Talk:Point (geometry)/Archive 1

Dimension?
Since we know that a line has length and curvature, it is a 2 dimensional entity. We also know that a point has no length, so therefore it must have infinite curvature, making it a 1 dimensional entity. --anon
 * Your definition of "dimension" is wrong. It is not about length or curvature, rather, about how many variables control the object in question. For a line, one variable is enough, so it is one dimensional. The curvature and length have to do with where the line is embedded. If you take it that way, a line has three dimensions, which are length, slope, and curvature. No? Oleg Alexandrov (talk) 10:03, 26 October 2005 (UTC)


 * Uhm, rather four "dimensions". At least if you add torsion, too... ;D \Mike(z) 10:25, 10 May 2006 (UTC)

Doesn't it seem strange that a point can have 0 dimensions ? When you think of it, it's like it's nothing. I think I challenge that fact. This doesn't mean that I am going to change the article.--Granpire Viking Man 22:20, 14 October 2006 (UTC)


 * Strange, but true. It is nothing.  Quite simply, it's something with no volume, area, or even length, which makes it a nonexistent physical entity (or at least an infinitely small one).  If you challenge the existence of points, by a similar notion you could challenge the existence of many limits, and by extension all of calculus.  Disbelieving points is like disbelieving math. Liempt 14:29, 8 October 2007 (UTC)


 * Equally strange to me that a line segment can have one dimension. A line is nothing also in the 3 dimensional world. Well, I just think of degrees of freedom - no where to go if you're stuck on a point in space. Tom Ruen 01:20, 15 October 2006 (UTC)


 * This is not really strange when you realize the important difference between an entity and a concept. --Profero 11:59, 14 November 2006 (UTC)
 * Consider an infinite dimensional space. A point is essentially infinitesimal (possibly in all dimensions), but it never becomes zero (at least in one dimension). You can make it as small as you want: i.e. it can become 0.0001 units or 0.00000000000000000000000000000001 units or 0.0000000000000000000000000000000000000000000000000000000000000000000000001 units or 0.000000000000000000000000000... (A trillion zeros)...1 units, but never zero. But how big is a "unit"? There cannot be an absolute material definition of a point. So one word should help: infinitesimal - A point just gives a position. The degree of precision can keep on increasing as the the "point" becomes smaller and smaller (i mean a "point" for a locating a city on the world map, and a "point" for locating an atom in a salt crystal can have different sizes).-59.95.25.242 (talk) 19:26, 9 December 2011 (UTC)
 * By extension, would a line (an infinite series of points constricted by a single limit) be too a non-physical entity... or at least and infinitely small one., so too with two, and three dimensional figures. this would make calculating perimeter a rather pointless task, because how can you measure the distance between two concepts, abstracts, ideas, and further non-physical or imaginary objects... things that aren't a part of the universe have no place in the universe... that is to say location. --anon —Preceding unsigned comment added by 67.142.130.20 (talk) 03:54, 21 August 2010 (UTC)


 * What if a point has mass??? 68.173.113.106 (talk) 19:03, 3 December 2011 (UTC)


 * I have a way of trying to understand a point. Anyone is free to analyse this

The definition of a point, actually, strictly depends on how small the position to be located needs to be. Hence the "diameter" or "width" of a point may be 10 100 meters (m), 1010 m, 1,000 m, 1 m, 1 cm, 1 mm, 1 μm, 1 nm, 10 -10 m, 10 -100 m, and so on. So relatively, the point actually is infinitesimal in size. The diameter of a point may be very, very small but can never become zero, because then, that would wipe out the existence of the point itself.

