Fibonacci sequence
The Fibonacci sequence is the series of numbers where each number is the sum of the two preceding numbers. For example,
O+1=1
1+1=2
2+1=3
3+2=5
5+3=8
8+5=13
13+8=21
21+13=34
OR 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, etc.
Fibonacci sequence
Many sources claim this sequence was first discovered or "invented" by Leonardo Fibonacci, the Italian mathematician, born around 1170, originally known as Leonardo of Pisa. In the 19th century, historians came up with the nickname Fibonacci to distinguish the mathematician from another famous Leonardo of Pisa.
But others say it came from ancient Sanskrit texts that use the Hindu-Arabic numeral system, predating Leonardo of Pisa by centuries.
But, in 1202 Leonardo of Pisa published a mathematical text, Liber Abaci that was a “cookbook” written for tradespeople on how to do calculations. The text laid out the Hindu-Arabic arithmetic useful for tracking profits, losses, remaining loan balances, etc., introducing the Fibonacci sequence to the Western world.
Fibonacci sequence
Why is it important:
Because there is a special relationship between the Fibonacci numbers and the Golden Ratio, a ratio that describes when a line is divided into two parts and the longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a), which both equal 1.618. This is represented by the Greek letter (φ)--phi.
The ratio of any two successive Fibonacci numbers approximates the Golden Ratio value ( φ = 1.6180339887 . . . ). The bigger the pair of Fibonacci numbers, the closer the approximation.
From there, mathematicians can calculate what's called the golden spiral, or a logarithmic spiral whose growth factor equals the golden ratio.
Fibonacci sequence
In Nature
There are many examples of Fibonacci numbers appearing in the natural world. And they appear often enough to prove they reflect some naturally occurring patterns.
You can commonly spot these by studying the manner in which various plants grow. Many seed heads, pinecones, fruits and vegetables display spiral patterns that when counted express Fibonacci numbers. Look at spirals of seeds in the center of a sunflower and you'll observe patterns curving left and right. If you count these spirals, your total will be a Fibonacci number.
Divide the spirals into those pointed left and right and you'll get two consecutive Fibonacci numbers. You can decipher spiral patterns in pinecones, pineapples and cauliflower that also reflect the Fibonacci sequence in this manner.
The Fibonacci sequence is considered important in nature because it often appears in the growth patterns of plants and animals, suggesting that this pattern is an efficient way to optimize space and access to resources like sunlight, maximizing their survival and reproduction in a given environment; essentially, organisms that exhibit Fibonacci patterns may have an evolutionary advantage due to their efficient growth structure.
Fibonacci in art
https://www.youtube.com/watch?v=wTlw7fNcO-0 (start at 1:10)
BBC documentary, Planet Earth III—Conger the humpback whale
Biography
Kristin has been writing professionally since the age of 16, when she began her career as a sportswriter, covering major league baseball and NHL hockey for a local magazine in Tampa Bay, Florida in the late 1990s. In addition to a long magazine writing career, primarily writing and reporting for PEOPLE magazine, Kristin was also a frequent contributor to the national television morning show The Daily Buzz.
Kristin was born just outside Boston, Massachusetts and spent her childhood there, as well as in Worthington, Ohio, and St. Petersburg, Florida. After graduating with a degree in journalism (with a minor in Spanish) from the University of Florida, she spent time living in Paris and Los Angeles and now lives in Orlando, with her husband and young son. She is also the co-founder and co-host of the popular weekly web show and podcast Friends & Fiction.
Publications
2006: How to Sleep with a Movie Star
2007: The Blonde Theory
2007: The Art of French Kissing
2008: When You Wish
2009: Italian for Beginners
2010: After
2012: The Sweetness of Forgetting
2014: The Life Intended
2016: How to Save a Life: A Novella
2016: When We Meet Again
Publications
2018: The Room on Rue Amelie
2019: The Winemaker's Wife
2020: The Book of Lost Names
2021: The Forest of Vanishing Stars
2022: The Paris Daughter
The Stolen Life of Colette Marceau (coming Spring 2025)
Coming Spring 2025: Colette Marceau has been stealing jewels for nearly as long as she can remember, following the centuries-old code of honor instilled in her by her mother, Annabel: take only from the cruel and unkind, and give to those in need. Never was their family tradition more important than seven decades earlier, during the Second World War, when Annabel and Colette worked side by side in Paris to fund the French Resistance.
But one night in 1942, it all went wrong. Annabel was arrested by the Germans, and Colette’s four-year-old sister, Liliane, disappeared in the chaos of the raid, along with an exquisite diamond bracelet sewn into the hem of her nightgown for safekeeping. Soon after, Annabel was executed, and Liliane’s body was found floating in the Seine—but the bracelet was nowhere to be found.
Seventy years later, Colette—who has “redistributed” $30 million in jewels over the decades to fund many worthy organizations—has done her best to put her tragic past behind her, but her life begins to unravel when the long-missing bracelet suddenly turns up in a museum exhibit in Boston. If Colette can discover where it has been all this time—and who owns it now—she may finally learn the truth about what happened to her sister. But she isn’t the only one for whom the bracelet holds answers, and when someone from her childhood lays claim to the diamonds, she’s forced to confront the ghosts of her past as never before. Against all odds, there may still be a chance to bring a murderer to justice—but first, Colette will have to summon the courage to open her own battered heart.
Videos
South Florida PBS
YouTube interview
Cast of characters
Eva Traube Abrams:
The main character, in both youth and old age, who becomes a document forger during World War II.
Her parents--Tatus and Mamusia—are Polish Jews living in Paris, where her father repairs typewriters. He is caught in an early raid and sent to Auschwitz; Eva and her mother escape to a remote French village, Aurignon, with their first fake identities as Colette and Sabine Fontain.
