The Internet forum that shall not be named has a question on how many dimensions a circle has.

A reply (from someone who claims to have a PhD in maths) says the answer is one.

That seems strange to me. I had always envisaged the dimensionality of a shape as being the minimum number of dimensions that you would need to draw it, so a straight line is 1D, but any curve or collection of line segments is 2D.

Am I wrong, and if so, why?

The circle exists in a two-dimensional plane. A point on a particular circle can be specified with a single real parameter.

If you count a dot as a circle is that one dimension

dv said:

The circle exists in a two-dimensional plane. A point on a particular circle can be specified with a single real parameter.

That’s what the PhD answer said (in many more words).

Still seems strange to me, but I’m no mathemagician.

The Rev Dodgson said:

The Internet forum that shall not be named has a question on how many dimensions a circle has.

A reply (from someone who claims to have a PhD in maths) says the answer is one.

That seems strange to me. I had always envisaged the dimensionality of a shape as being the minimum number of dimensions that you would need to draw it, so a straight line is 1D, but any curve or collection of line segments is 2D.

Am I wrong, and if so, why?

Segments are arcs?

Cymek said:

If you count a dot as a circle is that one dimension

what if it is a raised dot ie; a hemisphere?

Cymek said:

If you count a dot as a circle is that one dimension

Why would you count a dot as a circle?

A dot would have zero dimensions according to my (quite likely wrong) system.

roughbarked said:

The Rev Dodgson said:

The Internet forum that shall not be named has a question on how many dimensions a circle has.

A reply (from someone who claims to have a PhD in maths) says the answer is one.

That seems strange to me. I had always envisaged the dimensionality of a shape as being the minimum number of dimensions that you would need to draw it, so a straight line is 1D, but any curve or collection of line segments is 2D.

Am I wrong, and if so, why?

Segments are arcs?

No, lines of finite length (is what I meant).

roughbarked said:

Cymek said:

If you count a dot as a circle is that one dimension

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

The Rev Dodgson said:

roughbarked said:

Cymek said:

If you count a dot as a circle is that one dimension

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

Like a full stop sized dot or smaller round in shape

The Rev Dodgson said:

roughbarked said:

Cymek said:

If you count a dot as a circle is that one dimension

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

Watchmakers may think differently. Consider an endstone or a drop of oil.

Cymek said:

The Rev Dodgson said:

roughbarked said:

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

Like a full stop sized dot or smaller round in shape

Depends how far down the slide rule goes. Some of uus use micrometers to measure such circles.

An infinitesimal dot has no shape and is not a circle. A very small non-infinitessimal circular dot has the same topological properties of a large circle.

Cymek said:

The Rev Dodgson said:

roughbarked said:

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

Like a full stop sized dot or smaller round in shape

Then the size is irrelevant. A filled circle (or disc) of any size is (I believe) 2D.

The Rev Dodgson said:

Cymek said:

The Rev Dodgson said:

I took a “dot” to be a “point” i.e. having zero size.

Like a full stop sized dot or smaller round in shape

Then the size is irrelevant. A filled circle (or disc) of any size is (I believe) 2D.

correct. :)

https://www.sliderulemuseum.com/PocketWatch.htm

dv said:

An infinitesimal dot has no shape and is not a circle. A very small non-infinitessimal circular dot has the same topological properties of a large circle.

?

Doesn’t being filled in the middle make a difference?

dv said:

An infinitesimal dot has no shape and is not a circle. A very small non-infinitessimal circular dot has the same topological properties of a large circle.

Man this bloke’s good.

The Rev Dodgson said:

dv said:

An infinitesimal dot has no shape and is not a circle. A very small non-infinitessimal circular dot has the same topological properties of a large circle.

?

Doesn’t being filled in the middle make a difference?

Not as much as a circumference.

The Rev Dodgson said:

roughbarked said:

Cymek said:

If you count a dot as a circle is that one dimension

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

Are you looking for a singularity? (I’m currently reading about zero and infinity and my head is not understanding a lot of it)

dv said:

An infinitesimal dot has no shape and is not a circle. A very small non-infinitessimal circular dot has the same topological properties of a large circle.

this is the state of affairs I have always been lead to believe is the correct interpretation of dimensionality.

buffy said:

The Rev Dodgson said:

roughbarked said:

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

Are you looking for a singularity? (I’m currently reading about zero and infinity and my head is not understanding a lot of it)

the “singularity” at the centre of a blackhole would have zero dimensions. by definition.

buffy said:

The Rev Dodgson said:

roughbarked said:

what if it is a raised dot ie; a hemisphere?

I took a “dot” to be a “point” i.e. having zero size.

Are you looking for a singularity? (I’m currently reading about zero and infinity and my head is not understanding a lot of it)

well don’t try and divide by it.

