Re: [math-fun] Dandelin hyperbola proof
Animated gif's work just fine, and have been supported since the middle ages (of the Internet). FFMPEG can convert any movie or image sequence into an animated gif, although if you want decent color rendition, the process is currently more complicated than one might want. But if color accuracy isn't an issue -- e.g., animated mathematical objects -- then it isn't difficult. Also, the symbolic algebra system Maxima can generate animated gif's, and I believe that other CAS systems can, as well. At 07:04 AM 11/12/2018, Fred Lunnon wrote:
An interactive fly-through demo with fancy lighting?
On Wikipedia?
It might just be feasible, if XML is up to this sort of job ... current user PC's have plenty of power to run what is effectively a simple 3-D game.
This might make a nice student project.
But I never even got around to uploading the static paper to ArXiV yet, let alone getting it past Math. Intell. --- so don't hold yer breath!
WFL
On 11/12/18, Bill Gosper <billgosper@gmail.com> wrote:
On 2018-11-11 17:21, Fred Lunnon wrote:
Sadly, technological progress has relegated our early (and usually laboriously crafted) efforts to museum exhibits --- compare the demo at https://en.wikipedia.org/wiki/Dandelin_spheres
WFL And where might we find a similarly technologically ultraprogressive Wikipedient obsoletion of your laboriously crafted gosper.org/binomial.pdf ? Ârwg
> >> >> On 11/11/18, Billl Gosper <billgosper@gmail.com> wrote: Eons ago, trying to prove that locus-of-constant-difference is a conic section, I reinvented Dandelin spheres, with a possibly simpler proof that does not refer to their centers nor radii. gosper.org/hyperb.GIF uses instead the lemma that all tangents to a sphere from a point are equally long. The drawing probably needs stereo vision to be convincing. I'm not sure I realized at the time that the spheres could be unequal. Ârwg
Maple will produce passable animated .GIF files for simple demos; and can happily interactively rotate the solid originals of the stills in the paper. [ Script available to anybody wanting to investigate further --- always supposing byte-rot has not supervened in the meantime! ] These images required patching together from numerous simpler parts, and any animated sequence would surely generate an inconveniently enormous .GIF file. The strategy I had in mind would utilise in-line generation of those parts of the surface currently in view; I doubt if that is practicable without some kind of preliminary, suitably interfaced graphical toolbox. WFL On 11/12/18, Henry Baker <hbaker1@pipeline.com> wrote:
Animated gif's work just fine, and have been supported since the middle ages (of the Internet).
FFMPEG can convert any movie or image sequence into an animated gif, although if you want decent color rendition, the process is currently more complicated than one might want. But if color accuracy isn't an issue -- e.g., animated mathematical objects -- then it isn't difficult.
Also, the symbolic algebra system Maxima can generate animated gif's, and I believe that other CAS systems can, as well.
At 07:04 AM 11/12/2018, Fred Lunnon wrote:
An interactive fly-through demo with fancy lighting?
On Wikipedia?
It might just be feasible, if XML is up to this sort of job ... current user PC's have plenty of power to run what is effectively a simple 3-D game.
This might make a nice student project.
But I never even got around to uploading the static paper to ArXiV yet, let alone getting it past Math. Intell. --- so don't hold yer breath!
WFL
On 11/12/18, Bill Gosper <billgosper@gmail.com> wrote:
On 2018-11-11 17:21, Fred Lunnon wrote:
Sadly, technological progress has relegated our early (and usually laboriously crafted) efforts to museum exhibits --- compare the demo at https://en.wikipedia.org/wiki/Dandelin_spheres
WFL And where might we find a similarly technologically ultraprogressive Wikipedient obsoletion of your laboriously crafted gosper.org/binomial.pdf ? —rwg
>> >> >> On 11/11/18, Billl Gosper <billgosper@gmail.com> wrote: Eons ago, trying to prove that locus-of-constant-difference is a conic section, I reinvented Dandelin spheres, with a possibly simpler proof that does not refer to their centers nor radii. gosper.org/hyperb.GIF uses instead the lemma that all tangents to a sphere from a point are equally long. The drawing probably needs stereo vision to be convincing. I'm not sure I realized at the time that the spheres could be unequal. —rwg
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