"RG" <rnospa...@flownet.com> wrote in message news:rnospamon-20651e.17410012102...@news.albasani.net...
In article <i92dvd$ad...@news.eternal-september.org>,
"BartC" <b...@freeuk.com> wrote:

"Thomas A. Russ" <t...@sevak.isi.edu> wrote in message

> But radians are dimensionless.

But they are still units

No, they aren't.

so that you can choose to use radians, degrees or gradians

Those aren't units either, any more than a percentage is a unit.  They
are just different ways of writing numbers.

All of the following are the same number written in different notations:

0.5
1/2
50%

Likewise, all of the following are the same number written in different
notations:

pi/2
pi/2 radians
90 degrees
100 gradians
1/4 circle
0.25 circle
25% of a circle
25% of 2pi

See?

But what exactly *is* this number? Is it 0.25, 1.57 or 90?

I can also write 12 inches, 1 foot, 1/3 yards, 1/5280 miles, 304.8 mm and so on. They are all the same number, roughly 1/131000000 of the polar circumference of the Earth.

This does depend on the actual size of an arbitrary circle, but that seems little different from the choice of 0.25, 1.57 or 90 for your quarter circle.

--
bartc


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