What is the best square in New York? Well, I'm here in Times Square,

and in a previous math video I've made in New York,

I expressed my disappointment that even though it's called 'Times',

very little multiplication is taking place.

But then afterwards, I realized that 'Times' is not actually worst part of the name.

You see, it's called 'Times Square'

but if you look at it on a map, it is actually shaped like a triangle.

So are any of the squares in New York actually square?

Well, to find out I took all the area on Manhattan, which is below Central Park,

the kind of stereotypical bit of New York,

and in there I counted 14 different locations which are described as being square.

And I figured, come on it's on a grid street system,

some of them are going to have to be pretty square-ish.

Well in fact, a full 5 of them are triangle-shaped.

1 of them, Peretz Square, is actually described on Google Maps as a 'triangle of landscaped green space'.

I'm like, "Oh come on. What about the rest of them?"

Well, only 2 of them were close enough to be called a square.

But before we get to those, let's first of all, look at the worst of the offenders, of the square-oids.

I am here in Washington Square Park & when you remove all the square attempts

which are actually triangles & you take anything which is not a mathematical shape,

and then there are a few squares which are a shape that in the US, is called a 'trapezoid',

the rest of the world calls it a 'trapezium'.

Once you remove those, you're left with all the squares which at least have the

decency to use right angles. Then, of those orthogonal attempts,

George Washington Square is the worst offender.

This is very much a square & wide-screen.

While I'm in New York looking for shapes

I'm going to take a quick detour to check out a triangle

Behind me on the ground is the Hess triangle

So back in the early 1900s, David Hess owned the land around here.

But in 1914, the U.S government used its eminent domain right to take the land back,

But in 1914, the U.S government used its eminent domain rights to take the land back for public use.

However, later on in 1922, his heirs discovered that the surveying kind of outline of

the land the government wanted missed a tiny bit of his property which is that triangle there.

They technically still own that bit & so they put a mosaic on it to say that they own it.

As of 1938 they sold it to the cigar store next to me here, which I believe still owns it.

A lot of people know about the Hess triangle because they heard about it in

the '99% Invisible' podcast, which is where i first came across it, I highly recommend it,

and in the podcast, they described it as being about the size of a very large slice of pizza,

which probably says more about New York than the triangle.

However, on the Wikipedia page for the Hess triangle, it's described as an isosceles triangle,

That's a very specific way to talk about a triangle.

Don't get me wrong, big fan of describing types of triangles, but, is it really isosceles?

I should check.

OK, I got sides of... Well, one is 62 & a half, the other 67, 67 & a half.

I'm prepared to call that pretty isosceles.

In 2nd place, our honorable mention is this square here. This is Stuyvesant Square.

I'm pronouncing that incorrectly, it's named after a guy from the Netherlands

you can see his statue in the background over there and I have no

idea how to say it correctly. But there's no better way to find out how to say a word

than by using it incorrectly in a YouTube video. I found this out last time

I did a video in New York and I pronounce 'Houston' as 'Houston' I mean

Howsthen was I supposed to know that was the wrong way?

So yes, this square whose name I'm not saying again, actually has the best ratio

of all the squares I looked at in New York. If you compare its height to its width

they're within 1% of each other but the reason it's not my

number 1 square, is because it's got a few fatal flaws. For a start

there is a road, running right through the middle of it. So it's less a square

and more two adjacent rectangles. On top of that its sides aren't straight.

The corners are quite orthogonal and so that 1% figure i gave you that's

actually what you get if you kind of line up a square of best fit

so it's pretty good, it's worth a mention but it's not the best. The best is where we're going next.

At last! Here I am, in the number 1 square in New York and it is

Tompkins Square! My goodness, is it orthogonal! It's got nice right angles

got very straight edges, AND the width compared to the length are within 2% of each other

And on top of all of that, it's actually a very nice Square

I mean I have seen a lot of squares at this point in the day, and I can confirm this is quite a good one.

So here you are Tompkins Square, the best square in New York

Undoubtedly, some people will have other opinions as to what the best square is

For the 14 I looked at (are in the description below, along with a GPS coordinates),

I just put images of them into Photoshop & kind of measure around to see how

many pixels across, and how many pixels down. If you find a better one please do let me know.

I mentioned earlier on my previous video when I was in New York last time, when I

calculated the linear equation of Broadway. If you haven't seen it you can

check it out there. And as always, if you haven't subscribed to my videos

I usually appreciate that. You will see more videos with both maths and Matt.

Just got recognized by someone in Times Square but very sadly they declined

my invitation to appear in the video.