If parabola means 1 bola, why is hyperbola 2 bolas?

[Karlheinz Fenstermacher]

If parabola means 1 bola, why is hyperbola 2 bolas?

Hyper means, to me, "many", not "two".

[Peter Moylan]

On 02/07/15 14:46, Karlheinz Fenstermacher wrote:
> If parabola means 1 bola, why is hyperbola 2 bolas?

This is what etymology online has to say.

hyperbola (n.)
1660s, from Latinized form of Greek hyperbole "extravagance,"
literally "a throwing beyond" (see hyperbole). Perhaps so called because
the inclination of the plane to the base of the cone exceeds that of the
side of the cone.

No bolas in sight. The entry for "parabola" is less clear, but there I
can see the "para" as referring to being parallel to the side of the cone.

> Hyper means, to me, "many", not "two".

Does hyper even have a count sense? To me it means "beyond"; it can
refer to something in a continuum, but probably not to a countable
number of things.

--
Peter Moylan http://www.pmoylan.org
Newcastle, NSW, Australia

[occam]

On 02/07/2015 06:46, Karlheinz Fenstermacher wrote:
> If parabola means 1 bola, why is hyperbola 2 bolas?
>
> Hyper means, to me, "many", not "two".
>

Who said it meant '2 bolas'? Lot 'a' bolax if you ask me.


On the other hand, could an 'e-bola' be a virus you catch on the net?

[Athel Cornish-Bowden]

On 2015-07-02 07:40:37 +0000, occam said:

> On 02/07/2015 06:46, Karlheinz Fenstermacher wrote:
>> If parabola means 1 bola, why is hyperbola 2 bolas?
>>
>> Hyper means, to me, "many", not "two".
>>
>
> Who said it meant '2 bolas'? Lot 'a' bolax if you ask me.

+1. Who indeed (apart from Karlheinz Fenstermacher) said that "parabola
means 1 bola"? Maybe it's a sort of joke, but if so it isn't very funny.

>
>
> On the other hand, could an 'e-bola' be a virus you catch on the net?

--
athel

[Peter Duncanson [BrE]]

As others have already said "parabola" doesn't mean "one bola".

Parabolas and hyperbolas are what are known as "conic sections". They
are the result of a "plane" (a flat surface) intersecting a "cone"
(strictly one cone with an inverted one on top with the points
together).

Mathematical descriptions with diagrams:
https://www.mathsisfun.com/geometry/conic-sections.html

https://en.wikipedia.org/wiki/Conic_section

http://mathworld.wolfram.com/ConicSection.html

Dictionary definitions:
http://www.oxforddictionaries.com/definition/english/parabola

http://www.oxforddictionaries.com/definition/english/hyperbola

http://www.yourdictionary.com/parabola

http://www.yourdictionary.com/hyperbola

--
Peter Duncanson, UK
(in alt.usage.english)

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 15:32:06 +1000, Peter Moylan wrote:

> No bolas in sight. The entry for "parabola" is less clear, but there I
> can see the "para" as referring to being parallel to the side of the
> cone.

Usually you guys are better than that, so, I didn't supply my
references.

A "bola" is certainly part of the word, where "bola" comes from
the Greek/Latin roots for the weapon of a string with two weights
on the end.

Even Wikipedia has this, so, I was pretty sure you guys would
get the reference (since most of you are smarter than I am).

A very nice question, for the answer of which you have to look into
ancient
Greek.
The verb from which "parabola" is derived is "paravallo" (the last letter
actually being an "omega", more or less pronounced as an o. The v of
ancient
Greek is changed to a b, as often done when a word is borrowed in English,
following the Erasmian pronunciation).

Now, the verb "paravallo" comes from the preposition "para", roughly
meaning "from", "near", "against" and the verb "ballo" . This last has a
spectrum of meanings, but the one relevant here is "to compare". All in
all,
"paravallo" means roughly "to place close for comparison" .

