## Archive for May 17, 2013

### 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.