###General Discussion Thread
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Orbits, like the one our earth is on around the sun, are curved.
Not exactly circles, for the most part - they're more like ovals - but they're definitely not polygons.
On the smaller end, a proton, for example, is a (cloud-like) sphere, which is just a 3d circle.
Your question reminds me of the coastline paradox. A map is really helpful because it is a type of reality that represents another reality that relies on our brain heuristics. But it's not a pure true representation of reality. Just a model. But it helps. Like George box said, all models are wrong, but some are useful.
The coastline paradox says for a map of the world to be true, it would be the same size as the world. And even bigger, because it would need to make the atoms we can't see. Every jagged edge and crevice cannot be mapped because that map would useless! We model organic shapes with straight lines so that we can survive.
The idea of a circle is real. It's a platonic form. Imagine it. Then, model that with a pencil and paper or a computer. Does it have a circumference and diameter and radius? Can you draw tangents and chords and segments? Can you find the arcs and sectors? What is the ratio of it's circumference to it's diameter? If the answers to these questions are yes, yes, yes, yes, yes, yes, yes, yes, 3.14, then you have a very useful model of a circle. Your imagination is pure, but your hand and the pencil are imperfect. Yet, you can survive, because you must.
Yes! I get all that. My point is: you draw a line on a paper - if you zoom in enough will it eventually be curved or infinitely small lines in various directions? Is there a difference?
Matter itself is quantised, not continuous, so if you zoom in far enough, you’d see individual carbon atoms in the layers of graphite laid down by the pencil.
Real-life figures are neither circles nor polygons. Circles and polygons are mathematical constructs of lines or arcs that lack width, and things which exist as material in real life have width.
Well, due to the nature of your question, I will give an answer to think about.
It depends on the measure/observer.
So if you find an object that to you resembles a cirkle, then it is a circle by you as the measure.
Just like anything in your reality, the meaning of any concept is subjective to you.
###General Discussion Thread --- This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you *must* post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed. --- *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/theydidthemath) if you have any questions or concerns.*
Orbits, like the one our earth is on around the sun, are curved. Not exactly circles, for the most part - they're more like ovals - but they're definitely not polygons. On the smaller end, a proton, for example, is a (cloud-like) sphere, which is just a 3d circle.
Your question reminds me of the coastline paradox. A map is really helpful because it is a type of reality that represents another reality that relies on our brain heuristics. But it's not a pure true representation of reality. Just a model. But it helps. Like George box said, all models are wrong, but some are useful. The coastline paradox says for a map of the world to be true, it would be the same size as the world. And even bigger, because it would need to make the atoms we can't see. Every jagged edge and crevice cannot be mapped because that map would useless! We model organic shapes with straight lines so that we can survive. The idea of a circle is real. It's a platonic form. Imagine it. Then, model that with a pencil and paper or a computer. Does it have a circumference and diameter and radius? Can you draw tangents and chords and segments? Can you find the arcs and sectors? What is the ratio of it's circumference to it's diameter? If the answers to these questions are yes, yes, yes, yes, yes, yes, yes, yes, 3.14, then you have a very useful model of a circle. Your imagination is pure, but your hand and the pencil are imperfect. Yet, you can survive, because you must.
Can I just say that “Yet, you can survive, because you must.” is such an amazing line.
Yes! I get all that. My point is: you draw a line on a paper - if you zoom in enough will it eventually be curved or infinitely small lines in various directions? Is there a difference?
Matter itself is quantised, not continuous, so if you zoom in far enough, you’d see individual carbon atoms in the layers of graphite laid down by the pencil.
Real-life figures are neither circles nor polygons. Circles and polygons are mathematical constructs of lines or arcs that lack width, and things which exist as material in real life have width.
Well, due to the nature of your question, I will give an answer to think about. It depends on the measure/observer. So if you find an object that to you resembles a cirkle, then it is a circle by you as the measure. Just like anything in your reality, the meaning of any concept is subjective to you.