Figured Numbers - Sacred Tetractys One particular...

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Figured Numbers The Pythagoreans represented numbers by patterns of dots, probably a result of arranging pebbles into patterns. The resulting figures have given us the present word figures. Thus 9 pebbles can be arranged into 3 rows with 3 pebbles per row, forming a square. Similarly, 10 pebbles can be arranged into four rows, containing 1, 2, 3, and 4 pebbles per row, forming a triangle. From these they derived relationships between numbers. For example, noting that a square number can be subdivided by a diagonal line into two triangular numbers, we can say that a square number is always the sum of two triangular numbers. Thus the square number 25 is the sum of the triangular number 10 and the triangular number 15.
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Unformatted text preview: Sacred Tetractys One particular triangular number that they especially liked was the number ten. It was called a Tetractys, meaning a set of four things, a word attributed to the Greek Mathematician and astronomer Theon (c. 100 CE). The Pythagoreans identified ten such sets. Ten Sets of Four Things Numbers 1 2 3 4 Magnitudes point line surface solid Elements fire air water earth Figures pyramid octahedron icosahedron cube Living Things seed growth in length in breadth in thickness Societies man village city nation Faculties reason knowledge opinion sensation Seasons spring summer autumn winter Ages of a Person infancy youth adulthood old age Parts of living things body three parts of the soul...
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