I find it interesting that the sequence of numbers in nature known as the Fibonacci Sequence or F. Numbers is found in bees. The numbers start at 0,1,1,2,3,5,8 & so on, you just add the previous 2 numbers together to get the next one. These numbers are in the golden spiral, the golden rectangle. It’s all around us. These numbers are in the family tree of the drones.
2 Likes
Just don’t try to sell me on the ratio of workers to drones being a constant of the golden mean… (see Dan Brown’s “The DaVinci Code”) since drone populations fluctuate constantly…
Fibonacci numbers permeate the universe, it is part of the design. The Milky Way, our galaxy, DNA code, the Bible Wheel, the list goes on forever, all use complex mathmatical design. He numbers the hairs on our head and counts our steps and numbers our days.
Hi Volbee, it’s fantastic, I discovered it a few years ago when I googled how to grow pineapples. As you can imagine, I’m the bloke who counts flower petals everywhere he goes. The number 5 is interesting, apparently all of the flowers of edible fruit have five petals. When you cut through a pawpaw, you find five segments. Most of the alloy wheels on motor cars have five spokes.
Not all edible fruit flowers have five petals.
Hi Skegly, you notice I used the word “apparently”, leaving a little bit of room for error. I read that on the internet recently, that’s why I used the word “apparently”. Five is evident in all the food I grow here. Also non-edible flowers. Three is also interesting, in clover, creeping oxalis, bananas have 3 segments. The spikes on dragon fruit come out in clusters of 3. Another Fibonacci number is evident in motor cars, the number 8. You can’t beat the sound of a good v8. At the risk of being accused of getting off the subject, it’s great to discover that if you follow a drones family tree, the number of members at each stage is the same number as the F.Sequence.
Perhaps not directly related to the topic at hand but odd numbers are more visually pleasing to the eye then even numbers. Check out any food stylists rendition of a plate of food in a magazine, or almost any chefs plated meal, and nearly every component that can be visually separated from the other items (ie not grains of rice etc) will have odd numbers. Even in cases where there are two of something such as an eggs Benedict where there are typically two of them on the plate there is usually a third element to the plate hash browns or potatoes etc to “odd out” the plate.
This is also the case with the spokes on rims that you mentioned. Compare a 4 spoke rim with a 5 or 7 spoke rim, and you will see your mind is more at ease looking at the odd numbered rim. Something about even numbers just screws with your brain.
1 Like
Thanks Adam, I agree. If you look at bulk carrying ships & count the covers over each section, it is always odd numbers, 5’s, 7’s or 9’s. Apparently 5 spokes is the strongest most efficient use of material. I took a look at the Koenigsegg hypercar. The owner/builder/inventor is making a lot of parts in carbon fiber, even some wheels recently in carbon fiber. This is to shave as much weight off the car as possible & achieve maximum efficiency. He built those wheels with five spokes. Getting back to the bees, or the drones for that matter. So at #5 the drone has 3 queens & 2 drones represented.
I’m happy to revive this old topic.
Not only are Fibonacci numbers found in bees, they are also found in pineapples, my home-grown pineapple is no exception. I marked the lines that represent the divergence angles & phylotactic ratios which are all connected with the Fibonacci sequence of numbers.
After removing the permanent marks, this is my preferred method of peeling a pineapple.
Nothing goes to waste, I replant the top & make a pineapple skin, ginger skin with honey drink.
cheers
4 Likes
Jeff- that is masterful cutting of the pineapple! that’s how they do it in Thailand- street vendors sell pineapples and peel them for you just like that. They can do it in just a minute or two.
Thanks Jack, I take a lot longer than that 
I first discovered that method while googling how to grow a pineapple. That was the same time as when I discovered the Fibonacci sequence of numbers.
I started wondering if it’s in dragon fruit & sure enough it is: as marked in my photo.
I had to eat half of one to see if the seeds follow a pattern, similar to the pattern on a sunflower head. I could’t see one, but that doesn’t mean it’s not there, and I’m sure there is a pattern there, but hard to see with the way the seeds are set in the flesh.
I’ll do some more research with the other half tonight, with some honey & grated crystallized ginger, with a dollop of Greek yogurt.
3 Likes
If you study a pineapple you can see those lines more clearly than what I showed on the dragon fruit.
Edit:- I forgot that I uploaded those photos last March.
cheers
I’m intrigued by the Fibonacci sequence & how you can count the members of each step in a drone’s family tree. I started to wonder what would happen if we went back 10 generation. Well that would be 55. 11 generations would be 55+34=89.
What if we go back 50 generations, that would be 12,586,269,025.
Let’s go back a 100 generations, that number is: 354,224,848,179,261,915,075. I don’t know how to say that number. Maybe I can if I think about it long enough… I think 354 quintillion.
What if we go back a thousand generations: That number starts with 4 & is 73 digits long.
Jeff, you lost me with the drone generation figures a bit, but I love the lines, the patterns in nature and the visual balance that thoughtful humans can achieve. I just found this topic by the way - I must try peeling my next pineapple like that!
PS: your last post was an F number🥳
3 Likes
Hi Eva, if we follow the Fibonacci sequence, we start at 0, then 1. After that we add the previous 2 numbers together. So 0+1=1. Then 1+1=2. Then 2+1=3, 3+2=5, 5+3=8, 13+8=21, 21+13=34 & so it goes like that. The fibonacci sequence is in the golden spiral as well as the golden rectangle.
It’s interesting that the number of members at each stage of the family tree of a drone follows the fibonacchi sequence. This is because a drone, as you know, has no father, only a grandfather.
Therefore drone=1
mother=1
mother/father=2
mother/father, mother=3
mother/father, mother, mother/father=5
mother/father, mother, mother/father, mother/father, mother=8
mother/father, mother, mother/father, mother/father, mother, mother/father, mother, mother/father=13
Now I don’t have enough room on one line for the next stage of the family tree, which will be 21, then 34, 55, 89 & so on.
It had been on my mind for a while about how the sequence gets rapidly larger, while wondering about a drone’s family tree, the further back in time we go.
1 Like
This looks like a Fibonacci spiral to me too. Spooky?
2 Likes
Hi Dawn, thanks for sharing that. It’s all incredibly interesting.
1 Like