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There is the sentence in the book which includes words like fall foliage angle. What is the intention of the author in the highlighted sentence. What the author wants to convey in this line from Phil Knight's Shoe Dog?

We hashed it out some more and finally decided New York and Boston were the most logical places. Especially Boston. "It's where most of our orders are coming from," one of us said. "Okay," he said. "Boston, here I come."

Then I handed him a bunch of travel brochures for Boston, playing up the fall foliage angle. A little heavy-handed, but I was desperate.

In the story the narrator very much wants John Bork to go to Boston.

Then I handed him a bunch of travel brochures for Boston, playing up the fall foliage angle.

The narrator is trying to convince Bork to go to Boston by promoting the perspective, or "angle" (a particular way of approaching or considering an issue or problem) of Boston with beautiful fall foliage.

The brochures would be travel brochures with pictures of Boston in the fall when all the trees are turning shades of red and gold.

The goal of the author is to indicate to the reader that the narrator was desperate to convince John Bork to go to Boston.

A little heavy-handed, but I was desperate

If you are making an argument, you can approach the argued/desired conclusion from many different ways, or "angles." "Angle" as a word highlights that it is not a direct approach (although that would technically still be a 90* angle), but rather an indirect approach.

In the excerpt, the author is arguing to go to Boston over New York. To strengthen the argument for going to Boston, he mentions that the leaves and trees (foliage) are very colorful/scenic during fall. So to persuade the listener, he "play[s] up the fall foliage angle."

This excerpt is from an autobiography written in an informal style. In this segment, Phil Knight relates that he told a Japanese partner that his company, Blue Ribbon Sports (now known as Nike), had an office on the East Coast of the United States, before they actually did. He therefore had to send his most trusted employee, Jeff Johnson, back east to create one as quickly as possible. Johnson loved Los Angeles, however, and had no personal interest in moving to the other side of the country.

So, Knight is trying to convince Johnson that living on the East Coast is not so bad. He is presenting different perspectives about Boston, i.e. different angles:

a particular way of presenting or thinking about a situation, problem, etc.

We need a new angle for our next advertising campaign. [OALD]

One angle specifically is of fall foliage, foliage referring to leaves on trees and other vegetation, and fall referring to the autumn, the more common name for the season in North America, but which fell out of use in Britain long ago.

Specifically, fall foliage (or fall color) refers to the color of woodlands in the autumn, a mix of intense reds and yellows. The change in leaf color occurs everywhere there are deciduous trees, including Los Angeles, but is more intense in colder climates (and where there are more such trees). It is particularly associated with New England, thanks to Robert Frost and others; "leaf peeping" is a major tourist attraction. So, Knight is trying to encourage Johnson by pointing out that living in Boston, he will be able to enjoy the fall foliage.