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Feb 3 2016

Tetractys or ten in math and in laungage

“Euclid, the mathematician of classical times, considered the number series 1, 2, 3, 4 to have mystical significance because its sum is 10, so he dignified it with a name of its own – Tetractys”. – Ray Stebbing

This post is a compilation from two sources mentioned at the end of the post. Don’t feel daunted by the name. “Tetractys” or ten, a triangular number composed of the sum of one, two, three and four.

 What are Tetractys?

The over-riding dictum of Pythagoras’s school was “All is number” or “God is number”, and the Pythagoreans effectively practiced a kind of numerology or number-worship, and considered each number to have its own character and meaning. For example,

the number one was the generator of all numbers;

two represented opinion;

three, harmony; four, justice;

five, marriage;

six, creation;

seven, the seven planets or “wandering stars”; etc.

Odd numbers were thought of as female and even numbers as male.

However, Pythagoras and his school – as well as a handful of other mathematicians of ancient Greece – was largely responsible for introducing a more rigorous mathematics than what had gone before, building from first principles using axioms and logic. Before Pythagoras, for example, geometry had been merely a collection of rules derived by empirical measurement. Pythagoras discovered that a complete system of mathematics could be constructed, where geometric elements corresponded with numbers, and where integers and their ratios were all that was necessary to establish an entire system of logic and truth.The holiest number of all was “tetractys” or ten, a triangular number composed of the sum of one, two, three and four. It is a great tribute to the Pythagoreans’ intellectual achievements that they deduced the special place of the number 10 from an abstract mathematical argument rather than from something as mundane as counting the fingers on two hands.

 

He is mainly remembered for what has become known as Pythagoras’ Theorem (or the Pythagorean Theorem): that, for any right-angled triangle, the square of the length of the hypotenuse (the longest side, opposite the right angle) is equal to the sum of the square of the other two sides (or “legs”). Written as an equation: a2 + b2 = c2.

Tetractys in language 

Since the kids have been introduced to syllabification in school, I thought it apt to introduce them at this stage to tetractys in language. This way they can relate math to language art.

Tetractys, was first used in language in a poetic form invented by Ray Stebbing. It consists of at least 5 lines of 1, 2, 3, 4, 10 syllables (total of 20). Tetractys can be written with more than one verse, but must follow with an inverted syllable count. Tetractys can also bereversed and written 10, 4, 3, 2, 1.

Double Tetractys: 1, 2, 3, 4, 10, 10, 4, 3, 2, 1

Triple Tetractys: 1, 2, 3, 4, 10, 10, 4, 3, 2, 1, 1, 2, 3, 4, 10

and so on.

What is a Tetractys?

The poetic form of the tetractys is a poem with only five lines. Each line adds another syllable until the last line which has ten.

What is the Stucture of a Tetractys?

A tetractys consists of 5 lines, each line has a set number of syllables see below:

Line 1 – 1 syllable
Line 2 – 2 syllables
Line 3 – 3 syllables
Line 4 – 4 syllables
Line 5 – 10 syllables

An Example of a Tetractys Poem

(1 syllable) I
(2 syllables) Am four
(3 syllables) And I go
(4 syllables) To big school where
(10 syllables) I learn to read and write and spell my name.

Double Tetractys Poem

For a more complex form there is the double tetractys, which is similar but has ten lines and is structured as shown below:

Line 1 – 1 syllable
Line 2 – 2 syllables
Line 3 – 3 syllables
Line 4 – 4 syllables
Line 5 – 10 syllables
Line 6 – 10 syllables
Line 7 – 4 syllables
Line 8 – 3 syllables
Line 9 – 2 syllables
Line 10 – 1 syllable

An Example of a Double Tetractys Poem

I 1
Am four 2
And I go 3
To big school where 4
I learn to read and write and spell my name. 10
It is fun and I play games with my friends 10
My best friend is 4
Called Rosie 3
She is 2
Nice. 1

 

Sources:

  1. http://www.storyofmathematics.com/greek_pythagoras.html
  2. https://www.forwardpoetry.co.uk/tetractys.php
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