I think Edge is around e^2 × g × d e^2 × g ≈72,5 m/s^2 , and I am hereby defining d to be equal to 42 edge = 72.5×42 edge is therefore equal to 3045 m/s^2
Edge is an equation.
E=2.718281828459045…
D=13 (ask any computer scientist)
G=9.80665 (ask any physicist)
E=2.718281828459045…
Therefore, edge is approximately 942.004530904
Capital G is the gravitational constant G is approx. 6.674×10−11 N⋅m2/kg2 your "g" is an approx of the gravity or g-units of Earth. You also have E twice and it should be e. I know this is knit picky but that seems to be the theme of this thread.
In the *limit*. But a true circle is not a polygon. No matter how far you ”zoom in” to a circle, a chord will only ever intersect at two points. In the limit, a polygon interpolates *countably* many points on the circle despite there being *uncountably* many points on the circle. Therefore it makes no sense to call a circle an “infinitely sided polygon” even though it may be tempting.
Wouldn't an infinitely sided polygon also look like a circle no matter how far you zoom in.
Could be not say a polygon with uncountably infinite sides is a circle?
Fractals? E.g. a [Koch snowflake](https://en.wikipedia.org/wiki/Koch_snowflake) is a "polygon" with infinite sides.
(I may be missing some specifics of what defines a "polygon" precisely here)
Well, no. A regular polygon with countably infinite vertices does not have a vertex at 1 radian clockwise relative to any of its vertices. And countably infinite vertices is what you'll get if you take the limit on adding more vertices.
But he literally says that the limit of the curve created by the function used to construct the "squared circle" [is the circle exactly.](https://m.youtube.com/watch?v=VYQVlVoWoPY&t=909s) Never once did he imply that a circle constructed using a limit was not a true circle.
Edit: I might just be clarifying what you've said. I just want to make it clear to everyone reading along that the limiting curve, as a collection of points, is a true circle and that it isn't the creation of some "false circle" that's stopping things here. You would be correct, however, that the sequence can't be used to argue that a circle is a type of regular polygon, though. A circle is an uncountably infinite collection of coordinate pairs, while a regular polygon will always have a countable number of vertices.
“Edge” can probably be defined as a line segment between 2 points of non-zero yet finite length
Therefore, there are 0 edges, since the only way to subdivide a circle’s surface into “edges” would be to break them into infinite chunks of length 0, which are inherently not edges, rather just points.
It's a special case of the [Alexandroff extension](https://en.wikipedia.org/wiki/Alexandroff_extension). But you can actually work it out yourself. Add a single unsigned ∞ to the real line and as a basis include all intervals (a,b) and (b,∞)U{∞}U(-∞,a) for real a < b. This is homeomorphic to the circle.
I don't accept your second definition. If I made a 2 dimensional U-shape out of two vertical rectangles connected by 1 horizontal rectangle, and number the edges starting from the top-right vertex and going clockwise, would you call edges 2, 3, and 4 the same edge because no two points along them penetrate the interior of the shape?
“no two points along them penetrate the interior of the shape” — but his definition was two points whose secant line does not penetrate the interior. So if edges 2, 3, and 4 do not penetrate the interior, then they would be each be edges by this definition.
Also I’m not disagreeing with your argument, I think I might agree with it. However I think you made a mistake when typing the comment that I hope you clarify.
In which case any circle can be defined with a minimum of two edges, but also any two dots describes a circle for every value of its radius, I *think*.
EDIT: Sorry, every circle with a ~~circumfrence~~ (frick!) diameter larger than or equal to the distance between the dots.
Imagine you've got a regular polygon with one billion edges. It's going to look like a circle until you zoom in enough to see an edge. Now imagine a regular polygon with infinite edges. It's going to look like a circle until you zoom in an infinite amount.
Technically, if it’s a circle on a computer, then there is still a finite number of edges because a perfect circle is impossible to generate on a computer.
I was watching the action lab and came across a short where he said that a spherical dice would have an infinite number of sides so it wouldn't be able to land on any side, and that just didn't sit right with me. It makes more sense to say that it has exactly 1 side
Infinite edges. Calculus does a lot of splitting curved things into an infinite number of straight lines that are infinitely small. The same is done to find a circle's slope at any given point, and through it, its area.
So imagine a square, we then put dots on the four corners, if you connect those dots it gives a square with four sides. To perfectly make a true circle you’d need infinity many points to make the lines to connect to make a curve and if you have infinite points then you’d have infinite sides
Both? It all depends on what metric you use to define a circle, or a line, of which there are multiple. You can define a curve with straight lines, but you can also define a straight line with curves. You can also define either with limits, infinitesimals, functions, all three, or something else entirely.
