Greek mathematician Pythagoras is known for his theorem that states, “In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.” This theorem is still used extensively in modern mathematics and science.
Below is a table showing some of the numbers used by the ancient Greeks:
| Type of Number | Example |
|---|---|
| Whole Number | 1, 2, 3, 4, etc. |
| Fraction | 1/2, 3/4, 5/6, etc. |
| Irrational Number | √2, π |
In conclusion, the ancient Greeks made significant contributions to mathematics and used whole numbers, fractions, and irrational numbers such as the square root of 2 and pi in their calculations. Their use of deductive reasoning and the development of geometry have had a lasting impact on the field of mathematics.
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In Attic Greek (Attica = Athens) strokes were used for 1–4 and larger numerals used the first letter of the words for 5, 10, 100, 1000 and 10000. For example, Πεντε (pente) is Greek for five, whence Π denoted the number 5. Δεκα (deca) means ten, so Δ was 10.
The ancient Greeks used two numeral systems: the acrophonic Attic numerals and the Attic or Herodianic numerals. The Attic or Herodianic numerals were fully developed by about 450 BCE and were in regular use possibly as early as the 7th Century BCE. It was a base 10 system similar to the earlier Egyptian one and the later Roman system, with symbols for 1, 5, 10, 50, 100, 500, and 1,000 repeated as many times needed to represent the desired number.
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, …
In this video, you may find the answer to “What numbers were used in Ancient Greek mathematics?”
The video explores the roots of Greek mathematics, highlighting the Greeks’ passion for the subject and their emphasis on proofs. Although little original work remains, historians have reconstructed the Greeks’ mathematical ideas and theories. Additionally, the video discusses the Greeks’ numeral system, which consisted of 24 letters from the Greek alphabet and three Phoenician letters. This system was additive, and bar extensions or accents were used to differentiate numerals from normal language. It is speculated that all of the mathematicians and their discoveries discussed in the series would have been written and solved using this numeral system.
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What numbers did Greek mathematicians use? The ancient Greeks used the 24 letters of their alphabet plus three special signs called episemons–vau or digamma or stigma (6), koppa or qoppa (90), and san or sampi (900)–as the basis of their numeral system (Cajori 1993, p.
Regarding this, What numbering system did ancient Greeks use?
In reply to that: The ancient Greeks had two numeral systems. The acrophonic system was used until around 100 BCE and inspired the Roman numeral system. The alphabetic numerals use 27 different symbols in different combinations.
Hereof, How did Greeks do math without zero? As a response to this: The Greeks knew of zero as a concept but did not think of it as a number with the same usefulness in mathematics as the numbers 1–9. According to Aristotle, it was not possible to divide by 0 and get a meaningful result, so the Greek system was based on 9 numbers—no zero.
Also question is, What is 1 2 3 in Greek? One – ένα – ena. Two – δύο – thio (th pronounced like “the”) Three – τρία – tria. Four – τέσσερα – tessera.
Similarly one may ask, What are the two systems of Ancient Greek numerals? The response is: There are two major systems of ancient Greek numerals, one of which is still in common usage in mathematics today. These two systems are called the acrophonic number system and the alphabetic number system.
In respect to this, What was the earliest numerical notation used by the Greeks? The response is: Next:About this document Greek Numbers and Arithmetic The earliest numerical notation used by the Greeks was the Atticsystem. It employed the vertical stroke for a one, and symbols for “5", “10", “100", “1000", and “10,000".
Secondly, How did the ancient Greeks contribute to modern mathematics? The response is: The contributions made by the ancient Greeks to the field of mathematics gave birth to modern math. In general, the Greeks were mostly focused on geometry, hoping to explain shapes using numbers. This focus led to some pretty significant discoveries, all of which are still relevant to the mathematics we do today.
Keeping this in consideration, What are the two systems of Ancient Greek numerals?
Response will be: There are two major systems of ancient Greek numerals, one of which is still in common usage in mathematics today. These two systems are called the acrophonic number system and the alphabetic number system.
Beside this, What was the earliest numerical notation used by the Greeks?
Next:About this document Greek Numbers and Arithmetic The earliest numerical notation used by the Greeks was the Atticsystem. It employed the vertical stroke for a one, and symbols for “5", “10", “100", “1000", and “10,000".
How did the ancient Greeks contribute to modern mathematics? As an answer to this: The contributions made by the ancient Greeks to the field of mathematics gave birth to modern math. In general, the Greeks were mostly focused on geometry, hoping to explain shapes using numbers. This focus led to some pretty significant discoveries, all of which are still relevant to the mathematics we do today.