Re: [Phys-L] Fictitious Mathalon.

[<dgpolvani@gmail.com>]

Thanks to Brian Whatcott for submitting this.  It led me to not only solve
the 6th grade problem, but to look at how calculus makes finding the area
and perimeter of figures like circles and ellipses reasonably easy to do.
This led me to review my calculus 1 techniques of finding areas and
perimeters of closed curves.  This, in turn, led me to review my knowledge
of arc length integrals and elliptic integrals.  All of this made for an
enjoyable afternoon not worrying about global warming, the pandemic, the
Ukrainian war, politics, inflation, immigration, etc.

Does anyone know how Kepler (died 1630) computed the area and perimeter of
an ellipse?  Newton was born in 1642, so Kepler didn't have the advantage of
calculus.

Don
Don Polvani  

> -----Original Message-----
> From: Phys-l <phys-l-bounces@mail.phys-l.org> On Behalf Of Brian Whatcott
> Sent: Saturday, July 2, 2022 3:07 PM
> To: Phys-L: Forum for Physics Teachers <phys-l@phys-l.org>
> Subject: [Phys-L] Fictitious Mathalon.
>
> I came upon a TV offering which served as light entertainment in the form
of
> an unlikely rom-com, in which a pop star (JLo)marries a math teacher as a
> stunt, on finding her intended was unfaithful. "Marry Me") The teacher ran
a
> math club for 6th graders (or thereabouts) and was preparing for a
mathalon,
> in the not-distant venue of Peioria.His daughter stumbled at the final
question
> in the finals, to the effect:
> A circle of perimeter 8 pi is inscribed in an ellipse which is twice as
wide as its
> height. What is the ellipse's area, in square units?
> I had forgotten the area formulation, but I was motivated to find it
online (of
> course!)Enjoy a moment of light entertainment.....
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