Triangle! — Everything about everything.

ewgeniy

18 years ago

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Hello everyone!
The other day, I had a debate with a friend about what a triangle is...
I formulated it something like this:
A triangle is 3 line segments that do not lie on the same line, connected to each other.
A line segment is a part of a line, bounded by two points.
A line is an imaginary line, etc....
The essence of the argument:
Since a triangle consists of imaginary parts, it CANNOT be touched.
Is that true?
Thank you in advance for your answers.

Kreesanya

18 years ago

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Yes. The triangle itself is indeed composed of elements whose existence can only be expressed by relying on the concept of infinity. If anything here can be "touched," it will not be the triangle itself, but only its MODEL: a drawing on paper, a triangular ruler, three connected sticks – these are all models, material constructions that represent the properties of the object being studied, but are not the object itself.

Loken

18 years ago

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Strange question). If we are talking about a triangular ruler, which is called a triangle, then, without a doubt, it is possible). If you imagine a triangle in your mind, then you can only touch it mentally. I don't know what else can be said about this.

In reply to Loken

Dirty_Player

18 years ago

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If the author of the topic is interested in a scientific definition: So, as a mathematician, I'll say: A triangle is a geometric figure consisting of three points that do not lie on the same line, and three line segments that connect these points in pairs. Regarding touching it, of course, you can! Why not? For example, a ruler-triangle. It's still a triangle!

In reply to Dirty_Player

ewgeniy

18 years ago

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Dirty_Player;154377

If the author of the topic is interested in a scientific definition:
As a mathematician, I'll say:
A triangle is a geometric figure consisting of three points that do not lie on the same line, and three line segments that connect these points in pairs.

Regarding touching it, of course, you can! Why not? For example, a ruler in the shape of a triangle. It's still a triangle!

I disagree here – you can touch a ruler in the shape of a triangle, anything that resembles a triangle in shape. But there's one caveat:
if you can touch it, then it has height, length, and width (you can even calculate time), which a figure in a plane cannot have!
And a ruler is called a triangle for simplicity.
(this is my opinion, which is what the dispute is about...)

Loken;154350

strange question) if you mean a triangular ruler, called a triangle, then, without a doubt, you can) if you imagine a triangle in your mind, then you can only touch it mentally. I don't know what else to say.

No, let's call things by their names: a ruler is a ruler, a triangle is a figure in a plane, otherwise you could call a pyramid a triangle :D
Regarding touching it in your mind – I specifically chose the word "touch" to emphasize materiality

Nagan-4

18 years ago

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2 Eugene. I agree. A "triangle ruler" is just a template of a geometric triangle. We don't think that a fighter jet model is a real fighter jet. As soon as width appears, the figure loses the properties of a triangle. The sides and angles of a real triangle always lie in the same plane, i.e., it is a geometrically flat figure. I don't know how to touch it.

Kreesanya

18 years ago

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Guys, read the text above – you can only interact with the triangle MODEL, not the triangle itself.

In reply to Kreesanya

Dirty_Player

18 years ago

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A triangle is not just a figure on a plane; it is also the external shape of an object. To be precise, you can actually touch the MODEL! BUT! This doesn't change the essence. In my opinion, a model of a triangle is also a triangle. Therefore, I believe that a triangle can be touched!

In reply to Dirty_Player

Kreesanya

18 years ago

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Dirty_Player;154473

In my opinion, a triangle model is still a triangle. Therefore, I believe that a triangle can be touched!

Quote from dictionary one: "A model is a man-made imitation of the objects being studied: layouts, images, diagrams, verbal descriptions, mathematical formulas, maps, etc. Models are always simpler than real objects, but they allow you to highlight the main points without being distracted by details."

Quote from dictionary two: "A mathematical model is a model of an object, process, or phenomenon, represented by mathematical patterns that describe the main characteristics of the modeled object, process, or phenomenon."

Thus, a model of an object simply cannot be the object itself. You can "touch" a model as much as you like, but a triangle consisting of points (and the segments that make it up are also formed by points) – unfortunately, you cannot. Because a mathematical point, although it is a component of objects, has infinitely small dimensions in space, i.e., its existence tends to zero.

In reply to Kreesanya

Dirty_Player

18 years ago

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I read the posts above and realized that higher education is harmful to some people! We need to take a simpler approach to these issues, rather than delving into philosophy and the concepts of models and points. Personally, I will stick to my opinion.

A triangle is not only a figure on a plane, but also the external shape of an object.

In reply to Dirty_Player

ewgeniy

18 years ago

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Dirty_Player;154476

I read the posts above and realized that higher education is harmful to some people! You need to take a simpler approach to these issues, rather than delving into philosophy and the concepts of models and points. Personally, I will stick to my opinion.

By the way, my friend (with whom I argued) suggested that I ask this question to someone with a higher education.
If this is delving into philosophy, I feel like an academic in the field of philosophical sciences :smile21:

Added after 34 seconds
PS Please provide a link to where this is written.

In reply to Dirty_Player

invisible

18 years ago

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I agree with Kreesanya. A triangle is a geometric shape, and it cannot be physically "touched." One can only touch a model of this geometric shape. The concept of a triangle itself is a kind of mathematical abstract noun, while "the external form of an object" is a specific noun used to name an object that is externally similar in shape. One cannot touch an abstract object. A simple example: it is impossible to touch such abstract concepts as "a person's intelligence" or "love." These may not be the best examples, but the essence is the same.

Гур

18 years ago

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Examples involving love and human intelligence are not entirely successful. It is impossible to answer the question of whether they can be touched, as there is no precise definition of what "love" and "human intelligence" are, as these are rather subjective concepts. It is quite possible that love and human intelligence are just a piece of paper lying on your desk among scattered documents.
However, let's move on to our triangles. I hope no one will argue that the MODEL of this geometric figure can be touched. Therefore, the question should be asked differently: is the model of a triangle a triangle? If so, then the triangle can be touched.

Sincerely,
Gur

Drnik

18 years ago

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Definition from a geometry textbook:
A triangle is a geometric figure consisting of 3 points and straight lines connecting these points.
A triangle is a figure from plane geometry (on a plane, not in volume); it can be drawn, and you can touch the plane on which it is drawn (if it is material). However, it is an abstraction, and you cannot touch it; it is comparable to a thought or a dream... you understand me... a model can have the shape of a triangle, but it is just a model...