As there seems to be no naming of this, I would like to call this Golden Square.
Tuesday, October 24, 2006
Phi-by-Phi Square
I have tried to use my Excel sheet to make calculation on various angles of the golden rectangle, which is 1 by phi. I have found out that by extending the shorter side from 1 to phi, a phi-by-phi square is formed, and the new diagonal line on the extended area (1/phi by phi) is SQRT(3) and forms tangent 2.61803399.. on the corner, as compared with tangent 1.61803399.. on the corner of the original rectangle.
As there seems to be no naming of this, I would like to call this Golden Square.
Excel Trigonometry
As there seems to be no naming of this, I would like to call this Golden Square.
Friday, October 13, 2006
Excel as Decoding Tool
"Study this paragraph and all things in it. What is vitally wrong with it? Actually, nothing in it is wrong, but you must admit that it is most unusual. Don't just zip through it quickly, but study it scrupulously. With luck you should spot what is so particular about it and all words found in it. Can you say what it is? Tax your brains and try again. Don't miss a word or a symbol. It isn't all that difficult.... "
I have tried, first glancing and then staring at it, but could'nt find out how there is something particular or unsual about it. Sarah Flannery, a talented young mathematician and author of 'A Mathematical Journey', says in her book that "anyone acquainted with encoding algorithm should have no difficulty finding an answer."
Here is my spreadsheet designed to verify the answer. It is used to locate the position where any of the alphabetical letter, both small and capital, appears first, if any.
I have then used this spreadsheet to find out if there is something similarly particular or unusual about Samuel Ullman's prose "Youth", which has more than twice as many characters and symbols as "study this paragraph ..".
"Youth" by Samuel Ullman
"Youth is not a time of life, it is a state of mind; it is not a matter of rosy cheeks, red lips and supple knees; it is a matter of the will, a quality of the imagination, a vigor of the emotions; it is the freshness of the deep springs of life.
Youth means a temperamental predominance of courage over timidity, of the appetite for adventure over the love of ease. This often exists in a man of sixty more than a boy of twenty. Nobody grows old merely by a number of years. We grow old by deserting our ideals.
Years may wrinkle the skin, but to give up enthusiasm wrinkles the soul. Worry, fear, self-distrust bows the heart and turns the spirit back to dust.
Whether sixty or sixteen, there is in every human being's heart the lure of wonder, the unfailing child-like appetite of what's next, and the joy of the game of living. In the center of your heart and my heart there is a wireless station; so long as it receives messages of beauty, hope, cheer, courage and power from men and from the infinite, so long are you young.
When the aerials are down, and your spirit is covered with the snows of cynicism and the ice of pessimism, then you are grown old, even at twenty, but as long as your aerials are up, to catch the waves of optimism, there is hope you may die young at eighty."
The result shows that the paragraphs do not contain a z, but they do contain all of the other letters.
Samuel Ullman and "Youth": The Life, the legacy
In Code: A Mathematical Journey
Prose in Pi
I have tried, first glancing and then staring at it, but could'nt find out how there is something particular or unsual about it. Sarah Flannery, a talented young mathematician and author of 'A Mathematical Journey', says in her book that "anyone acquainted with encoding algorithm should have no difficulty finding an answer."
Here is my spreadsheet designed to verify the answer. It is used to locate the position where any of the alphabetical letter, both small and capital, appears first, if any.
I have then used this spreadsheet to find out if there is something similarly particular or unusual about Samuel Ullman's prose "Youth", which has more than twice as many characters and symbols as "study this paragraph ..".
"Youth" by Samuel Ullman
"Youth is not a time of life, it is a state of mind; it is not a matter of rosy cheeks, red lips and supple knees; it is a matter of the will, a quality of the imagination, a vigor of the emotions; it is the freshness of the deep springs of life.
Youth means a temperamental predominance of courage over timidity, of the appetite for adventure over the love of ease. This often exists in a man of sixty more than a boy of twenty. Nobody grows old merely by a number of years. We grow old by deserting our ideals.
Years may wrinkle the skin, but to give up enthusiasm wrinkles the soul. Worry, fear, self-distrust bows the heart and turns the spirit back to dust.
Whether sixty or sixteen, there is in every human being's heart the lure of wonder, the unfailing child-like appetite of what's next, and the joy of the game of living. In the center of your heart and my heart there is a wireless station; so long as it receives messages of beauty, hope, cheer, courage and power from men and from the infinite, so long are you young.
When the aerials are down, and your spirit is covered with the snows of cynicism and the ice of pessimism, then you are grown old, even at twenty, but as long as your aerials are up, to catch the waves of optimism, there is hope you may die young at eighty."
The result shows that the paragraphs do not contain a z, but they do contain all of the other letters.
Samuel Ullman and "Youth": The Life, the legacy
In Code: A Mathematical Journey
Prose in Pi
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