Hilchos Techum Shabbos

For better or for worse, my family is spending the summer up in the Catskills or the "country" as native New Yorkers like to call it. (Derech agav, my Shabbos shiur is on hiatus until after the summer so I will no longer be posting summaries of my shiurim until after the summer). One of the more popular shailos wich comes up in the bungalow colony that you usually don't have the rest of the year are the halachos of techum Shabbos. B"H this year we are in Monticello so we don't have any major issues, but a few years ago we were in an isolated colony and we had to deal with it. Yesterday I went to hear a shiur from Rabbi Reisman on this topic and he had a couple of he'oros that I found interesting.

It might be a little confusing, but I will try and write it clearly. Also, I apologize if my drawings don't come out so well.

First a short hakdama.

When calculating the techum you start counting 2000 amos from the edge of the city. A city in halacha is defined as all the houses in an enclosure or an eruv as well as all the houses that are within 70.66 amos of each other. From the edge of the city you draw straight lines and "square off" the city. It should look something like this. (The "xx" represent houses within 70.66 amos. Your techum starts at the edge of the sides of the rectangle.
___________________
[ xx xx x x ]
[ x x xxxx ]]]]]
[xx xxxxxx]



1) What happens if you have a house (we'll call it House A) that is within 70.66 amos of the squaring off but it is more than 70.66 amos from the last house. In the diagram below, House A is more than 70.66 amos from House Y and Z but it is withon 70.66 amos of the edge of the rectangle.

___________________
[xx xx
[ Y
[Z xx
[
[
[A

Can you extend the city borders down to House A (the blue lines) ? The question is based on how do you view the area that is squared off? Is the corner area of the rectangle considered part of the city or do we say that it is not part of the city, but when it comes to measuring where the techum starts, Chazal tell us you don't have to start counting until the edge of the rectangle.

Apparently this was a big machlokes in Lakewood about 10 years ago and the practical nafka mina was whether one could walk from Lakewood to the hospital on Shabbos.

2) When you have 2 cities whose squared off area overlap you can count them as one city.

This is one reason why you can walk from Brooklyn to Manhattan. Apparently, when you square off Manhattan you will wind up on Ocean Parkway and when you square off Brooklyn you will wind up on the Upper West Side. Since these areas overlap you can count Brooklyn and Manhattan as one city.

3) There is another reason why Brooklyn and Manhattan are counted as one city. There is a halacha of "triangulation", where you have 3 cities that from a triangle.

X
Y Z

The halacha is that even though city Y and city Z are more than 70.66 amos apart, we can "move" city X in between them and if by moving X, the distance between Y and X and X and Z would be less than 70.66 amos we can look at it as one big city.

In our case, Roosevelt Island is between Manhattan and Brooklyn. If you moved Roosevelt Island down you would be able to create one big city from Manhattan and Brooklyn.