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Other small Pythagorean triples such as (6, 8, 10) are not listed because they are not primitive; for instance (6, 8, 10) is a multiple of (3, 4, 5). Each of these points (with their multiples) forms a radiating line in the scatter plot to the right. Additionally, these are the remaining primitive Pythagorean triples of numbers up to 300:
In English-language poetry, a tetractys is a syllable-counting form with five lines. The first line has one syllable, the second has two syllables, the third line has three syllables, the fourth line has four syllables, and the fifth line has ten syllables. [13] A sample tetractys would look like this: Mantrum Your / fury / confuses / us all ...
In a traditional French triolet, the second and third non-repeating lines rhyme with the repeating first, fourth, and seventh lines, while the non-repeating sixth line rhymes with the second and eighth repeating lines. However, especially in German triolets of the 18th and 19th centuries, one will see this pattern often violated. [1]
English-language haiku is an example of an unrhymed tercet poem. A poetic triplet is a tercet in which all three lines follow the same rhyme, AAA; triplets are rather rare; they are more customarily used sparingly in verse of heroic couplets or other couplet verse, to add extraordinary emphasis. [2]
First and third lines have a feminine rhyme and the second and fourth lines have a masculine rhyme. A 1 abA 2 A 1 abA 2 – Two stanzas, where the first lines of both stanzas are exactly the same, and the last lines of both stanzas are the same. The second lines of the two stanzas are different, but rhyme at the end with the first and last lines.
The poet Heraclitus of Ephesus (fl. c. 500 BC), who was born across a few miles of sea away from Samos and may have lived within Pythagoras's lifetime, [14] mocked Pythagoras as a clever charlatan, [8] [14] remarking that "Pythagoras, son of Mnesarchus, practiced inquiry more than any other man, and selecting from these writings he manufactured ...
The unstressed syllables were relatively unimportant, but the caesurae (breaks between the half-lines) played a major role in Old English poetry. [16] In place of using feet, alliterative verse divided each line into two half-lines. Each half-line had to follow one of five or so patterns, each of which defined a sequence of stressed and ...
With a the shorter and b the longer legs of a triangle and c its hypotenuse, the Pythagoras family of triplets is defined by c − b = 1, the Plato family by c − b = 2, and the Fermat family by | a − b | = 1. The Stifel sequence produces all primitive triplets of the Pythagoras family, and the Ozanam sequence produces all primitive triples ...