## Posts tagged ‘golden ratio’

### Stupid Stats

C’mon, now… really?

Uterine size in non-pregnant women varies in relation to age and gravidity [number of pregnancies]. The mean length-to-width ratio conformed to the golden ratio at the age of 21, coinciding with peak fertility.

Claiming that a uterine golden ratio coincides with peak fertility is highly suspect. The good folks at Ava Women claim that, “Most women reach their peak fertility rates between the ages of 23 and 31.” Information at Later Baby states, “Female fertility and egg quality peak around the age of 27.” And WebMD says, “A woman’s peak fertility is in her early 20s.” So, there seems to be some debate about when peak fertility actually occurs. Consequently, this strikes me as retro-fitting, and it seems that Dr. Verguts and his colleagues may have played loose with the age of peak fertility in order to make a connection to the golden ratio.

In their defense, though, it’s not the first time that folks have gone uptown trying to find a connection to the golden ratio. A claim by The Golden Number states, “[The DNA molecule] measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral,” and 34/21 ≈ 1.6190476, which is approximately equal to φ, 1.6180339.

Though this guy — an honest-to-goodness biologist — seems to disagree:

I’ve also heard folks say that people are perceived as more beautiful if certain bodily proportions are in the golden ratio. The most extreme example of this that I’ve found involves the teeth:

…the most “beautiful” smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on.

In a study of 4,572 extracted adult teeth, Dr. Julian Woelfel found the average width of the central incisor to be 8.6 mm. If the teeth in a beautiful smile follow the geometric progression described above, well, that would imply that the first molar would be just 8.6 × 0.6185 ≈ 0.8 mm wide, which isn’t reasonable and, moreover, is not even remotely close to the average width that Dr. Woelfel found for the first molar: approximately 10.4 mm.

But all of these claims involving the golden ratio are not even close to being the stupidest statistics I’ve heard in my life. Mary Anne Tebedo made a remark on the floor of the Colorado State Senate in 1995 that may hold that distinction:

Statistics show that teen pregnancy drops off significantly after age 25.

Of course, it’s hard to call that a statistic, since it’s completely nonsensical. Maybe it’s only the stupidest statement I’ve ever heard.

Then there’s this one, from the New York Times on August 8, 2016, which couldn’t be more useless:

No presidential candidate has secured a major party nomination after an FBI investigation into her use of a private email server.

Well, duh. Email didn’t even exist before the 1970’s. Moreover, besides Hillary Clinton, has any presidential candidate ever had their use of a private server investigated by the FBI? This is like saying, “No one has ever been named People‘s Sexiest Man Alive after writing a math joke book.” (Not yet, anyway.)

Randall Munroe made fun of these types of “no politician has ever…” claims in 2012 with his cartoon Election Precedents:

And it’s true:

But perhaps my all-time favorite is one that Frank Deford — may he rest in peace — included in his piece “The Stupidest Statistics in the Modern Era” on NPR’s Morning Edition:

He’s [Brandon Phillips] the first National League player to account for as many as 30 steals and 25 double plays in one season.

About this stat, Deford commented, “Steals and double plays together? This is like saying, ‘He’s the first archaeologist to find 23 dinosaur bones and 12 Spanish doubloons on the same hunt.'” (I sure am going to miss him.)

The preponderance of dumb stats shouldn’t come as a surprise, though. A recent study found that people deemed real news headlines to be accurate 83% of the time and fake news headlines to be accurate 75% of the time. So, if we can’t tell truth from fiction, how can we possibly distinguish useful statistics from inane?

If you’d like to test your ability to detect fake news, check out Factitious from American University.

### Is It Phi Day Yet?

There are several pressing matters that needs to be resolved.

Let’s use the following poll to resolve the first…

Don’t be swayed by the giant.

The second matter concerns the date of Phi Day.

As if it weren’t enought that the contrivance known as Pi Day is celebrated on 3/14, simply because the three digits of that date agree with the first three digits of π. Now the folks at www.phiday.org say that Phi Day should be celebrated on June 18, since 6/18 are the first three digits after the decimal point of φ, the golden ratio. What’s next? Are we gonna say that e Day should be celebrated on 7/18, since e = 2.718? Please.

But wait, there’s more. The folks (or should I say folk, since I think it’s just one guy) at www.goldenratio.org have proposed that Phi Day should be celebrated on October 31 in the Northern Hemisphere and May 6 in the Southern Hemisphere. The convoluted calculations for these dates can be found in this white paper.

Let’s settle this once and for all. The Golden Ratio divides a line into mean and extreme ratio, so Phi Day ought to divide the year into mean and extreme ratio, too.

The golden ratio divides a line segment into two parts, a and b, such that

$\frac{a}{b} = \frac{1}{\phi}$

For a non-leap year, then, we are looking for the date that divides a 365-day year into the golden ratio.

This formula yields

$\frac{a}{b} = \frac{1}{\phi} \Rightarrow \frac{a}{365 - a} = \frac{1}{1.618} \Rightarrow a \approx 139.4$

For leap years, which contain 366 days, the result is

$\frac{a}{b} = \frac{1}{\phi} \Rightarrow \frac{a}{366 - a} = \frac{1}{1.618} \Rightarrow a \approx 139.8$

In non-leap years, the 139th day of the year is May 19; in non-leap years, the 140th day is May 19. Consequently, a rather satisfying result occurs: the same date can be used for Phi Day in leap and non-leap years.

Further, it’s nice that the date occurs during the school year. One last chance to have a math party before summer break. And while a standard cake pan measures 9″ × 13″, you are strongly encouraged to use an 8″ × 13″ cake pan to concoct a treat for this special day.

So there you have it. An official MJ4MF declaration:

Whereas, phi represents the golden ratio, which divides a length into the ratio 1:1.618; and,

Whereas, the 19th day of May divides the year into the golden ratio; therefore, be it

RESOLVED, that Phi Day henceforth shall be celebrated on May 19; and be it further

RESOLVED, that there shall be no further discussion of this matter.

We’ll use the results of the poll above to determine whether it should be pronounced National Fee Day or National Fie Day.

## About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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