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Pythagoras and Pythagoreanism, Summaries of Educational Mathematics

A brief account of the life of Pythagoras, the eponymous founder of Pythagoreanism, and the beliefs and contributions of the Pythagoreans. It discusses his birthplace, education, and the mystical and mathematical principles that he and his followers believed in. The document also mentions the Pythagorean theorem and other discoveries attributed to Pythagoras in various fields. The use of commas, colons, and semicolons is briefly explained.

Typology: Summaries

2020/2021

Available from 06/21/2023

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Pythagoras
He was an ancient Greek philosopher and the eponymous founder of
Pythagoreanism.There is not a single detail in the life of Pythagoras
that stands uncontradicted. But it is possible, from a more or less
critical selection of the data, to construct a plausible
account.Herodotus, Isocrates, and other early writers agree that
Pythagoras was the son of Mnesarchus, and that he was born on the Greek
island of Samos in the eastern Aegean.His mother was a native of Samos,
descending from a geomoroi family Pythagoras is traditionally thought to
have received most of his education in the Near East. Like many other
important Greek thinkers, Pythagoras was said to have studied in Egypt.he
so-called Pythagoreans, who were the first to take up mathematics, not
only advanced this subject, but saturated with it, they fancied that the
principles of mathematics were the principles of all things.According to
Aristotle, the Pythagoreans used mathematics for solely mystical reasons,
devoid of practical application.They believed that all things were made
of numbers.The number one (the monad) represented the origin of all
things and the number two (the dyad) represented matter.The number three
was an "ideal number" because it had a beginning, middle, and end and was
the smallest number of points that could be used to define a plane
triangle, which they revered as a symbol of the god Apollo.The number
four signified the four seasons and the four elements. The number seven
was also sacred because it was the number of planets and the number of
strings on a lyre, and because Apollo's birthday was celebrated on the
seventh day of each month. They believed that odd numbers were masculine,
that even numbers were feminine, and that the number five represented
marriage, because it was the sum of two and three.
Ten was regarded as the "perfect number" and the Pythagoreans honored it
by never gathering in groups larger than ten.
Although Pythagoras is most famous today for his alleged mathematical
discoveries, classical historians dispute whether he himself ever
actually made any significant contributions to the field. Many
mathematical and scientific discoveries were attributed to Pythagoras,
including his famous theorem,as well as discoveries in the fields of
music, astronomy, and medicine. Since at least the first century BC,
Pythagoras has commonly been given credit for discovering the Pythagorean
theorem, a theorem in geometry that states that "in a right-angled
triangle the square of the hypotenuse is equal [to the sum of] the
squares of the two other sides" that is,
a^{2}+b^{2}=c^{2}
Uses of the following:
Commas- Use commas to separate words and word groups in a simple series
of three or more items. Example: My estate goes to my husband, son,
daughter-in-law, and nephew.
colons: We knew who would win the game: the Eagles.
Semicolons:Use semicolons to connect related independent clauses
I ordered a cheeseburger for lunch; life's too short for counting
calories.
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Pythagoras He was an ancient Greek philosopher and the eponymous founder of Pythagoreanism.There is not a single detail in the life of Pythagoras that stands uncontradicted. But it is possible, from a more or less critical selection of the data, to construct a plausible account.Herodotus, Isocrates, and other early writers agree that Pythagoras was the son of Mnesarchus, and that he was born on the Greek island of Samos in the eastern Aegean.His mother was a native of Samos, descending from a geomoroi family Pythagoras is traditionally thought to have received most of his education in the Near East. Like many other important Greek thinkers, Pythagoras was said to have studied in Egypt.he so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.According to Aristotle, the Pythagoreans used mathematics for solely mystical reasons, devoid of practical application.They believed that all things were made of numbers.The number one (the monad) represented the origin of all things and the number two (the dyad) represented matter.The number three was an "ideal number" because it had a beginning, middle, and end and was the smallest number of points that could be used to define a plane triangle, which they revered as a symbol of the god Apollo.The number four signified the four seasons and the four elements. The number seven was also sacred because it was the number of planets and the number of strings on a lyre, and because Apollo's birthday was celebrated on the seventh day of each month. They believed that odd numbers were masculine, that even numbers were feminine, and that the number five represented marriage, because it was the sum of two and three. Ten was regarded as the "perfect number" and the Pythagoreans honored it by never gathering in groups larger than ten. Although Pythagoras is most famous today for his alleged mathematical discoveries, classical historians dispute whether he himself ever actually made any significant contributions to the field. Many mathematical and scientific discoveries were attributed to Pythagoras, including his famous theorem,as well as discoveries in the fields of music, astronomy, and medicine. Since at least the first century BC, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that "in a right-angled triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides" that is, a^{2}+b^{2}=c^{2} Uses of the following: Commas- Use commas to separate words and word groups in a simple series of three or more items. Example: My estate goes to my husband, son, daughter-in-law, and nephew. colons: We knew who would win the game: the Eagles. Semicolons:Use semicolons to connect related independent clauses I ordered a cheeseburger for lunch; life's too short for counting calories.

Exclamations: Use an exclamation mark at the end of a strong command, an interjection, or an emphatic declaration. “Stop!” he yelled. “You've got two flat tires!” Quote Marks: These marks are always used to enclose dialogue or other quoted material within an existing set of quotation marks. Another example of this follows. “Did he say 'I love you' yet?” her mother asked. Apostrophes: Use an apostrophe when showing possession ex- one table's leg or several tables' legs. Parentheses: Use parentheses to enclose information that clarifies or is used as an aside. Example: He finally answered (after taking five minutes to think) that he did not understand the question. Dashes: To divide a compound adjective with two equal parts.Ex-the India– Pakistan issue Hyphens: We have a two-year-old child. Citation in APA format (at least one resource): APA in-text citation style uses the author's last name and the year of publication, for example: (Field, 2005).