Mathematically, the "diameter" (a point cannot have a fixed "diameter") of a point, d, may be defined as:

$$\lim_{d \to 0}d$$

In two dimensions, a point may be considered to be an ever shrinking circle, in 3 dimensions an ever shrinking sphere, in 4 dimensions an ever shrinking hypersphere (3-sphere), and so on. Thus a point may exist in all higher dimensions up to infinity, but the "widths" in all the dimensions approach zero. -59.95.2.174 (talk) 21:00, 6 December 2012 (UTC)

Random, but must ask...
I'll admit, I've been puzzling about this. Could it be that a line has dimensions surrounding a coordinate, such as the Height of a point is equal to the limit of (any) function of X as the change in (any values) X approaches zero? Sure, it doesn't really say anything except that its height is really really small, but does it seem at all significant? I was just thinking about this along the applications of single-point-energy, but the only person I've ever asked of yet has been my Calc. teacher.. --Kazarian 24.176.171.123
 * read the post above yours -59.95.2.174 (talk) 21:01, 6 December 2012 (UTC)

points
Points are most often considered within the framework of Euclidean geometry, where they are one of the fundamental objects. Euclid originally defined the point vaguely, as "that which has no part". In two dimensional Euclidean space, a point is represented by an ordered pair, (x,y), of numbers, where the first number conventionally represents the horizontal and is often denoted by x, and the second number conventionally represents the vertical and is often denoted by y. This idea is easily generalized to three dimensional Euclidean space, where a point is represented by an ordered triplet,, with the additional third number representing depth and often denoted by z. Further generalizations are represented by an ordered tuplet of n terms, where n is the dimension of the space in which the point is located.

Many constructs within Euclidean geometry consist of an infinite collection of points that conform to certain axioms. This is usually represented by a set of points; As an example, a line is an infinite set of points of the form L={}, where through  and  are constants and n is the dimension of the space. Similar constructions exist that define the plane, line segment and other related concepts.

In addition to defining points and constructs related to points, Euclid also postulated a key idea about points; he claimed that any two points can be connected by a straight line, this is easily confirmed under modern expansions of Euclidean geometry, and had grave consequences at the time of its introduction, allowing the construction of almost all the geometric concepts of the time. However, Euclid's axiomatization of points was neither complete nor definitive, as he occasionally assumed facts that didn't follow directly from his axioms, such as the ordering of points on the line or the existence of specific points, but in spite of this, modern expansions of the system have since removed these assumptions. —Preceding unsigned comment added by Gon56 (talk • contribs) 07:24, 14 June 2008 (UTC) Points can exist any where in space! —Preceding unsigned comment added by 75.144.186.253 (talk) 12:16, 16 May 2011 (UTC)

--- I am unhappy with "Euclid originally defined the point vaguely". May I suggest at least omitting the word "vaguely"? I would even suggest replacing it by "concisely" althoug this might be at odds with Cantor's naive theory of point sets. Read my essay at http://www.fqxi.org/community/forum/topic/833. Moreover, I would like to suggest replacing "a point is represented by an ordered pair, (x,y), of numbers" by "a point is attributed to an ordered pair, (x,y), of numbers".

Eckard Blumschein — Preceding unsigned comment added by 94.223.197.198 (talk) 06:23, 14 March 2012 (UTC)

Postulates?
Since points are included in the postulates of Euclidean geometry, should we include those with a special note to the Playfair Axiom?Mrchapel0203 (talk) 05:56, 5 September 2008 (UTC)

Suggested Elaborations of this Article
My regrets for my intrusion into this article as a nonmathematician. I am surprised that the word "position" does not appear in this article, as I thought that was the main point of a point. I list below several comments intended to prod the more knowledgeable to expand this article.

Descartes
I recall from my early schooling being introduced to the Cartesian coordinate system. I had the impression that Renee Descartes introduced the x, y and z axes, and thus believe that he should at least be mentioned in this article. Of course, now we can have as many dimensions as we want.

Singularities
This topic of physics appears to be related, perhaps a mathematical discussion of that topic could be added.

Quantum Mathematics?
Is there a branch of mathematics that would limit the number of points on a line segment, or deals with points that have only a probable position? Proactivedave 63.66.64.246 (talk) 15:54, 2 January 2013 (UTC)

What do we mean by point?
See following link:

http://www.spacetimeandtheuniverse.com/math/4507-0-999-equal-one-324.html#post21608

You can now rewrite the nonsense you have written in this article. Knowing that most of you are idiots, I somehow doubt that you can make any difference either way. 197.79.12.107 (talk) 07:48, 8 July 2013 (UTC)

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