"Name ist Schall und Rauch", i.e. name it as you please - as long as the definition is clear. [This might better belong to chat]
Am 24.08.2017 um 11:08 schrieb R.E. Boss: > With so many people you can provide a long list of papers which support your > memory, I suppose. > > > R.E. Boss > > >> -----Original Message----- >> From: Programming [mailto:[email protected]] >> On Behalf Of Jens Pfeiffer >> Sent: donderdag 24 augustus 2017 07:56 >> To: [email protected] >> Subject: Re: [Jprogramming] "n-volume" of an "n-sphere" >> >> I can from experience (>20 years) confirm n-(dimensional)-disk and n- >> (dimensional)-ball are used interchangeably in mathematics, at least here in >> Bonn, Germany among these people here: >> >> http://www.hcm.uni-bonn.de/people/faculty/ >> https://www.mpim-bonn.mpg.de/taxonomy/term/4 >> https://www.mpim-bonn.mpg.de/peoplelist?pltype=0&plgroup=visitors >> http://www.math.uni-bonn.de/members?mode=struc >> >> Sometimes, we use the terms n-ball vs (n-1)-disk to talk about an n- >> dimensional ball vs the intersection of an (n-1) dimensional hyperplane with >> an n-ball. >> >> >> >> >> Am 23.08.2017 um 21:13 schrieb Roger Shepherd: >>> Is there something specifically wrong with common sources of >>> definitions such as http://dictionary.sensagent.com/N-sphere/en-en/ >>> >>> Just checking >>> >>> Sent from Mail for Windows 10 >>> >>> From: Jimmy Gauvin >>> Sent: Wednesday, August 23, 2017 9:20 AM >>> To: [email protected] >>> Subject: Re: [Jprogramming] "n-volume" of an "n-sphere" >>> >>> Even in Mathworld it is not clear that disk is in common usage. >>> >>> from http://mathworld.wolfram.com/Ball.html we have : >>> >>> The [image: n]-ball, denoted [image: B^n], is the interior of a sphere >>> <http://mathworld.wolfram.com/Sphere.html> [image: S^(n-1)], and >>> sometimes also called the [image: n]-disk >>> <http://mathworld.wolfram.com/Disk.html>. (Although physicists often >>> use the term "sphere <http://mathworld.wolfram.com/Sphere.html>" to >>> mean the solid ball, mathematicians definitely do not!) >>> >>> and from http://mathworld.wolfram.com/Disk.html we have : >>> >>> The [image: n]-disk for [image: n>=3] is called a ball >>> <http://mathworld.wolfram.com/Ball.html>, and ... >>> >>> >>> >>> On Wed, Aug 23, 2017 at 6:50 AM, R.E. Boss <[email protected]> >> wrote: >>>> The question is "Is an n-disk a well-established mathematical term?". >>>> >>>> A disc originally had only meaning in 3 dimensions, being " a >>>> circular flat object", e.g. a cd or compact disc; >> http://dictionary.cambridge. >>>> org/dictionary/english/disc. >>>> Also: a disk is normally "a flat, circular device that is used for >>>> storing information"; >> http://dictionary.cambridge.org/dictionary/english/disk. >>>> You reference to mathworld is not supported by other references on >>>> that page, so is probably a private generalization of mr. Weisstein. >>>> In any case not convincing. >>>> I respond with https://www.encyclopediaofmath.org/index.php/Disc >>>> where a disc is defined as "The part of the plane bounded by a circle >>>> and containing its centre." So they stick to the 2-dimensional case. >>>> Also a topological disc is 2-dimensional https://www. >>>> encyclopediaofmath.org/index.php/Disc,_topological. >>>> Another reference is >> https://www.wikiwand.com/en/Disk_(mathematics) >>>> which states "In geometry, a disk (also spelled disc)[1] is the >>>> region in a plane bounded by a circle. " >>>> >>>> Your reference to math.stackexchange is also an instance of one >>>> person using this term once, not convincing at all. >>>> >>>> John Lee in his book explicitly states on the pages indicated: >>>> "In the case n=2, we sometimes call B^2 the (open) unit disk. >>>> (...) >>>> We sometimes call B^2 the closed unit disk." (where this B has a >>>> superbar, which is not copied) So he also restricts a disk to 2 >>>> dimensions. >>>> >>>> Finally, your reference concerning CW-complexes. Perhaps in that, >>>> rather restricted area of mathematics it seems disk is used as >>>> synonym for ball, see also https://www.wikiwand.com/en/CW_complex. >>>> >>>> My final conclusion is that an n-disk is NOT a well-established >>>> mathematical term, apart from n=2 and, which I cannot decide, perhaps >>>> in the area of CW-complexes. >>>> >>>> >>>> R.E. Boss >>>> >>>> >>>>> -----Original Message----- >>>>> From: Programming [mailto:programming- >> [email protected]] >>>>> On Behalf Of Murray Eisenberg >>>>> Sent: maandag 21 augustus 2017 17:56 >>>>> To: [email protected] >>>>> Subject: Re: [Jprogramming] "n-volume" of an "n-sphere" >>>>> >>>>> To the contrary, “n-disk” is a well-established mathematical term, >>>>> for arbitrary dimension n = 1, 2, 3, 4, .... See, for example, >>>>> http://mathworld.wolfram.com/Disk.html >>>>> <http://mathworld.wolfram.com/Disk.html> >>>>> (which, alas, mangles