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

[John Mallinckrodt <ajm@cpp.edu>]

The problem seems straightforward enough, but I am quite sure that I am missing something because I don’t see what it says about the structure of the world that our HS math and physics books didn't tell us and JD doesn’t say stuff like that idly. 

> On May 3, 2022, at 9:45 PM, John Denker via Phys-l <phys-l@mail.phys-l.org> wrote:
>
> Let's try again, with the image link:
>  https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fav8n.com%2Fphysics%2Fimg48%2Fvector-sum-difference.png&amp;data=05%7C01%7Cajm%40cpp.edu%7C0fef7fb8d24343c1b37908da2d88d977%7C164ba61e39ec4f5d89ffaa1f00a521b4%7C0%7C1%7C637872363038872067%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&amp;sdata=oTXAGtpSwraBkRv8rvrsUNQLqWPCeiTWoE8aST90uPs%3D&amp;reserved=0
>
> 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?
>
>
>
>
> > On 5/3/22 9:23 PM, bernard cleyet wrote:
> >
> > Is it missing or am I too dim?
>
> The link was missing. My bad.
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