One of the best aspects of the internet as well as the worst (most embarrassing) is the fact that if you make a mistake it is permanent and you cannot go back and erase it. I have discovered an error in my mathematical terminology and need to correct it. What I have been calling "congruent triangles" are not congruent triangles they are “similar triangles.” "Congruent triangles" are referring to two triangles that are the same size. Similar triangles have the same shape but different sizes. Obviously, my memory is not good as it needs to be. If conveying this error has caused any embarrassment to anyone one, I am sorry.
--However--
The good thing is that it does not affect the meaning, mechanics or the importance of this poetic form. However, I must clean up the mess and continue. What you have known to be the "Congruent Triangles Poem" is now correctly re-identified as a "Similar Triangles Poem". Furthermore, if you notice a mistake on my blog or website please challenge it. I appreciate all help.
The mathematical poem today is a similar triangles poem inspired by the text below which appeared in the delancyplace blog Tuesday, August 21, 2007
Delanceyplace.com 08/21/07-The Guillotine
In today's excerpt--Dr. Guillotin's invention, the guillotine, which debuted in Paris in 1792 and was still being used for capital punishment in the 1950s. Guillotin's motive was to introduce a more humanitarian form of capital punishment, and his success in that was evident from the very first use of the guillotine when "the crowds, accustomed to bloody bouts with the ax and sword, thundered in disappointment, 'Bring back the block!' " Yet almost immediately, guillotine executions became Paris's favorite form of entertainment, with families bringing picnic lunches and reveling in the carnival atmosphere that surrounded them. During the French Revolution, with a virtual civil war raging in the provinces, "at least half a million people were slaughtered on local guillotines or in battles between opposing forces." Here is a description of France's last public guillotine execution, which occurred in Versailles in 1939 when convicted murderer Eugene Weidmann, a German, was decapitated:
"Weidmann's execution was slated for June 17, and throngs had been pouring in from Paris and elsewhere for days, lending a holiday mood to the town. Permitted to stay open all night, bistros overflowed with customers as elated by the event as fans on the eve of a football match. The guillotine, which had normally done its deed inside the jail, was moved to the street outside, and proprietors of apartments above were cashing in by renting seats in their windows. From his cell Weidmann could hear loudspeakers blaring jazz interspersed with commentaries on his impending demise. ...
"Despite his years of experience, Desfourneaux [the executioner] was slow and jittery. Only after three tries did he manage to squeeze Weidmann's neck into the lunette, and he also fumbled with the lever. The operation lasted twelve seconds--twice the normal time. The crowd, which had been waiting in hushed anticipation, stormed the police barrier as the blade fell. Men shouted anti-German epithets; elegant ladies, avid for souvenirs, rushed to dip their handkerchiefs in the blood; and, for the rest of the day and far into the night, revelers chanted songs and swilled wine. ...
"Perched on rooftops, photographers recorded the tumult, and their pictures quickly appeared in newspapers around the world and became a staple of postcards. The fiasco shocked even the most intransigent proponents of capital punishment, and also cast doubt on the doctrine that public executions deterred crime. Fearing that future outbursts would damage France's image abroad, Premier Edouard Daladier decreed that guillotinings were henceforth to be conducted within prison enclosures."
Stanley Karnow, Paris in the Fifties, Three Rivers Press, Copyright 1997 by Stanley Karnow, pp. 161-162.
A few days ago, Pablo Kagioglu shared a power point presentation that he made in where he had constructed a verbogeometric coordinate system, which displays 12 contiguous orthogonal space poems that share a common axis system. This is important for what I see him having done is creating is a crystal-like dodecaorthogonal space poem! He has shown us another beautiful mathematical poetic structure. Now I must say that his philosophy may be controversial and I have to admit that I find some of the poems a bit problematic. However, I really am not interested in critiquing what he has said. What I find extremely important here is that he has discovered a new mathematical poetic form that we all can use, build upon or do what ever our creative hearts desire. Furthermore, I want to congratulate him on doing so!
As I said, I am not going to analyze his content I am going to post it just as he sent it to me. He has graciously allowed me to post the following for everyone to enjoy.
Planes of Truth and Perception by Pablo Kagioglu
As I have become more interested in what goes on around the world, I have also become somewhat frustrated by the actual lack of true information available; this in a world that is literally flooded with news. Long ago there were only Newspapers, then Radio came along, then Television. Each time adding the medium more immediacy to the availability of information, but not necessarily more relevant content. So, in the age of 24-hour news channels, it is amazing how miss informed most people are about important world events…
I have traveled around Europe and the Americas quite bit, and listened to the opinions of many people, watched their newscasts, read their newspapers. On occasion, I was asked about my own opinions, and as I gave my opinions I slowly came to this realization:
“The futility of formulating an opinion on important events based on what we see on news broadcast alone”
- Our perceptions or opinions are constructed in the same manner as a drawing a picture using dots with numbers
- Different newscasts give us only a partial number of the dots required to come up with the correct picture
- Some of the newscasts number give us properly “located” dots, but numbered with the incorrect sequence
- If you are unfortunate enough to watch an unreliable source, you will get wrong positioned dots altogether.