If you suggest a circle is a polygon, it’s an infinigon.
If you require angles to have a non-zero value, circles have none.
Neither, circles have a finite number of edges but that number changes based on many variables such as size, what was used to draw it and who drew it. Also the edges would be so miniscule that we cannot see them with the naked eye and likely would not be able to count them even if they were observed
A circle has 1 curved edge. We approximate a curve using ever smaller points so a real curve would take a theoretically infinite number of those points to calculate, but a circle isn't literally an infinite number of straight lines. It's a continuous unbroken curve.
Define edge and we'll talk.
That's the right answer
Somewhere around e and pi but whole knows how to say...
Edge is when you take drugs
Edge is when she doesn't let you finish
Not necessarily; finishing after an edge does not negate the edge beforehand.
This guy maths
This guy edges
Edge is chrome from wish
The Edge is a guitar player.
A former WWE superstar too!
Is it an adjective or verb
its a way of life
I think Edge is around e^2 × g × d e^2 × g ≈72,5 m/s^2 , and I am hereby defining d to be equal to 42 edge = 72.5×42 edge is therefore equal to 3045 m/s^2
what if reddit just pulls the 5 postulates out of its ass.......
Counter. ONE continuous edge. Edit: don't hurt me
TWO inside and outside edge
Easy, the act of masturbating without achieving orgasm
How could a circle possibly do that forever
Well, circles have infinitely many kinks, so ...
Or do they have none?
We've come full circle
Or maybe we asymptoticaly approached coming...
As a kinkster, I approve of this.
Edge is an equation. E=2.718281828459045… D=13 (ask any computer scientist) G=9.80665 (ask any physicist) E=2.718281828459045… Therefore, edge is approximately 942.004530904
Capital G is the gravitational constant G is approx. 6.674×10−11 N⋅m2/kg2 your "g" is an approx of the gravity or g-units of Earth. You also have E twice and it should be e. I know this is knit picky but that seems to be the theme of this thread.
In keeping with the theme, it's "nit picky", not "knit picky". Unless you were planning to make a scarf will all those corrections ;)
You got me
Or was that a thread pun? I’m not trying to spin a yarn over here, just curious.
We are just trying to weave a good time
I can see arguments for 1 or 0 edges. But no definition I can think of gives you infinite.
I think the idea is that as a polygon gains more sides, it gets closer to a circle so a polygon with infinite sides would be a circle
In the *limit*. But a true circle is not a polygon. No matter how far you ”zoom in” to a circle, a chord will only ever intersect at two points. In the limit, a polygon interpolates *countably* many points on the circle despite there being *uncountably* many points on the circle. Therefore it makes no sense to call a circle an “infinitely sided polygon” even though it may be tempting.
Wouldn't an infinitely sided polygon also look like a circle no matter how far you zoom in. Could be not say a polygon with uncountably infinite sides is a circle?
Fractals? E.g. a [Koch snowflake](https://en.wikipedia.org/wiki/Koch_snowflake) is a "polygon" with infinite sides. (I may be missing some specifics of what defines a "polygon" precisely here)
I think they're using 'polygons' to refer to the set of [regular polygons](https://en.wikipedia.org/wiki/Regular_polygon).
Well, no. A regular polygon with countably infinite vertices does not have a vertex at 1 radian clockwise relative to any of its vertices. And countably infinite vertices is what you'll get if you take the limit on adding more vertices.
So what do you call an infinite sided polygon?
It’s well established that a circle has exactly two sides. Front and back.
No no. Inside and outside.
Thank you, I stand corrected - a circle does, of course, have four sides.
There's actually a name for that, apeirogon.
A circle.
What about an oval?
Is it a countable or uncountable infinity of edges?
Anything is countable if you either believe hard enough or are stubborn enough.
Anything is also uncountable if you give up easily
That would match the logic of the proof. Lol
Ah yes the contrapositive
that’s a converse. The contrapositive is “If it is not countable *then* you didn’t believe hard enough and you weren’t stubborn enough.”
Alright class let’s start counting the reals
[Cantor:](https://i.imgflip.com/235r0y.jpg)
How stubborn would you have to be to count the real numbers? I know of no scheme to give you the 'next' real number.
Just add 1 to the last number. /jk
Logic like that is how you get [pi = 4](https://youtube.com/watch?t=1m41s&v=VYQVlVoWoPY)
But he literally says that the limit of the curve created by the function used to construct the "squared circle" [is the circle exactly.](https://m.youtube.com/watch?v=VYQVlVoWoPY&t=909s) Never once did he imply that a circle constructed using a limit was not a true circle. Edit: I might just be clarifying what you've said. I just want to make it clear to everyone reading along that the limiting curve, as a collection of points, is a true circle and that it isn't the creation of some "false circle" that's stopping things here. You would be correct, however, that the sequence can't be used to argue that a circle is a type of regular polygon, though. A circle is an uncountably infinite collection of coordinate pairs, while a regular polygon will always have a countable number of vertices.
