Happy Friday the 13th: End Triskaidekaphobia Today!

[DrClaude]

Anybody else tired of triskaidekaphobia?

I once chose an airplane seat in row 14 just because I find it ridiculous. Don't people realize that whatever you call it, it's still the 13th row?

 

[nuuskur]

I'm hiding under the bed (I know the bed can fall on me!). Is it safe, yet?

 

[DrClaude]

Is it safe, yet?

That depends on your time zone

 

[fresh_42]

Reminds me of one of the first exercises in my calculus book (1.5.).

Show that in the Gregorian Calendar (... explanation of leap years ...) the 13th of a month in the long term average is more frequently a Friday than any other day. (Hint: Gauß was born on a Wednesday.)

I wonder whether Pope Gregor XIII. (sic!) knew this. The Friday anomaly, not Gauß' birthday of course.

 

[DrClaude]

Show that in the Gregorian Calendar (... explanation of leap years ...) the 13th of a month in the long term average is more frequently a Friday than any other day. (Hint: Gauß was born on a Wednesday.)

Really? I'd like to see the proof of that.

 

[jbriggs444]

Really? I'd like to see the proof of that.

In a four year cycle you have 365*4 + 1 = 1461 days.
In a one hundred year cycle you have 25 * 1461 - 1 = 36524 days.
In a four hundred year cycle you have 4 * 36524 + 1 = 146097 days.

146097 is a multiple of 7 -- there are a exactly 20871 weeks in 400 Gregorian years. The day of the week for Jan 1 2000 will match the day of the week for Jan 1 2400.

It follows that if one [laboriously] tots up the number of Monday the 13ths, Tuesday the 13ths, etc for any given 400 year span, the frequency over that 400 year span will match the long term average.

Edit: One likely could accelerate the crank and grind labor by starting at March 1 2000 and noting that there are only 14 year types (all identical except for the weekday of March 1 and whether Feb 29 exists and that they repeat in a standard cycle every 28 years [almost - look out for century years]. So if you can look at a calendar and tot up the 13'ths for one year, you are already halfway there.

 

[fresh_42]

Really? I'd like to see the proof of that.

It's at the end of the first chapter about induction, therefore the base of Gauß' birthday. However, they mention that it's less an exercise of induction rather than correct counting.

 

[jim mcnamara]

Since I failed Laborious 101 and wanted to see the "magnitude", wrote simple C program using @jbriggs444 parameters as specified:

$ ./sumdow
Count of calendar days for 13th
Sun  Mon  Tue  Wed  Thu  Fri  Sat
687  685  685  687  684  688  684