the distinction between “disk” and “ball”). >>>>> >>>>> [Often, for emphasis or disambiguation, the terms “closed n-disk” or >>>> “closed >>>>> n-ball” are used for the set of points in Euclidean n-space of >>>>> distance >>>> at most >>>>> r from a given point; and then “open n-ball” for the set of points >>>>> of >>>> distance >>>>> strictly less than r. (And, in fact, the terms “disk” and “ball” are >>>> well- >>>>> established even, more generally, for arbitrary metric spaces.)] >>>>> >>>>> For a typical recent instance of the usage, see: >>>>> >>>>> https://math.stackexchange.com/questions/24785/the-n-disk-dn- >>>>> quotiented-by-its-boundary-sn-1-gives-sn >>>>> <https://math.stackexchange.com/questions/24785/the-n-disk-dn- >>>>> quotiented-by-its-boundary-sn-1-gives-sn> >>>>> >>>>> The usage is defined in many sources. See, e.g.: >>>>> >>>>> John Lee, Introduction to Topological Manifolds, 2nd ed., pages 21-22. >>>>> >>>>> Soren Hansen, "CW complexes”, page 1 >>>>> (https://www.math.ksu.edu/~hansen/CWcomplexes.pdf >>>>> <https://www.math.ksu.edu/~hansen/CWcomplexes.pdf>). >>>>> >>>>> >>>>>> On21 Aug 2017 11:15:20 +0000,"R.E. Boss" <[email protected] >>>>> <mailto:[email protected]>> wrote: >>>>>> AFAIR disk is not a mathematically defined term for high dimensions. >>>>>> Ball is as you defined it, where one can argue whether the distance >>>>>> is >>>>> "strictly less" or " at most" r. >>>>>> Sphere is the definition where the distance is equal to r. >>>>>> >>>>>> >>>>>> R.E. Boss >>>>>> >>>>>> >>>>>>> -----Original Message----- >>>>>>> From: Programming [mailto:programming- >>>>> [email protected] >>>>>>> <mailto:[email protected]>] >>>>>>> On Behalf Of Murray Eisenberg >>>>>>> Sent: zondag 20 augustus 2017 16:33 >>>>>>> To: [email protected] >> <mailto:[email protected]> >>>>>>> Subject: Re: [Jprogramming] "n-volume" of an "n-sphere" >>>>>>> >>>>>>> Re Don Kelly’s comment: >>>>>>> >>>>>>> NO the ball of radius r at a point p in n-space is the set of >>>>>>> all points of distance strictly less than than r from p; >>>>>>> the disk of radius r at a point p in n-space is the set of >>>>>>> all points of distance at most r from p. >>>>>>> >>>>>>> “Infinitesimal” has utterly nothing to do with it, nor does >>>>>>> transfinite math (although the set of points in such a ball, or >>>>>>> such a disk, is definitely infinite and, in fact, uncountable. >>>>>>> >>>>>>> Re Jimmy Gauvin’s comment: >>>>>>> >>>>>>> It is utterly trivial to prove that a ball (or disk) in >>>>>>> euclidean n-space is convex. It requires nothing more than what is >>>>>>> commonly taught in standard courses in sophomore linear algebra >> today. >>>>>>> Specifically, basic properties of the euclidean norm, including >>>>>>> the >>>> triangle >>>>> inequality. >>>>>>>> On 2Sat, 19 Aug 2017 18:03:49 -0700,Don Kelly <[email protected] >>>>>>>> <mailto:[email protected]> >>>>>>> <mailto:[email protected] <mailto:[email protected]>>> wrote: >>>>>>>> If one considers a point as infinitesimal -as usually >>>>>>>> considered-, then we have an infinite number of points at an >>>>>>>> infinitesimal distance from the origin and at a larger distance >>>>>>>> from the origin there are still an infinite number of points on >>>>>>>> the surface and an infinite number of points enclosed . Isn't >>>>>>>> this getting into >>>> transfinite >>>>> math? >>>>>>>> What's the point? >>>>>>>> >>>>>>>> Don Kelly >>>>>>>> >>>>>>>> >>>>>>>> On 2017-08-15 8:23 PM, Jimmy Gauvin wrote: >>>>>>>>> The construction of the sphere implies it cannot be convex but >>>>>>>>> you will have to find a topologist to prove it to you. >>>>>>>>> >>>>>>>>> The sphere is the collection of points whose distance to the >>>>>>>>> origin is equal to the radius of the sphere. >>>>>>>>> >>>>>>>>> The ball or volume is comprised of the points whose distance to >>>>>>>>> the >>>>> —— >>>>> Murray Eisenberg [email protected] >>>>> Mathematics & Statistics Dept. >>>>> Lederle Graduate Research Tower phone 240 246-7240 (H) >>>>> University of Massachusetts >>>>> 710 North Pleasant Street >>>>> Amherst, MA 01003-9305 >>>>> >>>>> >>>>> >>>>> >>>>> -------------------------------------------------------------------- >>>>> -- For information about J forums see >>>>> http://www.jsoftware.com/forums.htm >>>> --------------------------------------------------------------------- >>>> - For information about J forums see >>>> http://www.jsoftware.com/forums.htm >>>> >>> ---------------------------------------------------------------------- >>> For information about J forums see >> http://www.jsoftware.com/forums.htm >>> ---------------------------------------------------------------------- >>> For information about J forums see >> http://www.jsoftware.com/forums.htm >> >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
