Farming Fibonacci

Today is the birthday Guido Grandi born 1671 in Cremona, Italy . Grandi was an Jesuit that made contributions in the area of geometry and hydraulics.

My math quote of the day is attributed to an anonymous contributor. "Mathematics may not teach us how to breathe oxygen or exhale carbon dioxide; or to love a friend and forgive an enemy. It may not even help us to find our way to our one true love but it gives us every reason to hope there is a solution to every problem."

I grew up on the edge of a small rural town in southeastern Minnesota. My dad was a self-employed welder who employed my siblings and I at a young age. On the first day of my employment I was given the task on cleaning a manure spreader so that my dad could repair it. I initially was a reluctant employee but I eventually became accustomed to the apperception, timbre, and aroma that defined for me the life of a farmer.

My first teaching job was in a rural community and I commuted to that district for 18 years. I enjoyed the 45 minute commute. I was able to view the rhythmic patterns of farming; preparation, planting, and harvesting. There was a strong FFA presence in that school community much like there is in the one I am teaching at now. FFA no longer means Future Farmers of America but is an organization focused on Agriculture Education. I have purchased fruit from the members of the FFA for 34 years and will again this year. The selling of fruit around Christmas has been a fundraiser for the FFA ever since I can remember. I have noticed a shift in the membership since I have started teaching. More female students are involved and they usually have taken on leadership positions within the organization. The "ag" teachers that recently have been recently hired have been female. Our current FFA advisor (nicknamed Taylo) is an energetic, dynamo graduate of the University of Minnesota. She suggested to me the idea of blogging about the connection between mathematics and agriculture. I suggested to her the topic of Fibonacci numbers.

I first learned of the Fibonacci sequence when I was a freshman in college. Fibonacci was an Italian mathematician who did not discover the sequence but used the sequence to spread the use of the Hindu-Arabic numeral system. The sequence is as follows: 0, 1, 1, 2, 3, 5, 8, … . After 0 and 1 each new term is formed by adding the two previous terms. The explicit form is also called Binet's Formula and is an = [(1 + √5)^n - (1 - √5)^n]÷(2^n√5). If a decimal representation is formed by dividing the new term by the previous term the following sequence is formed: 1/1 = 1; 2/1 = 2; 3/2 = 1.5; 5/3 = 1.667; 8/5 = 1.6; 13/8 = 1.625; 21/13 = 1.615; 34/21 = 1.619; 55/34 = 1.617; 89/55 = 1.618; 144/89 = 1.618. (1 + √5)/2 is called the golden ratio. 

Fibonacci numbers occur in nature such as in the growth pattern of rabbits, cows, and bees. My particular interest is how the sequence appears in cones, particularly, the hop cone. One of my hobbies is brewing beer. I have been doing this for 21 years. My oldest son has convinced me of growing hops. 

The hop flower or seed cone is picked, dried, and then dry hopped into a container holding the fermenting beer. The hops remains in that wort for 1 to 3 weeks. After which the beer is bottled or kegged. Using hops in this manner enhances the aroma of a beer.

In the above photo of a common pitch pine cone, the spirals have been highlighted for easy counting. There are 8 red spirals opening to the left and 13 blue spirals opening to the right. 8 and 13 are consecutive Fibonacci numbers. Other species of pine cones also have spirals that are consecutive Fibonacci numbers such as 5 and 8. I have not examined the hop cone in particular nor have I found any research that details the existence of consecutive Fibonacci numbers but I will continue to examine each hop that I grow in my quest of producing the elusive perfect beer.

The Fibonacci sequence is truly fertile ground for mathematical exploration and growth. Taylo, herself, was bursting in pride when seeing my Fibonacci t-shirt, baffled her boyfriend when she detailed her knowledge of Fibonacci.