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zorro
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What is a point?
Mentallic said:A point has no dimensions. It just just an arbitrary way to visualize a certain point (can't think of any other simile) in a single or multi-dimensional plane.
Fortunately, lines in mathematics aren't defined using pens or pencils.Abdul Quadeer said:If we draw two intersecting lines with a sketchpen, we get a big point.
If we do the same with a sharpened pencil, we get a small point.
I wonder if a point is really 'dimensionless'.
Fredrik said:Fortunately, lines in mathematics aren't defined using pens or pencils.
Abdul Quadeer said:If we draw two intersecting lines with a sketchpen, we get a big point.
If we do the same with a sharpened pencil, we get a small point.
I wonder if a point is really 'dimensionless'.
Abdul Quadeer said:Can you draw a line without a pen or pencil? There is something beyond just definition.
ask_LXXXVI said:Points,circles,lines are definite mathematical concepts.They have an existence in an objective sense.Some prefer to say they exist in a Platonic world (the concept of Platonic world was envisaged by the Greek Philosopher Plato). Perfect circles,lines points may or may not be there in our physical universe.So don't try to "find" point in our universe.Think of a "point" as a mathematical concept.
We don't. I just checked my high school geometry book, which says the terms "point", "line", and "plane" are accepted as intuitive concepts and not defined. They are used in the definitions of other terms, however.Abdul Quadeer said:If a point is undefined, then there should not be any definition for a line either as line is a collection of points. Why do we define a line then?
Borek said:No. Whatever you draw is an approximation. But if you calculate hypotenuse of right triangle with legs 3 & 4 to be 5, it is an exact result.
And that definition will make sense if you first define "monad", "position", "space", and "location". Do you really consider those to be more fundamental notions than "point"?G037H3 said:A monad having position.
It's the concept of a position in space, a location.
HallsofIvy said:And that definition will make sense if you first define "monad", "position", "space", and "location". Do you really consider those to be more fundamental notions than "point"?
You will also need to specify what discipline you are referring to- physics, mathematics, philosophy, ... ?
Abdul Quadeer said:How did you measure those legs?
By drawing them and using a scale?
1) Drawing them is an approximation.
2) Taking the reading is an approximation.
We can't do geometry without approximations!
Fredrik said:You're missing the point.
Mentallic said:Most certainly not! If we try draw them and measure them that way, we will be making approximations and as such we won't be getting a perfect 3,4,5 side triangle.
Why do we label two identical angles as being the same? Couldn't we just see it? No, because drawings aren't always perfectly accurate. The idea that they are exactly equal is still valid and we make theories and assumptions on that idea.
A proof to show that the angles in any triangle add to 180o is a definite requirement. We can't just draw up any triangle and measure the angles that way, we will get an approximation and this doesn't prove anything.
Abdul Quadeer said:What is a point?
Perhaps so, after you have defined "monad"!G037H3 said:math+philosophy
I personally find monad with position to capture the essence of what a point is more than saying 'point'
Aristotle said that they have to be accepted as axioms, which is obviously true, but for the sake of illuminating the concept, monad with position is accurate
Define "part".Diffy said:What is a point? That which has no part.
And what definition is that?Prpan said:Why should point have no definition? I guess it has a pretty good definition in integral calculus as a device for integration of 0-dimensional infinitesimally small quantities (points in algebraic and geometric sense) into multidimensional objects. 1-D integral will give a path, which is still an abstract object but integration over volume will give a real 3D object. Solving Zeno's paradox of the Tortoise and Achilles in integral calculus is a good example of linking the abstract concepts with the concepts of the real world.
But there are many different things that can be given in terms of a co-ordinate system. Which of them is a "point"?NotEnuffChars said:A point is something you make when debating a topic, eg debating about what a point is :D
Seriously though, I just define a point to be somewhere on a plane that I can describe using some sort of co-ordinate system, cartesian, polar and so forth. It seems to work for me.
How are you defining "dimension"?sk_saini said:A point is a geometrical figure which has existence with no dimensions.
Fredrik said:I'm laughing every time I open this thread, imagining people who haven't gotten to the pythagorean theorem yet being told that a point is a monad with position.
Fredrik said:I'm laughing every time I open this thread, imagining people who haven't gotten to the pythagorean theorem yet being told that a point is a monad with position.
HallsofIvy said:But there are many different things that can be given in terms of a co-ordinate system. Which of them is a "point"?
The point of HallsOfIvy's post was that, if you insist on a definition for everything, you'll then need to define all the terms used in those definitions. And the same for the definitions of those terms, etc. etc.NotEnuffChars said:I'm not sure what you're point is :tongue:
Here's an example to qualify my statement.
A point in cartesian co-ordinates can be defined by x units in one direction, y units in a perpendicular direction and z units in the final perpendicular direction, usually denoted by (x,y,z). Similarly in spherical co-ordinates, (r, theta, phi) and so forth.
A point is a fundamental concept in geometry and mathematics. It is a precise location in space, represented by a dot or a small circle. In scientific terms, a point has zero dimensions and no size, shape, or thickness.
The purpose of a point is to provide a reference for measuring and describing objects in space. It is used to define the position, direction, and distance between objects, and to create geometric shapes and patterns.
A point is typically represented by a dot or a small circle. In geometry, it is denoted by a capital letter. For example, point A is different from point B, and they can be used to describe the position of different objects in relation to each other.
A point and a dot are often used interchangeably, but there is a subtle difference between the two. A point is a mathematical concept, while a dot is a physical object that can be seen or touched. A dot can represent a point, but a point cannot represent a dot.
In scientific research, points are used to describe and analyze data. They can be used to plot graphs, create diagrams, and represent data in mathematical equations. Points are also used in computer programming to create 3D models and simulations.