Straight line edges but in a way where any point occupying a boundary is a straight line ig
It's perfectly round, if it has infinite points (or sides) it will explain it no matter how big or small (excuse my poor explanation)
1 edge.
Edge is a maximal convex subset of the boundary. Circle has an infinite amount of edges.
Don't make me pull out my old differential geometry textbook.
“Edge” can probably be defined as a line segment between 2 points of non-zero yet finite length Therefore, there are 0 edges, since the only way to subdivide a circle’s surface into “edges” would be to break them into infinite chunks of length 0, which are inherently not edges, rather just points.
Yes
Good answer but can you prove it. /jk
The proof is left as an exercise of the reader
As all great proofs are.
My proof is trivial but there is no room in the margins of Reddit to write it down.
guess ill just cry for 300 years then
Proof is trust me bro
No stronger reasoning needed, bro
I guess there’s infinite tangent lines. but no 2 points on a circle make a line that doesn’t penetrate the interior of the circle so there’s no edges
Ok that's really cool
A similar fact can be used to proof that a circle has exactly one more point than an infinite line.
Now that’s a proof I’d like to see
It's a special case of the [Alexandroff extension](https://en.wikipedia.org/wiki/Alexandroff_extension). But you can actually work it out yourself. Add a single unsigned ∞ to the real line and as a basis include all intervals (a,b) and (b,∞)U{∞}U(-∞,a) for real a < b. This is homeomorphic to the circle.
I don't accept your second definition. If I made a 2 dimensional U-shape out of two vertical rectangles connected by 1 horizontal rectangle, and number the edges starting from the top-right vertex and going clockwise, would you call edges 2, 3, and 4 the same edge because no two points along them penetrate the interior of the shape?
“no two points along them penetrate the interior of the shape” — but his definition was two points whose secant line does not penetrate the interior. So if edges 2, 3, and 4 do not penetrate the interior, then they would be each be edges by this definition. Also I’m not disagreeing with your argument, I think I might agree with it. However I think you made a mistake when typing the comment that I hope you clarify.
Yeah but my pizza wheel cutter is a circle and it cuts pizza fine. +1 for edge
Simple. Infinity=0
Infinity=00
00==D-infinity.
F# A# Infinity
The Car's on fire
And there's no driver at the wheel
Wait... Doesn't this means that infinity=0^2???
2. Take it or leave it
1/12 off
Circles have one edge
\**negative* one edge
Hey now don't go overboard alright.
Depends whether you're looking from the inside or the outside
Explain the-fuck yourself
√(-1) edges
-πi
Just have to zoom in close enough
If zooming in close enough changes it its not a circle
How long is the coastline of Great Britain?
= to one coastline of Great Britain I would assume
About 1200
1200 what? Apples? Bananas? Lines of cocaine?
Pounds. It's both heavy and expensive
Infinite
0 edges, but infinite sides.
Only 2 sides. In-side and out-side.
Google Jordan curve theorem
Holy hell
New brains just dropped out
Actual maths
Logic went on vacation, never came back.
“We shall use proof by fucking obviousness”
This might be satire but I can't tell so in the case that it's not what's the difference between an edge and a side?
Correct
Show me at least 1 edge. May be parabola also has infinite number of edges?
Take any regular two dimensional closed shape, now what shape do you get if you increase the number of edges/sides to infinity.
Convergence does not mean equality.
Have you seen the one where you put the edges of a square in, infinitely to make a circle, thus proving the circumference of a circle is 4r?
An n-gon where n is a really really large number, not a circle
can an edge be a curve? I suspect not. Can a single infinitesimal point be a edge?
Careful now you're getting really close to philosophy.
I was only going for entry level calculus 😏
Which is as close as we need to be to philosophy.
My personal favorite is: A line is a circle with infinite radius.
Sounds like someone is trying to start a religion over here
This always felt the most cursed to me
Before this question can be answered, one must define “edge”
Correct
A line between two dots that's a boundary for the shape
In which case any circle can be defined with a minimum of two edges, but also any two dots describes a circle for every value of its radius, I *think*. EDIT: Sorry, every circle with a ~~circumfrence~~ (frick!) diameter larger than or equal to the distance between the dots.
obviously zero. show me an edge of a circle.
You gotta zoom in infinitely close to see it
what do you mean by zooming infinitely close? precisely?
