FAQ - Frequently Asked Questions
1) What is the Fibonacci Sequence?
0, 1, 1, 2, 3, 5, 8, ... (where the next number is the sum of the previous two)
2) How did the Fibonacci Sequence get its name?
We give credit to the man we call Fibonacci because we learned about it from his influential book called "Liber Abaci", written in 1202, over 800 years ago. Fibonacci was not the first to discover this series, he learned about it indirectly from Indian mathematicians.
3) What is the Golden Ratio?
Approximately 1.618. It is also called phi. Its exact value is (1 + sqrt(5))/2.
4) How are the Golden Ratio and the Fibonacci sequence related?
As the Fibonacci numbers get larger, the ratio of adjacent numbers approaches the Golden Ratio.
5) What was Fibonacci's real name?
He was named Leonardo. He was called Leonardo Pisano, which means "Leonard of Pisa". He was also called Leonardo Fibonacci where the last name meant "son of Bonacci", which was his father's name.
6) When did Fibonacci live?
From about 1170 to about 1240. We don't know with certainty because no records were kept of his birth or death.
7) Where did Fibonacci live?
Pisa, which is now a famous city in Italy. It was an important trading town in his time.
8) Where was Fibonacci educated?
He traveled with his father to cities around the Mediterranean Sea. He was tutored by men from the Arab world. That is where he learned the "Arabic" numerals. Europe at the time was still using the Roman numerals, which were cumbersome in arithmetic.
9) What books did Fibonacci publish?
Liber Abaci in 1202 (2nd edition 1228), Practica Geomatriae (1220), Flos (1225), Liber Quadratorum (1225), Di Minor Guisa, Commentary on Book X of Euclid's Elements.
10) What are some examples of the Fibonacci Sequence in nature?
Plants that grow in spiralling patterns often use the Fibonacci numbers. The number of rows that spiral clockwise and counter-clockwise are adjacent numbers in the Fibonacci Sequence. For example, the pineapple typically has 8 spirals in one direction and 13 in the other. Other examples are the palm tree, sunflower, asparagus, artichoke, pinecone, even broccoli and cauliflower.
11) When did the first plants use Fibonacci-style spiralling growth?
Very early in the evolution of plants on land, as soon as growth occured from a stem. It was not seen plants whose branches simply divided (Cooksonia from 400 million years ago) or in stemless plants such as liverwort (350 million years ago). It is seen in mosses that first appeared about 320 million years ago. It was in cycads (300 million years ago).
12) Does the Fibonacci Sequence or the Golden Ration appear in animals?
No, it is wishful thinking when we see it in the dimensions of the body or the curve of horns and claws.
13) When was the Golden Ratio first discovered?
It is hard to say with certainty, but it was known over 1000 years ago in India.