- Newscasts keep giving us the same dots over and over, instead of additional (new) dots.
- Over time, we never get enough (properly numbered) dots to formulate the complete “true’ picture of what is really happening.
In general, it can be said that “true” information is broadcast all around the world, but no one is likely to get the “whole package” delivered to them from one source, specially only watching local/national news.
If one searches really hard, and looks at all possible “good” sources, you still may only end up with only half the dots anyway (the more controversial the subject, the fewer the dots you are likely to get).
In the end most people sit around and argue because some drew a House while others drew a Pyramid, when it reality it is probably neither.
So, I wondered if Truth and Perception could be plotted in a 3-dimensional space somehow, using various concepts as the 3 axes.
Words pairs that come to mind are: Truth/Lies, Knowledge/Perception, Openness/Deception, Order/Chaos, Guilt/Innocence, Censorship/Approval
What follows is the construct of the various planes of demarcation for Truth or Lies, Knowledge or Perception.
The mathematical structure that we use when making similar triangles poems provides an interesting result when used in conjunction with the creation of verbogeometric prisms. It appears that we can mathematically define a point in a verbogeometric space whereby we know the meaning of the word in that location however; there is no word in the dictionary for it. It seems to be some kind of phantom word that exists by a set of rules however, no spelling for it.
Let us look at the image above. We can see the points X1 and X2 in the image and notice there are no words in the dictionary to cover their meanings however, we know that it is a direct negation of the words sterile and Barren. These words could be described as "unsterile" and "unbarren" however it may be more fun to flavor them poetically as shown in the examples below.
Alternatively, even more fun … we can really emphasize the flavoring of X1 by using the expanded similar triangles form and including all of the antonyms and synonyms.
This page is reserved for all of Pablo Kagioglu Mathematical Poems
Dodecaorthogonal Space Poems
Electronic Paradigm Poems by Pablo Kagioglu
Pablo Kagioglu's Love
Pablo Kagioglu's Passion
Pablo Kagioglu's creation
The Paradigm Poem
Unlike a simple mathematical structure as in the “Similar Triangles Poem”, the “Paradigm Poem” is a mathematical poetry technique that borrows its structure from an existing equation from applied mathematics of scientific or cultural significance. The “Paradigm Poem has many sub-categories which are as numerous as there are categories for applied mathematics. Examples that we could consider would be: “Physics Paradigm Poem”, “Chemistry Paradigm Poem”, “Business Accounting Paradigm Poem”, “ Psychophysiological Paradigm Poem” etc.
If we think in terms of metaphor using the cognitive scientific language of George Lakoff then we would classify the language of the variables “inside the equation structure” as the ‘target domain’ and the context or traditional meaning of the equation as the “source domain’
Let me show an example of a “Physics Paradigm Poem” using Newton’s second law. For this example I am going to use an excerpt from my essay on “Polyaesthetics and Mathematical Poetry” Journal of Mathematics and the Arts, Volume 1, Issue 1 March 2007 , pages 35 - 40 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954
“My personal view is that almost all mathematic applications rely on using equations with the intent similar to simile. The variables in the equation are compared explicitly with the result for uses in denotation. For example, in the case of an application of
Newton’s second law F = ma, or Force equals Mass times Acceleration, we are comparing the variables m (Mass) and a (Acceleration) explicitly to F (Force).
I can now make a mathematical poem based on the latter example by expressing the Force of ‘yesterday’s freedom’ as being equal to ‘a lush clover patch’
multiplied by ‘the swelling sweet summer breeze traversing the morning’. We can then put this in the form of a mathematical equation as; Yesterday’s freedom = (a lush clover patch) (the swelling sweet summer breeze traversing the morning). In other words, I set the Force to ‘Yesterday’s freedom’, the mass to ‘a lush clover patch’, and I accelerated the mass by ‘the swelling sweet summer breeze traversing the morning’. All of these
phrases relate back to the original equation from physics F = ma. I want to emphasize that I was very careful when I made my choice for acceleration so that the phrase is evocative of the mathematical description of acceleration as defined by physics. Acceleration is the
change in velocity of an object per unit of elapsed time during that acceleration. Here, the change in velocity is implied by ‘swelling’ and the change in time is implied by ‘traversing’.”
In the above example we are using the words “Yesterday’s freedom; a lush clover patch; the swelling sweet summer breeze traversing the morning” as the variables of the equations which supply us with the target domain and then we are using the equation from physics F = ma, its scientific meaning and historical significance as the source domain.
The bottom line concerning the ‘paradigm poem’ is that we borrow an equation from the past which inherently contains historical significance and serves as an paradigm or mathematical model that seems almost “a vessel” to carry the mathematical poem. The paradigm poem always borrows an existing mathematical structure to serve as a source domain in our metaphor.
