From Newsgroup: uk.media.radio.archers

What's the volume of a pizza of radius z and thickness a?
--
J. P. Gilliver. UMRA: 1960/<1985 MB++G()ALIS-Ch++(p)Ar++T+H+Sh0!:`)DNAf
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From Newsgroup: uk.media.radio.archers

J. P. Gilliver wrote:

What's the volume of a pizza of radius z and thickness a?

;-)

Chris
--
Chris J Dixon Nottingham
'48/33 M B+ G++ A L(-) I S-- CH0(--)(p) Ar- T+ H0 ?Q
chris@cdixon.me.uk @ChrisJDixon1
Plant amazing Acers.
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From Newsgroup: uk.media.radio.archers

On 06/12/2025 22:08, J. P. Gilliver wrote:

What's the volume of a pizza of radius z and thickness a?

Assuming a circular pizza.

Cut the pizza into say eight equal segments. Lay them out side by side,
top to tail and you end up with a very crude wobbly rectangle.

Now divide each segment in to two equal segments, again, lay them side
by side and top to tail. The rectangle looks a bit better.

Repeat this procedure, stopping only when you have an infinite number of segments. You now have a perfect rectangle. The circumference of the
pizza was 2*pi*z, so the top and bottom of your rectangle both measure
pi*z. The height of the rectangle is the original radius, z. So the
area is pi*z*z. The thickness hasn't changed, so the volume of the
rectangle (which must be the same as the volume of the pizza is z*a*pi*z.
--
Cheers
Clive

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From Newsgroup: uk.media.radio.archers

On 10/12/2025 12:51, Simon Simple wrote:

On 06/12/2025 22:08, J. P. Gilliver wrote:

What's the volume of a pizza of radius z and thickness a?

Assuming a circular pizza.

Cut the pizza into say eight equal segments.-a Lay them out side by side, top to tail and you end up with a very crude wobbly rectangle.

Now divide each segment in to two equal segments, again, lay them side
by side and top to tail.-a The rectangle looks a bit better.

Repeat this procedure, stopping only when you have an infinite number of segments.-a You now have a perfect rectangle.-a The circumference of the pizza was 2*pi*z, so the top and bottom of your rectangle both measure pi*z.-a The height of the rectangle is the original radius, z.-a So the
area is pi*z*z.-a The thickness hasn't changed, so the volume of the rectangle (which must be the same as the volume of the pizza is z*a*pi*z.

I think it might be simpler to drop the pizza into a blender with
graduated markings on the side and give it a jolly good whizz. Then just
read the volume off the side.
--
Ric
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From Newsgroup: uk.media.radio.archers

On 10/12/2025 12:51, Simon Simple wrote:

On 06/12/2025 22:08, J. P. Gilliver wrote:

What's the volume of a pizza of radius z and thickness a?

Assuming a circular pizza.

Cut the pizza into say eight equal segments.-a Lay them out side by side, top to tail and you end up with a very crude wobbly rectangle.

Now divide each segment in to two equal segments, again, lay them side
by side and top to tail.-a The rectangle looks a bit better.

Repeat this procedure, stopping only when you have an infinite number of segments.-a You now have a perfect rectangle.-a The circumference of the pizza was 2*pi*z, so the top and bottom of your rectangle both measure pi*z.-a The height of the rectangle is the original radius, z.-a So the
area is pi*z*z.-a The thickness hasn't changed, so the volume of the rectangle (which must be the same as the volume of the pizza is z*a*pi*z.

Must I stop when I have an infinite number of segments?
How about a Baker's Infinity?
--
Sam Plusnet
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From Newsgroup: uk.media.radio.archers

On 10/12/2025 19:01, Sam Plusnet wrote:

On 10/12/2025 12:51, Simon Simple wrote:

On 06/12/2025 22:08, J. P. Gilliver wrote:

What's the volume of a pizza of radius z and thickness a?

Assuming a circular pizza.

Cut the pizza into say eight equal segments.-a Lay them out side by
side, top to tail and you end up with a very crude wobbly rectangle.

Now divide each segment in to two equal segments, again, lay them side
by side and top to tail.-a The rectangle looks a bit better.

Repeat this procedure, stopping only when you have an infinite number
of segments.-a You now have a perfect rectangle.-a The circumference of
the pizza was 2*pi*z, so the top and bottom of your rectangle both
measure pi*z.-a The height of the rectangle is the original radius, z.
So the area is pi*z*z.-a The thickness hasn't changed, so the volume of
the rectangle (which must be the same as the volume of the pizza is
z*a*pi*z.

Must I stop when I have an infinite number of segments?
How about a Baker's Infinity?

And which sort of infinity, countable or uncountable?

john
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From Newsgroup: uk.media.radio.archers

On 10/12/2025 19:01, Sam Plusnet wrote:

On 10/12/2025 12:51, Simon Simple wrote:

On 06/12/2025 22:08, J. P. Gilliver wrote:

What's the volume of a pizza of radius z and thickness a?

Assuming a circular pizza.

Cut the pizza into say eight equal segments.-a Lay them out side by
side, top to tail and you end up with a very crude wobbly rectangle.

Now divide each segment in to two equal segments, again, lay them side
by side and top to tail.-a The rectangle looks a bit better.

Repeat this procedure, stopping only when you have an infinite number
of segments.-a You now have a perfect rectangle.-a The circumference of
the pizza was 2*pi*z, so the top and bottom of your rectangle both
measure pi*z.-a The height of the rectangle is the original radius, z.
So the area is pi*z*z.-a The thickness hasn't changed, so the volume of
the rectangle (which must be the same as the volume of the pizza is
z*a*pi*z.

Must I stop when I have an infinite number of segments?
How about a Baker's Infinity?

Let us know when you get there and we'll put it to the vote. 13 good men
and true.

For me, this whole 'infinity' business just shows how maths can diverge
from reality. Nothing is or can be infinite. If anything were, then by comparison everything else would be effectively zero. Speed of light?
Pah, standing still.

Speaking of zero, that don't exist neither. Singularity my arse. Very
small, very heavy, fairy nuff, but there ain't no zero size, infinite
density which just happens to change. Prove me wrong.
--
Cheers
Clive


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