The Fibonacci sequence is a series of numbers, which is related to many features in biology and other branches of science. This is a recursive sequence; each number is the sum of the two previous numbers. The sequence begin with 0,1,1,2 ,.. 1+2=3 as the next number and so on.

Understanding the Fibonacci sequence, help us see how math is related to our physical world. Fibonacci numbers appear in leaves of plants, pinecones and in flower blossoms are only a few examples. Humans see patterns every where and the Fibonacci sequence may be one key to unlock why we do so.

Leonardo da Piso, also known as Fibonacci

• Born in 1170 Italy, Piso studied mathematics and helped introduce Hindu-Arabic numerals to the European world (Gies).
• He found a sequence of numbers with relation to several science branches, including biology.
• When Fibonacci was asked why he studied these numbers he replied; “Someday these numbers will unlock the secret of nature and will explain why a drone does not have a father,” (Careggio).

#### Bee Genealogy

In every beehive there’s one female queen that lays all the eggs. She collects sperm from several male drones from other colonies. Every time she lays eggs, she has a choice of whether to lay a female or a male egg (fertilized or an unfertilized egg). If an egg is not fertilized, it will hatch into a male bee, called a drone. The unfertilized egg will only have DNA from the queen with only  half of the DNA of the females, and only one parent. If an egg is fertilized it will grow into a female bee, she will have the queen’s DNA and half DNA from one of the male bees.  The female offspring will have two parents (Careggio).

The Bee Family Tree

Gen 0: Our Male: Drone

Gen 1: His parent: Queen

Gen 2: Her Parents: Queen, Drone

Gen 3: Their parents: Queen, Drone, Queen

Gen 4: Their parents: Queen, Drone, Queen, Queen, Drone

Gen 5: Their Parents: Queen, Drone, Queen, Queen, Drone, Queen, Drone, Queen (Fenwick)

A male bee has one mother ( generation of size 1). His mother will have had both a mother and a father( generation of size 2), but his father will only have one female parent as the same the mother will have both a female and a male parent (generation 3). The single male has 1 parent, 2 grandparents, 3 great grandparents, 5 great-great grandparents, then 8,13,34,55,89 … his ancestors following the Fibonacci sequence (Knight).

###### References
•Careggio, P., and E. Indraccolo. “Module 6 – Livestock – Bees and Fibonacci Sequence.” Edisco, New Agriways, https://www.edisco.it/new-agriways/wp-content/uploads/sites/101/2019/07/36_Bees_and_Fibonacci_sequence.pdf.
•Fenwick, E. H. “The Bee, Fibonacci, and Genealogy.” Quirky Science, 27 June 2020, https://www.quirkyscience.com/fibonacci-and-genealogy/.
•Gies, Francis. “Fibonacci.” EncyclopædiaBritannica, Encyclopædia Britannica, Inc., 5 Oct. 2021, https://www.britannica.com/biography/Fibonacci.
•Knight, Kitty. “Fi-Bee-Onacci.” TheAperiodical, Irregulars, 31 Aug. 2020, https://aperiodical.com/2020/08/fi-bee-onacci/.