Most Possible Seudos

As this year comes to a close, here is a great little factoid I heard from the Rav's Friday night דרשה:
    This year, being a leap year, and since no יום טוב ever fell out on שבת we have a unique situation where we have the maximum number of סעודות you could possibly have in one year:

54 שבתות x 3 סעודות	=	162 סעודות
12 ימים טובים x 2 סעודות	=	24 סעודות
	=	186 סעודות

This hasn't happened since 1984!

Who is running the markets?

I just heard this and had to post it:

The fluctuation of the Dow Jones Industrial Average for the first three days of this week were as follows:

Monday: -634.76

Tuesday: +429.92

Wednesday: -519.83

If you take each number and add up the digits, each equals 26, the gematria of י-ה-ו-ה!

The least frequent הפטרות

This is really a calendar issue and has already been cross-posted in AstroTorah.

However, it does involve some statistics so it is applicable here, as well:

We just read the הפטרה of פרשת פינחס which is a pretty rare occurrence. However, it is not the most rare. The exact frequencies of each rare הפטרה are discussed here. The numbers are based on a chart of the frequency of each type of year found here.

However, there is one issue with the calculations. It assumes that whenever אחרי מות and קדושים are separate and קדושים is not a special פרשה, its הפטרה is read. However, as pointed out in R' Dovid Heber's שערי זמנים, this is not the custom, according to משנה ברורה. Rather, as long as the הפטרה of אחרי מות was not read for whatever reason, we read that in place of הפטרת קדושים. Therefore, the הפטרה of קדושים is only read when both אחרי מות and קדושים are not special פרשיות, thereby dropping the frequency under 6%! For more thorough details please see this excerpt from the ספר.

Astro Torah: Needing a GPS to Build a Sukkah

See R' Ari Storch's Needing a GPS to Build a Sukkah

Let us examine the mathematics behind this. We will find that they are slightly troubling.

As he states, the גמרא asserts that according ר' זירא the 20 אמות limit would only apply to a small Sukkah of 4x4 אמות. I know I have heard but can't remember where, that the specific issue that ר' זירא had was that the סכך needs to provide shade on the ground. If the walls of a small sukkah were 20 אמות high, there would never be shade on the ground provided by the סכך. This is certainly true. But according to the trigonometry of it, the limit should be far less than 20!

As stated by R' Ari, the highest angle the sun will reach in ארץ ישראל during this time is approximately 58°. The tan of 58° is approximately 1.6. That is to say that at a 58° angle, the opposite side (the wall) is about 1.6x the length of the adjacent (the ground.) That said, in a 4x4 sukkah, a wall of merely 6½ אמות would cause the walls to constantly cast a complete shadow on the ground and the סכך will never provide this shade. If we approach it from the other end, 20 אמות walls would prevent סכך-shade in any sukkah up to 12½ (20/1.6) אמות.