What is a circle?

Frederick Williams · Joined: 05 Aug 2007 Posts: 20

It may sound like a silly question, but is a circle (in UK schools) a
disk or an arc?
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Archived from group: uk>education>maths

Brendan Murphy · Joined: 05 Aug 2007 Posts: 5

In message , Frederick
Williams writes
>It may sound like a silly question, but is a circle (in UK schools) a
>disk or an arc?

A circle is the locus of points from which the distance to the centre is
a given value, the radius.

An arc is any continuous portion of a circle.

The interior of the circle is called a disk.

All above information easily available from wikipedia.

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Brendan

Frank F. Matthews · Joined: 05 Aug 2007 Posts: 60

Brendan Murphy wrote:
> In message , Frederick
> Williams writes
>
>> It may sound like a silly question, but is a circle (in UK schools) a
>> disk or an arc?
>
>
> A circle is the locus of points from which the distance to the centre is
> a given value, the radius.
>
> An arc is any continuous portion of a circle.
>
> The interior of the circle is called a disk.
>
> All above information easily available from wikipedia.
>

Unless, of course, you prefer to define it as a closed planar curve with
constant curvature.

Frederick Williams · Joined: 05 Aug 2007 Posts: 20

Brendan Murphy wrote:
>
> In message , Frederick
> Williams writes
> >It may sound like a silly question, but is a circle (in UK schools) a
> >disk or an arc?
>
> A circle is the locus of points from which the distance to the centre is
> a given value, the radius.

So no teacher in a UK school would talk about the "area of a circle"?

> An arc is any continuous portion of a circle.

Er, no. Though it is the case that a connected subset of a circle is an
arc.

> The interior of the circle is called a disk.

As is the interior plus the interior's boundary.

> All above information easily available from wikipedia.

I'm more interested in what UK teachers mean when they talk about
circles, hence the words "in UK schools" in my question.

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Remove "antispam" and ".invalid" for e-mail address.
"He that giveth to the poor lendeth to the Lord, and shall be repaid,"
said Mrs Fairchild, hastily slipping a shilling into the poor woman's
hand.

Ken Pledger · Joined: 05 Aug 2007 Posts: 9

In article ,
Frederick Williams <"Frederick
Williams"@antispamhotmail.co.uk.invalid> wrote:

> It may sound like a silly question, but is a circle (in UK schools) a
> disk or an arc?

I suspect that U.K. school teachers, like most of us, are still
prone to perpetuate the ancient Greek ambivalence about this. Euclid
(probably following earlier writers) is not careful about it. In Book I
of the "Elements", Definition 15 says "A circle is a plane figure
contained by one line such that ....", meaning a circle is a disk in the
modern sense. But then in the proof of Proposition 1 he refers to "the
point C, in which the circles cut one another," meaning that the circles
are now curves in the modern sense.

Even now, I readily talk of "the area of a circle". Doesn't
everybody?

Ken Pledger.

Frederick Williams · Joined: 05 Aug 2007 Posts: 20

Ken Pledger wrote:
>
> In article ,
> Frederick Williams <"Frederick
> Williams"@antispamhotmail.co.uk.invalid> wrote:
>
> > It may sound like a silly question, but is a circle (in UK schools) a
> > disk or an arc?
>
> I suspect that U.K. school teachers, like most of us, are still
> prone to perpetuate the ancient Greek ambivalence about this. Euclid
> (probably following earlier writers) is not careful about it. In Book I
> of the "Elements", Definition 15 says "A circle is a plane figure
> contained by one line such that ....", meaning a circle is a disk in the
> modern sense. But then in the proof of Proposition 1 he refers to "the
> point C, in which the circles cut one another," meaning that the circles
> are now curves in the modern sense.
>
> Even now, I readily talk of "the area of a circle". Doesn't
> everybody?

Yes, probably!

Can you cast any light on "circumference"?

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hand.

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