RectangularPrisms.mp4

Rectangular Prisms--Video Captions

In New York City, 432 Park Avenue is one of the world's tallest residential buildings.

It is also an ideal example of a rectangular prism.

A rectangular prism has a rectangular base and rectangular sides.

This two-dimensional net can be folded into a rectangular prism that has a square base.

This is the type of prism that defines 432 Park Avenue.

Unlike the other buildings that surround it, 432 Park Avenue is not an office building.

It is a residential building.

People live here.

How does that influence the architecture of the building and how is it reflected in the structure of the building?

First, office space is meant for many people.

Here are some statistics to consider.

The average amount of office space per person in the US is around 100 square feet.

The average number of employees can vary widely, but labor statistics show an average of around 15 employees.

Let's model this on a grid.

Let each of the small squares represent a 10' x 10' office space, so each square represents one employee.

What is the most ideal arrangement for 15 office spaces?

A 3 by 5 arrangement is the most efficient arrangement for a number of reasons.

Arranging 15 employees, you want them sitting near each other, since they are often collaborating with each other.

This is much better than arranging the office spaces in one long line of 15 offices.

A 3 by 5 arrangement is rectangular and if you think of multiple business in an office building, then it makes sense to have a rectangular prism office space, like the one shown here.

Have you noticed that most office buildings are rectangular in shape?

There are some square office spaces, but you'll notice the majority of them have rectangular bases.

Residential spaces have different considerations.

As before, let's start with some basic statistics.

The average size of a residential space in the US is about 2500 square feet.

The average number of people per household is about 2.5.

This means an average of 1000 square feet per person, a lot more space than in an office.

Let's model this on a grid.

Recall that each small square is a 10 foot by 10 foot office space, or 100 square feet.

A 2500 square foot space is ideally modeled by a 5 by 5 grid, which happens to be a square.

This arrangement works well for a residence, as you can envision bedrooms, a dining room, and other room arranged within this square.

There are other arrangements possible, but for the purposes of a residential skyscraper, a square base is really more efficient.

This helps account for the square base of 432 Park Avenue, but what about its height?

Why is this building so much taller than neighboring office spaces?

Keep in mind that in a business 15 people can work in a 1500 square foot work area.

But in a residential space there are far fewer people in a given amount of space.

In fact there are 10 times fewer people in a residential space than in a business.

That means that a residential tower would need many more units.

This accounts for the incredible height of 432 Park Avenue.

There's another advantage to a very tall residential skyscraper.

Think about when you look out your window from home to see the back yard and the neighboring houses.

What you see out of a tall residential unit is a vast landscape that gives the impression that your property is endless.

While you can get the same effect from a tall office building, living in a home that has such amazing panoramic views is a more meaningful experience.

Notice the large panoramic windows along each floor of 432 Park Avenue.

The view from this residential tower adds additional value to the experience of living there.