Later, when Remy forges papers for her to go back to Paris to rescue her father, he names her Marie Charpentier and he joins her on the train as husband Remy Charpentier.
While in Aurignon, Eva and her mother become Eva and Yelena Moreau.
In the final raid in the novel, when Joseph Pelletier (Gerard Faucon) has betrayed them all, Mamusia is taken and immediately executed, but Eva's father returns at the end of the war when Auschwitz is liberated.
He dies shortly after their reunion and Eva meets Louis Abrams, a fellow book lover; they marry, move to Florida, and have a son Ben.
Cast of characters
Remy Duchamp
Initially a forger working with Eva, he volunteers to escort children across the border into Switzerland and becomes more active as a resistance fighter with the Maquisards.
He loves Eva, but leaves her for 18 months, until the end of the novel when he joins her as her husband to smuggle the final group of 4 children into Switzerland. They travel as Lucie and Andre Besson.
Eva stays with him rather than following the children into Switzerland; he asks her to marry him but she has doubts because her parents, especially her mother, would not approve.
Because the forgers and people in the resistance movement have been identified, Remy fakes his death, Eva searches for him, but believes he has been killed. She wants to tell him she'll marry him, despite her parents disapproval, and leaves that message in the Book of Lost Names.
Remy has left her a book, The Adventures of Tom Sawyer, one of the first novels written on a typewriter, with a passage marked suggesting that he has faked his death.
When Eva sees the photo of her book and flies to Berlin to claim it, Remy has also seen it and flown to claim it. The book brings them together again.
Cast of characters
Père Clément:
the Catholic priest helping people to escape the Nazis; he provides the room in the church where forged documents are created.
a consistently kind and loving man, he provides spiritual support for anyone who needs it and functions as leader of the various people who assist with hiding and protecting those hunted by the Nazis, especially children.
a strong religious exemplar in the novel
Joseph Pelletier (Gerard Faucon)
a friend Eva has known since school days; handsome, charming, and Jewish, Eva's mother promotes him as a good marriage choice.
But he is also a high-ranking member of the resistance who ultimately sells them out to the Germans in return for his own life—and Eva. He forms a romantic relationship with Genevieve, the forger who takes Remy's place assisting Eva, and shoots her in the stomach when she will not reveal Eva's location.
Eva finds Genevieve when searching for Faucon and stays with her until she dies; Genevieve identifies Faucon as the traitor.
Cast of characters
Madame Barbier:
the woman who owns the boarding house where Eva and her mother find refuge; a former Russian émigré, she works with Pere Clement. She's killed, along with Eva's mother, in the final raid.
Madame Noirot:
She owns the book shop where Eva buys colored pens to create her first forgeries; she tells Pere Clement about Eva, and he contacts her offering help. A source of refuge for Eva at various times, she too is killed in the final round up of forgers and their helpers.
Erich:
A German soldier who cannot in good conscience support the Nazi effort. He passes critical information to Pere Clement, like the timing of raids and people who have been identified. He too is killed for helping them.
Otto Kuhn:
The librarian in Berlin who reveals the Book of Lost Names that brings Eva and Remy together. Based on Sebastian Finsterwalder, the real-life librarian working to restore confiscated books to their rightful owners.
Cast of characters
Aurignon is a fictional town in France where Eva, her mother, and others fleeing Nazi France find refuge. There was a factual town in France, Vivarais-Lignon, a small community credited with saving thousands of Jews during WWII (Time magazine, Sept. 19, 2019, Maggie Paxson)
Questions for discussion
One of the major themes in this novel is the role of family and religion in shaping a person's life. How big a role should it play? Should it be the determining factor when a person makes decisions?
Late in the novel, p. 370, Eva says:
We aren’t defined by the names we carry or the religion we practice, or the nation whose flag flies over our heads. I know that now. We’re defined by who we are in our hearts, who we choose to be on this earth.”
What is the role of family and religion in shaping a person's life?
Questions for discussion
What do you think of Mamusia's insistence that Eva search for, find, and return her father? On p. 16, before he has been taken, she says:
“If we shrink from them, if we lose our goodness, we let them erase us. We cannot do that, Eva. We cannot.”
What about her insistence that Eva marry within the Jewish faith, even someone like Joseph (Gerard) when the man she loves, Remy, is Catholic?
Questions for discussion
What does Eva's father say about her wish to marry Remy when she has found him again at the end of the war?
Questions for discussion
On page 165, Eva says:
“I’ve always thought that it’s those children—the ones who realize that books are magic—who will have the brightest lives.”
What do books offer? How did Eva’s love of books help her throughout different points in the story?
Questions for discussion
Eva feels terrible guilt about abandoning her parents, her father initially, then her mother. And she feels responsible for the death of those taken by the Germans. Is she responsible?
Questions for discussion
On page 117, Eva watches officers walking around unbothered in Drancy and thinks to herself:
“Could they all be that evil? Or had they discovered a switch within themselves that allowed them to turn off their civility? Did they go home to their wives at night and simply flip the switches back on, become human once more?”
What is going on with people capable of ignoring blatant evil?
Questions for discussion
Eva has never revealed the truth of her life to her son Ben until the very end of the novel. Basically, , he knows nothing about who his mother is, or has been.
On page 166, Eva thinks to herself:
“Parents make all sorts of errors, because our ability to raise our children is always colored by the lives we’ve lived before they came along."
Was her decision to keep this information from him a good one? Why did she do it?
Questions for discussion
In her author’s note, on page 384, Kristin Harmel says,
“You don’t need money or weapons or a big platform to change the world. Sometimes, something as simple as a pen and a bit of imagination can alter the course of history.”
Do you agree?
Questions for discussion
What did you take away from reading this novel?
Next week
Thanksgiving--No Class
Week After:
First Lie Wins