An Example of a "Learning Process" Journal (using the 2 colored box format)

Book: The Golden Ratio (2002) by Mario Livio

Source: New York: Broadway.

It is 10:45 am (Sunday). I read the first chapter on Friday and the second chapter earlier this morning. Modifying a mantra that the Pythagoreans used at the end of each day:

Upon the reading of a chapter
Reflect three times upon the following.
What was the key idea, what was understood
And what questions arise for deeper contemplation?

Chapter 1 Prelude to a Number

• Key idea: the golden ratio is an irrational number (1.618...) that occurs in many different situations
• Important points:
  • Defn.: if you divide a line segment into two unequal pieces such that the ratio of the length of the original piece to the length of the larger piece is the same as the length of the larger piece to the length of the smaller piece, then that ratio is usually called the golden ratio.
  • The early Greeks (Hippasus of Metapontum) knew (in 5th century BC) that this ratio was a never ending non-repeating decimal.
  • Professional mathematicians usually use the symbol t (tau) to represent this number, but in the last century the Greek letter f (phi) has become common.
  • phi is pronounced to rhyme with fly (I found this on a website) ( http://goldennumber.net/neophite.htm )

• Questions:
  • What does it mean to understand a special number such as f (or p, e or i )?
    • something about its history
    • something about its mathematical properties
    • something about its applications
  • Where can I find out more about f?
    • http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
    • http://mathworld.wolfram.com/GoldenRatio.html
    • http://goldennumber.net/
    • Mathematics: From the Birth of Numbers (1997). Ian Gullberg [p. 418-420]
    • The Nature of Mathematics. 10th ed. (2004). Karl J. Smith [p. 334 - 340]
• Among the people the author consulted were Mitch Feigenbaum, Roger Penrose & Stephen Wolfram.
• This book is currently available: A Mathematical History of the Golden Number (1999) Roger Herz-Fischler. I should try to order it from Chapters.

• Chapter 2 The Pitch and the Pentagram

  • Key idea: the golden ratio is closely tied to the pentagram
  • Important points:
    • the proof of Pythagoras's Theorem for a right angled triangle by means of two simple diagrams is insightful!

• Questions:
  • The book "Number: The Language of Science" (1930) is highly recommended. It is out of print (amazon.com) but is in the U of L library [ QA 9 D2 1954 ]
  • Another highly recommended book is The Universal History of Numbers (2000) by Georges Ifrah.
• Quotes:
  • Pythagoras emphasized the importance of learning ... because, in his words, "most men and women, by birth or nature, lack the means to advance in wealth and power, but all have the ability to advance in knowledge." [p. 26]

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