A consideration of the golden ratio and the shell in Holmes' poem

1. K N O W L E D G E I S N O T A L I S T O F F A C T S ; I T I S
A C O L L E C T I O N O F O B S E R V A T I O N S T H A T
E N A B L E U S T O S E E T H E H A N D O F G O D I N
E V E R Y F A C E T O F O U R U N I V E R S E .
“ N A T U R E ’ S G R E A T B O O K I S W R I T T E N I N
M A T H E M A T I C S . ” - - G A L I L E O
Math in
Literature
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2. Objectives
 Students will learn about the number Phi
 Students will conduct activities that utilize Phi
 Students will make connections between the number
Phi and the nautilus shell
 Students will learn why Holmes was able to grasp the
lessons of a chambered nautilus

3. Instructions
 As you read the slides, be sure to make note of any
slides with hyperlinks
 Connect to hyperlinks to access web pages that will
enable you to respond to the questions or to
complete activities

4. “Cracking the Da Vinci Code”
 Click on the article title above to respond to these
questions:
 What is Phi? Which Greek wrote about it?
 In Liber Abaci, Leonardo of Pisa poses a problem
involving rabbits. Paraphrase his observation.
 Why was he called Fibonacci?
 What IS the Fibonacci sequence?

5. The Golden Ratio
 Who was Johannes Kepler? (research it)
 Click on the slide title to access the article for answers to these
questions:
 What are math’s greatest treasures, according to Kepler?
 Illustrate Phi by cutting your string accordingly.
 Phi is the only number whose square is ____ and whose reciprocal is
____
 What geometric figures utilize Phi?
 Name 1 connection between Phi and the Bible.

6. Let’s Do Some Math!
 Use the graph paper and colored pencils to complete
the work for the lesson, borrowed from “Mensa for
Kids” at
 Mensa for Kids (Lesson 3, pp. 6-7)

7. Golden Ratio in Nature
 Visit
 http://jwilson.coe.uga.edu/emat6680/parveen/fib_
nature.htm
 Explain the presence of the golden ratio in:
 pine cones
 sunflowers
 branching plants
 starfish
 fingers
 ears

8. Oliver Wendell Holmes, Sr.
 To learn more about Holmes (Sr.), let’s visit
http://www.notablebiographies.com/He-Ho/Holmes-Oliver-
Wendell.html
 What professions did Holmes pursue?
 What was his father’s profession? How did Holmes seem to feel about
his father’s position?
 What did he first study at Harvard?
 What kinds of writing did he produce?
 Where did Holmes study medicine? Where did he teach?
 Whom did he marry? What important position did his firstborn hold?
 As a scientist and poet, he was able to bring to light lessons that might
have gone unspoken.

9. “The Chambered Nautilus”
 As a physician, Holmes was especially
knowledgeable about anatomy. You
can be sure he was very familiar with
the design of the chambered nautilus.
 Read the poem in the book to answer
questions about his famous poem.

10.  What does the word nautilus mean? Why is it “chambered”?
 What is the metaphor used in line 1, and what does “feign” mean in regards to it?
 Explain the allusion to “sirens” in line 5. Who are the “sea-maids” (l. 7)?
 Why would Holmes use mythical imagery in a poem about a shell?
 Why do the “webs . . . no more unfurl” (l. 8)?
 Describe the shell as it now appears.
 Explain the lines: “Where its dim dreaming life was wont to dwell / As the frail
tenant shaped his growing shell. . .” (ll. 11-12).
 What forces shaped the new chambers, and why were they forged?
 As the new chambers were created, what happened to the old ones?
 Line 22 contains an apostrophe (not the punctuation). What is being addressed?
 What is the paradox of line 25?
 Who is Triton (l. 26)?
 What message does the speaker gain?
 What do the last 2 lines mean?
 Research the purpose served by the closed chambers of the shell, then explain how
our pasts can influence our present and future.
Questions