## 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.

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• 1. xander  |  May 17, 2013 at 1:43 pm

Obviously, it is pronounced “phi” so that it rhymes with “xi”. Dur. 😛

• 2. venneblock  |  May 17, 2013 at 2:26 pm

Oh, of course!

• 3. Buddhagan  |  December 13, 2013 at 3:43 pm

Shouldn’t Phi (rhymes with Pi) Day be on the 225th day? Your formula is correct but if we want to celebrate phi on the date that the year is divided properly, it should be the 225th or 226th day of the year. 365.25 / 225.74 = 1.618 or Phi.

Now that the pronunciation is out of the way, we can talk about the convention. Which way is the correct way (and I’ve seen it both ways): phi (lowercase) = 1.618 and Phi (uppercase) = 1/1.618 or vice versa, Phi = 1.618 and phi = 1/1.618?

It seems that the golden ratio is named after a sculptor (argument for uppercase Phi = 1.618). I have no idea of which way is correct. What do you think?

• […] actually the ideal pick for both cases: (365 – 139)/139 = 1.626 and (366 – 140)/140 = 1.614.  See here for advocacy of this […]

• 5. Martin-2  |  March 20, 2015 at 12:20 pm

“What’s next? Are we gonna say that e Day should be celebrated on 7/18, since e = 2.718?”

I prefer your date, but this metaphor doesn’t work and you know it. 0.618 is the reciprocal of 1.618 and the choice of which to call the “Golden Ratio” is arbitrary. It’s not a matter of simply dropping the first digit*. The PhiDay person is perfectly clear about this.

*It’s not a matter of simply taking the reciprocal either, so don’t come back and say “why not celebrate e day on 3/6 since 1/e is 0.36?” Although the reciprocal of e does still have all those nice exponent properties…

• 6. Martin-2  |  March 20, 2015 at 12:22 pm

No wait, Buddhagan has the right date.

• […] a mathematical constant that’s roughly equal to 1.618 and is commonly denoted by the Greek letter phi, which looks a bit like the letter “p” but with an extra loop on the left-hand side of […]