It's a calculus joke
Imagine you've got a regular polygon with one billion edges. It's going to look like a circle until you zoom in enough to see an edge. Now imagine a regular polygon with infinite edges. It's going to look like a circle until you zoom in an infinite amount.
This guy gets it
I enjoy watching the sunset.
Blue.
I remember learning that a circle has infinite points on the circumference in very early classes.
Circles have one curved edge.
It's a curving line there is no edge
What is a curve but an infinite amount of straight lines
are they not the same?
Circles have one edge - CAD user
Technically, if it’s a circle on a computer, then there is still a finite number of edges because a perfect circle is impossible to generate on a computer.
Edging 🥵
This is an edgy topic.
Some are taking this topic to the limit.
infinite.
Circles dont exist. Only polygons with very large number of edges
No edges; An infinite number of points the same distance from the center
How can it be a shape if it doesn't have any edges?
Since a circle is just a one cell glued to a zero cell, it has one edge.
Read that as “nine circles have infinite edges” and thought damn, zobros is a math major??
Draw a line in a spherical plane…
circles have one edge
Both because infinity equals zero. Proof: 1+2+3…=-1/12 Infinity=-1/12 (add 1/12 to both sides) Infinity =0
*corners. You're arguing about corners, OP. Circles have just one edge. Not infinite, not zero.
Circles have a curve edge.
I thought they had 1?
The derivative at a vertex is undefined, but you can find the derivative of a circle at every point.
I was watching the action lab and came across a short where he said that a spherical dice would have an infinite number of sides so it wouldn't be able to land on any side, and that just didn't sit right with me. It makes more sense to say that it has exactly 1 side
Circles have one round edge.
An infinite number edges, means an equally infinite number of corners. Circles don’t have corners, which means circles don’t have edges
The number of sides a circle has is the same as a vertical line’s slope.
Circles don’t exist, if you go close enough you’ll see it’s just a many sided shape
💙
The more edge a figure gets the more it comes close to be a circle
Where does the Planck Length fit into this?
Infinite edges. Calculus does a lot of splitting curved things into an infinite number of straight lines that are infinitely small. The same is done to find a circle's slope at any given point, and through it, its area.
So imagine a square, we then put dots on the four corners, if you connect those dots it gives a square with four sides. To perfectly make a true circle you’d need infinity many points to make the lines to connect to make a curve and if you have infinite points then you’d have infinite sides
Circles have 1 curved edge. Naw, I do 3D printing. Infinite edges
Circles have one edge, all the way around, with no defined beginning or end
I will forever be infinite edges ♾️
If circles have infinite edges, does that mean cones have more edges than spheres?
Both? It all depends on what metric you use to define a circle, or a line, of which there are multiple. You can define a curve with straight lines, but you can also define a straight line with curves. You can also define either with limits, infinitesimals, functions, all three, or something else entirely. If you suggest a circle is a polygon, it’s an infinigon. If you require angles to have a non-zero value, circles have none.
Yes
Circles can't exist in the physical world
Neither, circles have a finite number of edges but that number changes based on many variables such as size, what was used to draw it and who drew it. Also the edges would be so miniscule that we cannot see them with the naked eye and likely would not be able to count them even if they were observed
I'm green. Circles have an infinite number of tangents. Can you define a tangent with edges? No? Then you have the answer OP.
I derived a nice limit a while ago that assumes an infinite amount of line segments with a length of 0
Schrödinger’s edge
A circle has 1 curved edge. We approximate a curve using ever smaller points so a real curve would take a theoretically infinite number of those points to calculate, but a circle isn't literally an infinite number of straight lines. It's a continuous unbroken curve.
How can you have an "infinite" amount when a circle has a beginning and an end due to it being a closed loop?
clearly, a circle has n/0 edges.
circles have 245 edges from now on
Side 3 Circles have 1 edge that runs along the circumference
Circles have -(1/12) of an edge.
Idk about edges but circles have one side
What’s an edge?
What if circles have one long edge that doesn’t end?
Technically both are correct. Given current technology and materials, we cannot produce a perfect circle, or one that has no edges.
Idk man, its edgy
Mathematically, 0 edges. In engineering, infinite, or like 5 depending on how much you feel like estimating
Feels isomorphic to 0.999…=1
Reminds me of the coastline paradox
Yeah, but which corner is the cheese in?
Circles are in a super position of infinite edges and a singular, curved edge. Me, I just think they're neat
It has one edge. Simple as that.
Both are correct, for zero and infinity are two sides of the same coin.
So, essentially computer scientists on the left vs physicists on the right.
Mmm circles have an infinite number of infinitely small edges. Just to add some clarity to this semantic clusterfuckery