Re: [Phys-L] puzzle about vectors (and the structure of the world)

[bernard cleyet <bernard@cleyet.org>]

Is it missing or am I too dim?

bc  …   means no link?

> On 2022/May/03, at 17:53, John Denker via Phys-l <phys-l@mail.phys-l.org> wrote:
>
> Hi --
>
> A cute little puzzle:
>
> Given two vectors A and B,
> what is the area of the gray-shaded annulus?
> More precisely:
> what what is the area inside the magenta circle (radius A+B)
> minus the area inside the green circle (radius A−B)?
>
> There are no wise-guy tricks here.
> The tails of the arrows meet at the center of the circles.
> The things that look like parallelograms are parallelograms.
> The more-precise version of the question works for any two
> vectors A and B.
>
> It's amusing to ask people to think out loud, i.e. to
> explain what they're thinking as they go along:
> — Some people know what it is, because they've seen it before.
> — Some people can understand it without writing anything down.
> — Some people can turn the algebraic crank.
> — Some people give up immediately.
>
> Extra credit: Why do we care?
>
> What does this say about the structure of the world that
> your HS math and physics books probably didn't tell you?
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