Friday, June 29, 2007

The Expanded Similar Triangles Poem

The similar triangles method for constructing mathematical poems easily enables us to manipulate a logical structure for metaphoric expression. What this pedagogical blog entry is trying to accomplish is the introduction and showing of the expanded version of the similar triangles poem. This poetic structure is logically more complex however, still easy to manipulate.

Before you read further, please be familiar with the similar triangles poem. You may read about it here.

The 'regular' similar triangles poem only utilizes two similar triangles and is defined as an expression of two ratios. The expanded similar triangles poem utilizes ‘n’ number of ratios and is able to create very large (infinite) complex mathematical poems and still have a logical structure to act as a source domain for our metaphoric expression.

I am going to create an expanded similar triangle poem made of three similar triangles to serve as our example.
The following image shows three similar triangles with three different sets of relationships:‘a is to b’ as ‘c is to d’ and ‘e is to f’

The trick in the construction of the poem is to add or subtract the numerators of two of the relationships and also add or subtract the two corresponding denominators of the same two relationships. The next image shows us how we construct our three ratios and associated them differently with subtraction and addition to form six flavors. There are actually 12 flavors possible however; I wish to focus on these six, which I consider the best ones to give us a good understanding of what is occurring in this method.

Each flavor yields a group of six equations after the flavor is solved for each variable. The next six images show the six syntactical arrangements for each flavor. There are at least seventy-two different syntactical arrangements however; I wish to focus on what I feel to be the thirty-six most important ones. The next six images show each of the six groups created by each flavor.

FLAVOR ONE YIELDS:
FLAVOR TWO YIELDS:

FLAVOR THREE YIELDS:

FLAVOR FOUR YIELDS:

FLAVOR FIVE YIELDS:

FLAVOR SIX YIELDS:

Lets now create a poem using the following text.

a = Love Lies
b = The Lonely
d = Sugar
e = The Starving
g = Sexual Conquests
h = The Insecure

The structure follows as thus: ‘Love Lies’ is to ‘The Lonely’ as ‘Sugar’ is to ‘The Starving’ as ‘Sexual Conquests’ are to ‘The Insecure’

We then substitute the variables with the poetic phrases to yield thirty-six poems in six groups relating back to the flavors shown above.

I find it interesting to savor each syntactical permutation to get a ‘feel’ for each poetic expression.

GROUP ONE CONSTRUCTED FROM FLAVOR ONE:

GROUP TWO CONSTRUCTED FROM FLAVOR TWO:

GROUP THREE CONSTRUCTED FROM FLAVOR THREE:

GROUP FOUR CONSTRUCTED FROM FLAVOR FOUR:

GROUP FIVE CONSTRUCTED FROM FLAVOR FIVE:

GROUP SIX CONSTRUCTED FROM FLAVOR SIX:

Many of the links below are examples of the expanded similar triangles poem.

Love And Ego

Today, I would like to express my gratitude to JoAnne Growney and Sarah Glaz for accepting one of my works (above) into their collection of mathematical love poems that they are editing for their upcoming book.

Wednesday, June 27, 2007

Another From Gregory Vincent St. Thomasino

The NYC philosopher/poet Gregory Vincent St. Thomasino would like to see a math poem of his cartoon shown above. The result is a similar triangles poem shown below.

Sunday, June 24, 2007

Two Emblem Poems From Thierry Brunet

I just received two images from Thierry Brunet and would like to discuss them. Both of these images I would consider emblem poems with a mathematical emphasis. Thierry has made some interesting connections in these poems. The first one I wish to point out is in his piece titled "HeXaedron". A Hexahedron is commonly known as a cube as well as being a regular polyhedral. Thierry asks “how many platonic solids do we need to dream TOMORROW? The answer depends on many things but my first thought is the question of what dimensions are we limited to? There are 5 platonic solids in the third dimension 6 in the fourth dimension and 3 in every dimension above the fifth. So if we include all dimensions we have an infinite choice. However, he is pointing at time by mentioning the PRESENT as well as TOMORROW so this also makes me entertain the idea of relativity.

Another thing I find interesting is the statement “Don’t forget the empirical BEAUTY of experience. Thierry now connects by capital letters time with beauty however, more important to me is the idea of an aesthetic of beauty tied directly to logic through an empirical process. Some artists would argue that beauty cannot be expressed with a logical statement. I feel they should be nauseous from eating only the icing and none of the cake.

The second piece is titled “mouTH THeory” I like this piece as well because I find my reality can be seen in terms of topology and beliefs are the forces that distort that topology. And here we have a lady whose scream swallows it.

Saturday, June 16, 2007

Two Mathematical Poems For Gregory Vincent St. Thomasino

“Profundity” is the title of the first mathematical poem and the second “Logoclasody”.

The drawing above is by Gregory Vincent St. Thomasino

If discourse is a river then what is a lake?
Is not the Philosopher a dam?

Logoclasody

The two mathpoems above are similar triangles poems
Also related is the Avrin proposition

Friday, June 01, 2007

The Account Of Oscar

The following is a mathematical adaptation and edition of an Oscar Wilde quote.

The later poem is in the form of an orthogonal space poem