Tag Archives: Golden Ratio

Fee, Fie, Foe — Fumble


There is an obscure monument located, pretty much, in the middle of nowhere, Kansas.  Well, not actually nowhere: it is among some corn fields and a pig farm, about 2 miles northwest of Lebanon, KS (population 218).  But then again, maybe as close to nowhere as you can get — Lebanon is in Smith County, whose population has dwindled to fewer than 3,800 … at a lonely 18 folks per square mile, it’s even less populated than when it was formed back in 1872.Slide1


To give an idea as to its significance, or lack thereof: the monument’s coordinates have precisely been determined to be 39 degrees, 50 minutes North Latitude; 98 degrees, 35 minutes West Longitude.  That puts it exactly 12 miles south of the Nebraska state line, and almost exactly halfway between Missouri and Colorado.  Evidently a whopping 1,200 people visit there each year, including the few who use the tiny chapel at the site to get married.


A century ago, in 1912, Arizona became the 48th state, completing the contiguous United States (plus DC, to be precise, so I will call it 48+).  At the time the United States Coast and Geodetic Survey decided that this point is the Geological Center of the United States. [1]


It will serve as a nexus for showing that you can pretty much find whatever it is you are looking for.



There is a number that mathematicians refer to by the Greek Letter, Φ.  It has a number of curious properties.  Before we drift into a bit of math (really, it won’t be overbearing), I wrote a poem about, or perhaps an ode, to Φ. [2]


FEE, FIE, FOE, — Fumble


Φ: a special number golden

Some say it rhymes with “me”.

But mathematicians told ’em:

“No it can’t be said as ‘fee’.

You should pronounce it ‘fie’.”

So now, it rhymes with “I.”


Its character irrational.

Its digits never ending.

Its ratio most fashionable;

Nature applies its trending.

So “me, myself and I,”

Could be compared with Φ.


This number, Φ represents something special to some people, most of whom are odd.  For instance, the author Dan Brown, of “The da Vinci Code” notoriety.  It is the “so-called” golden ratio, supposedly perfect and wondrous to behold.

Its decimal value is infinitely long, but we can simply refer to it as 1.618, or 1.618 …

Turns out it shows up in some unusual places, but before we go to those places, let’s consider some of its qualities.

The inverse of Φ (i.e. the number 1 divided by Φ, or 1/Φ) is 0.618… — or the exact same digits after the decimal point:  i.e Φ-1=1/Φ.

Some folks, Dan Brown included, make quite a deal of the fact that the ratio of sequential numbers in the Fibonacci series quickly converge to quite close to Φ.  [Quick Fibonacci overview.  Take the first 2 natural numbers: 0 and 1.  Add them to get 1.  Add the last two numbers in the series, now 1 and 1, to get 2.  Repeat.  Add 1 plus 2 to get 3.  Add 2 plus 3 to get 5.  So: 0,1,1,2,3,5,8,13,21,34,55 … Note that the ratio of 55/34 = 1.619)

In fact, who needs Fibonacci? Brown, supposed son of a mathematician, is a simpleton. If we take any two non-zero numbers (even complex numbers) and add them to get another number; and then keep adding the last two numbers in the sequence to get yet another … well, the ratio of the last two numbers quickly approaches Φ.

Folks get all worked up about how this ratio is the perfect construction for all sorts of things: from faces and limbs, to animal bodies and tree structure, to even architecture — ancient and modern.  Dan Brown contorts himself to prove this in The da Vinci Code; but careful checking shows that he was very discriminating in sharing his set of facts.  In other words, he only found (and shared) what he was looking for.

Fibonacci numbers do show up in nature, mostly in plant leaf and cone structure.  As a consequence Φ can be inferred.  Still, mostly you have to really be wanting to find it: it’s like saying “Ah ha!  I keep finding this ratio (fill in the blank … could be two or three or 3.14).”

But regarding Φ, I have found it in some unusual places …

To convert miles to kilometers, you multiply by 1.6093.  Dang near phi.

The ratio of earth’s orbital period, 365.24 days, to her planetary twin Venus’ orbital period of 224.7 (earth) days, is 1.625.  Pretty close, too.


Looking at a map of the United States and locate good ol’ center of the 48+, near Lebanon, Kansas, at almost exactly 40 degrees north latitude.  The distance coast-to-coast directly East-West through this point is 2550 miles.

Border-to-border, directly North-South through this point is 1570 miles. The ratio is 1.62.  Rather close to Φ, for no apparent reason, but I found what I was looking for, didn’t I? The United States is perfectly proportioned.


OK, just a couple more.  Here is a population density map of the United States, with population distributed by latitude.


Notice that really high peak around 40 degrees north?  That’s where I live, in northern Colorado.  There is sort of a wide band from about 38 deg to 42deg: this is on account of the Bay Area, Salt Lake City, Denver, Kansas City, Saint Louis, Chicago, Indianapolis, Columbus, Pittsburgh, Philadelphia, New York and surrounding areas lie here.

The days are getting short this time of year (well, actually they are all almost exactly 24 hours, but daylight is getting short).  In about two or three weeks, we’ll be at minimum duration of sunshine per day, on the average about 9.3 hrs in this band.  But, in 6 months we’ll be at almost exactly 15 hours.  The ratio?  About Φ, or 1.612. [3]

Almost exactly 38% of the population of the 48+ lies in this band.  Oddly, this is the complement to 1.000 of Φ’ (where Φ’=1/ Φ).  That means the ratio of the population of the rest of the country to this thin strip is 0.62/0.38, which is of course essentially equal to Φ.

Conclusion 1:  Φ is the perfect number and Φ is the golden ratio; therefore we at 40 degrees north latitude in the US live in the perfect place, with the perfect ratio of the nation’s population, and the perfect ratio of day lengths… in a country sized perfectly in accord with the Golden Ratio.

Conclusion 2: This essay demonstrates a huge part of the problem with political discourse today.  Namely: smart, creative people with time and resources on their hands can find or manufacture nearly any fact they want to support their positions – and then fill the web’s ether with them.  People who read or hear such “facts” typically don’t have the time or resources to do their own research.  So they typically exhibit one of two reactions.  One: if it confirms how they are inclined to think, they absorb it into their psyche, to share at appropriate moments later.  Two: if does not confirm their current positions, they dismiss it as apocryphal or anecdotal.

Let’s replace these options with two much better.  One: ignore it.  Or two: take some time to factually refute or substantiate it.

Wishing you peace


Joe Girard © 2013

The Girardmeister

[1] since the additions of Alaska and Hawaii in 1959, the center has of course moved to another insignificant spot, now in South Dakota.  These points technically must move back and forth several miles each year, owing to the vagaries of shoreline build-up and erosion, depending on vitality of storm seasons.

[2] The Greeks pronounce this letter Fee.  Europeans generally follow the Greeks.  In English speaking countries, among the mathematical literati, it is more customary to pronounce it Fie.  Dan Brown says Fee; so therefore obviously it should be said Fie.

[3] This sunlight ratio is closer to 1.60 in the Bay Area (around 38 deg north) and 1.65 Chicago (almost 42 deg north).

[4] Φ = ½ [1 + √5]