JudgeMental said:

dv said:

An infinitesimal dot has no shape and is not a circle. A very small non-infinitessimal circular dot has the same topological properties of a large circle.

this is the state of affairs I have always been lead to believe is the correct interpretation of dimensionality.

That’s an explanation that is easier to grok but I’d probably expect that from a printer.

I knew a printer who used to make up letters with dot sized words.

JudgeMental said:

buffy said:

The Rev Dodgson said:

I took a “dot” to be a “point” i.e. having zero size.

Are you looking for a singularity? (I’m currently reading about zero and infinity and my head is not understanding a lot of it)

the “singularity” at the centre of a blackhole would have zero dimensions. by definition.

Bear in mind that the definition is purely mathematical. Many (probably most) physicists don’t assume there’s a physical equivalent.

by circle they mean the thing we often describe as circumference right

Bubblecar said:

JudgeMental said:

buffy said:

Are you looking for a singularity? (I’m currently reading about zero and infinity and my head is not understanding a lot of it)

the “singularity” at the centre of a blackhole would have zero dimensions. by definition.

Bear in mind that the definition is purely mathematical. Many (probably most) physicists don’t assume there’s a physical equivalent.

yes and why i used “ “.

JudgeMental said:

Bubblecar said:

JudgeMental said:

the “singularity” at the centre of a blackhole would have zero dimensions. by definition.

Bear in mind that the definition is purely mathematical. Many (probably most) physicists don’t assume there’s a physical equivalent.

yes and why i used “ “.

Sensible :)

SCIENCE said:

by circle they mean the thing we often describe as circumference right

or as The Worm, Ouroboros

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

sorry we mean {(x, y): x^2 + y^2 = r^2}

as opposed to {(x, y): x^2 + y^2 < r^2} or {(x, y): x^2 + y^2 <= r^2}

dv said:

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

Haven’t we been here?

roughbarked said:

dv said:

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

Haven’t we been here?

we’ve been having a ball

SCIENCE said:

roughbarked said:

dv said:

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

Haven’t we been here?

we’ve been having a ball

Kind of a circular argument

dv said:

SCIENCE said:

roughbarked said:

Haven’t we been here?

we’ve been having a ball

Kind of a circular argument

now that does have a familiar ring to it

SCIENCE said:

roughbarked said:

dv said:

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

Haven’t we been here?

we’ve been having a ball

no. that’s a sphere?

dv said:

SCIENCE said:

roughbarked said:

Haven’t we been here?

we’ve been having a ball

Kind of a circular argument

That would be that oro .. orobo um that worm thingy.

roughbarked said:

dv said:

SCIENCE said:

we’ve been having a ball

Kind of a circular argument

That would be that oro .. orobo um that worm thingy.

Orrible

dv said:

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

“coughs”

Didn’t someone else make that same point before him?

The Rev Dodgson said:

dv said:

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

“coughs”

Didn’t someone else make that same point before him?

A rotating circle describes a wheel.

SCIENCE said:

dv said:

SCIENCE said:

we’ve been having a ball

Kind of a circular argument

now that does have a familiar ring to it

How many circular arguments can you fit on the head of a pin?

The Rev Dodgson said:

dv said:

SCIENCE raises a good point.

A circular closed curve can be parameterised by a single real number.

A circular disc is 2 dimensional.

“coughs”

Didn’t someone else make that same point before him?

It goes round and round
round and round
all the live long day

O how the wheel becomes it

dv said:

O how the wheel becomes it

is this the common wheel?

dv said:

O how the wheel becomes it

What goes up

JudgeMental said:

dv said:

O how the wheel becomes it

is this the common wheel?

does that have a beat rate like a balance wheel?

roughbarked said:

JudgeMental said:

dv said:

O how the wheel becomes it

is this the common wheel?

does that have a beat rate like a balance wheel?

Is it Flat round and concentric?

JudgeMental said:

dv said:

O how the wheel becomes it

is this the common wheel?

We’ll see

dv said:

JudgeMental said:

dv said:

O how the wheel becomes it

is this the common wheel?

We’ll see

That was the rotund approach?

roughbarked said:

dv said:

JudgeMental said:

is this the common wheel?

We’ll see

That was the rotund approach?

it was revolutionary for its time

The Rev Dodgson said:

The Internet forum that shall not be named has a question on how many dimensions a circle has.

A reply (from someone who claims to have a PhD in maths) says the answer is one.

That seems strange to me. I had always envisaged the dimensionality of a shape as being the minimum number of dimensions that you would need to draw it, so a straight line is 1D, but any curve or collection of line segments is 2D.

Am I wrong, and if so, why?

LOL. Brilliant question.

In Euclidean (flat) space a circle is two dimensions.
In Riemannian (curved) space, a circle is one dimension.
In topology, a circle is one dimension.

Why this matters.
This matters because to add coordinates to a topological object in n dimensions, you have to jump up to n+1 dimensions. This is called an embedding.