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From: Walter Landry (wlandry_at_[hidden])
Date: 2003-12-15 07:39:59

Matthias Schabel <boost_at_[hidden]> wrote:
> It should be clear that radian (length/length) and steradian
> (area/area) are fundamentally different quantities, even though they
> are technically both dimensionless numbers.

It is not uncommon to have expressions like sin(theta + theta^2). It
sure doesn't look clear to me that theta and theta^2 should have
different units. They should certainly be allowed to mix.

> > Radians are the ratio of one length to another. Degrees are a unit
> > that can be converted to a raw number by multiplying by pi/180. Much
> > like you can convert a speed into a raw number by dividing by the
> > speed of light or the speed of sound.
> No. Degrees and radians are two different ways of defining the same
> dimensionless quantity.

This is turning into a battle over semantics. Mach numbers are
dimensionless numbers. They can also be represented by quantities
with units.

Angles in radians are often mixed with numbers in expressions.
Degrees are not. Degrees are normally translated into radians before
being combined with ordinary numbers. Those are the conventions that
a library should follow.

Walter Landry

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