Fun with Math or Wisdom of Da Vinci

I know, I know, I can hear some of you crossing your eyes, eeuwwwwwww MATH, please stay till the end.

There's a math thing called;  The Fibonacci Sequence, which is the quotients of adjacent terms.  1 1 2 3 5 8 13 21 -------------- and so on.  These terms and quotients can be expressed as a ratio of 1.618 which is called PHI (fee), also the Divine Proportion,

Look at Da Vinci's The Vitruvian Man.  
If you measure from top of the head to floor, then measure from bellybutton to floor --- you will get a ratio of 1.618.
hip to floor/knee to floor, shoulder to fingertip, elbow to fingertip, yes you guessed it-again a ratio of 1.618.
We also find the same ratio in nature: female to male in a honeybee hive, nautilus shells as a ratio of each spiral's diameter, sunflower seeds grow in opposing spirals, ratio of each rotation's diameter to the next, spiraled pinecone petals same thing, leaf arrangement on plant stalks, same and in insect segmentation.

I guess my question for all of you is :  What was Da Vinci telling us?

What I think, would likely cross into the no-no area of postings to this site, so I'll just say, my belief is Strong.

Peace

( ok, uncross your eyes now, admit it this math wasn't that bad )



                                                                       

As always, it's not that simple. That said, spirals are cool, and the Fibonacci Sequence is a particularly cool one.

However, if people want to get over the "eeuwwww MATH" feeling, I highly recommend the book, The Number Devil: A Mathematical Adventure

https://www.goodreads.com/book/show/91358.The_Number_Devil

Yes - it's considered a children's book - why not! Adults deserve to play also, and since I read it aloud to #2 Son around age 10, I got to thoroughly enjoy it.

For the math phobic, here's a pretty version...

Burra, I'm at a loss for the right words other than thank you, I have watched the video three times.

Peace

Deane Adams wrote:If you measure from top of the head to floor, then measure from bellybutton to floor --- you will get a ratio of 1.618.
hip to floor/knee to floor, shoulder to fingertip, elbow to fingertip, yes you guessed it-again a ratio of 1.618.  

I've seen this before so I thought I'd measure it.  Some of the points are hard to define (where exactly is your shoulder), but here's what I got:
Head vs belly button - 1.615
Hip vs knee - 1.733
Shoulder vs elbow - 1.725

The first one is right on but those second ones are a bit off.  Maybe they're close enough???  So I did the math backwards from the hip and shoulder measurement and the calculated number was clearly not right for my actual knee and elbow location.  Again, it depends on where you think your hip, shoulder, elbow and knee actually are.  But it's far enough off that for the perfect ratio to be right, I'd have to be very generous with what I call my hip, knee, shoulder and elbow.  I wonder if other people can actually measure this to see what they get?

Mike Haasl wrote: Again, it depends on where you think your hip, shoulder, elbow and knee actually are.  But it's far enough off that for the perfect ratio to be right, I'd have to be very generous with what I call my hip, knee, shoulder and elbow.  

Having taken human anatomy a great many decades ago, my thought was still, "by hip do they mean the top of the pelvis, or the head of the femur". There's about a 3" difference between those two choices on my body!

I'll see if I can talk one of the family into letting me measure them up, or better yet, all three that are here.

WE can do the female to male thingy in a beehive.  I'll work the smoker, while you guys count!!

Peace

Hubby: Head to floor vs belly button to floor: 1.75
Hip vs knee to floor: 2.125
Shoulder vs elbow to middle finger tip: 1.64

G: Head to floor vs belly button to floor: 1.737
Hip vs knee to floor: 2.029
Shoulder vs elbow to middle finger tip: 1.724

Me: Head to floor vs belly button to floor: 1.617
Hip vs knee to floor: 2.171
Shoulder vs elbow to middle finger tip: 1.897

Target: 1.618 Interesting that the measurement that I felt was most flexible in the interpretation of what it meant is the one we seem the furthest off on. Do I use anatomical measures, or sewing measures.

I'm not at all surprised that the head vs belly button to floor is more different in me than Hubby or G, as I have always considered myself to be "short in the body and long in the legs, and the other two, relatively longer torsos.

Deane Adams wrote:
We also find the same ratio in nature: female to male in a honeybee hive,  

That doesn't sound right to me. As I understand it around 95% of a typical hive is female. Except in the winter, when it is 100%.

Burra Maluca wrote:

Deane Adams wrote:
We also find the same ratio in nature: female to male in a honeybee hive,  

That doesn't sound right to me. As I understand it around 95% of a typical hive is female. Except in the winter, when it is 100%.

You are correct - the male to female ratio in honeybee hive, despite the claim in “the da vinci code”, is variable throughout the year and never approaches 1.6 unless the hive is collapsing.
I did a quick search to see if there was anything about bees that matches the golden ratio or the fibonacci series, and found an interesting true fact though - the number of ancestors a male bee has in each generation does follow the series - 1 in the drone’s generation, 1 in his parent’s generation, 2 in his grandparents, 3 in his great grandparents, and so on.

And, back to the original question - I think Da Vinci was showing his idea of perfection.  There's probably not too many of us who fit the measures to a T, but who wants to be perfect anyhow?
The F-series is great for figuring pleasing stripe proportions though.

It is still a beautiful sentiment even if it isn't perfect.

Exploring the branching of tree limbs as it relates to the Fibonacci sequence: https://www.amnh.org/learn-teach/curriculum-collections/young-naturalist-awards/the-secret-of-the-fibonacci-sequence-in-trees

Math is something everyone uses every day without even thinking about math.

The wife gets eggs and bacon out of the fridge to cook breakfast.  Does she use math to determine how many eggs and how much bacon.

Back in the old days when there were cattle drives the boss or ramrod knew exactly how many cattle were in the herd, usually 100s.

Do you balance your checkbook?  Shop for the best prices?

The Da Vinci rule of tree branching is another example of the hidden math of nature.

https://www.independent.co.uk/news/science/da-vinci-mondrian-art-hidden-math-b2696608.html