Naturally you will ask what is the relevance to mathematics. Here it is:
In Euclid's celebrated geometry text, the Elements, there is a geometric
construction that asks to construct a rectangle on a given side and of
given
area. The wording there uses the verb "paravallo" in the sense that it is
required to produce a rectangle comparable in area to a given one.
This became in antiquity the standard terminology. Later it was taken up
by Apollonius in his celebrated book of Conic sections (of which the
parabola is an example). There, when he proved the property (in modern
notation) y^2 = a*x, he wrote that the area y^2 is comparable (in the
above
sense) to the rectangle whose one side "a" is given. Thus he called the
curve he was studying "a parabola". This is the name that survived up to
our
time, replacing the old name " section of a rectangular cone" used by its
inventor Menaechmos.
When Apollonius studied the curve now called a hyperbola, he proved that
for a similar comparison of areas, one of the two "exceeded". In his
terminology, it was "hyper" (meaning "larger"). Thus he coined the term
"hyperbola", roughly meaning "the one that exceeds in comparison",
replacing
its old name " section of an obtuse angled cone".
For the ellipse, the same area "fell short", in other words, "was
elliptic"
.

You are, then, right. The ellipse could be called "hypobola", only that
this word has a different meaning in Greek, and so perhaps was not
preferred.

Once into linguistics, I take the opportunity to mention the etymology of
a few other words in English that come into my mind, whose root is the
same
verb "vallo" in Greek. The reason I am doing this, is because the average
person does not realize that these words are related.

- Anabolic: from the preposition "ana" and the verb "vallo" . Its original
meaning being "to lift, to elevate" , from which the anabolics that
athletes use to improve their strength.
- Diabolic: from the preposition "dia" and the verb "vallo". Its original
meaning being "to slander, to calumniate", from which the devilish act.
- Metabolic: from the preposition "meta" and the verb "vallo". Its
original
meaning being "to alter", from which the action of metabolism, i.e. change
of a situation.

That's all then. As you see, "bola" comes in parabolic, hyperbolic,
anabolic, diabolic, metabolic and elsewhere.


All the best from hot Crete.

Michael Lambrou.

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 09:40:37 +0200, occam wrote:

> Who said it meant '2 bolas'? Lot 'a' bolax if you ask me.

It's clear that para means one, and hyper means more than one.
The bola is the curve.

That's obvious, without even looking it up.

Since I'm only looking at the MATHEMATICAL usage, the meaning
is more important than the common (literary) usage.

What wasn't obvious (but I found out later) is why the "hyper"
since I had thought that a hyperbola indicated that there were
two curves which resulted from a slice of a conic section.

But the hyper doesn't indicate the number "two" (which is
the correct amount of curves in a hyperbola, but, that's
not what the "hyper" indicates.

I only found out why after I had posted this, so I apologize
for asking.

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 09:52:42 +0200, Athel Cornish-Bowden wrote:

> +1. Who indeed (apart from Karlheinz Fenstermacher) said that "parabola
> means 1 bola"? Maybe it's a sort of joke, but if so it isn't very funny.

It's as obvious as the nose on your face that the mathematical wording
is clear as day.

Para = one
Hyper = more than one
Bola = curve

Since parabolas are a single curve (resulting from a conic section),
and since hyperbolas result in two curves (similar slice, but no longer
parallel to the sides of the conic), I had (erroneously) *assumed*
that the "hyper" in hyperbola indicated the number "2" (as in the
number of curves which resulted).

However, I was wrong.
The "hyper" means exactly what it always means (which is "many" or
"more"), which in this case, is "more than 1 but not necessarily only 2".

That was the KEY epiphany for me to better understand the mathematical
meaning of the two words.

This article explains it more clearly than I can.
http://english.stackexchange.com/questions/175756/rhetoric-vs-mathematics-ellipsis-ellipse-parable-parabola-hyperbole-hyperbol

Specifically see this image:
http://upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Eccentricity.svg/500px-Eccentricity.svg.png

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 11:50:46 +0100, Peter Duncanson [BrE] wrote:

> As others have already said "parabola" doesn't mean "one bola".

Hi Peter,
You guys are all just making wild guesses (and you're all wrong).

I'm disappointed in the ng because it's clear as day the meaning:
para = 1
hyper = more
bola = curve

Any quick look will show what a "bola" is, where the Greek etymology
clearly shows parabola's genesis (the hyperbola has a more convoluted
genesis because it came much later in time).

The part that confused me initially was that I *knew* a hyperbola
was two curves while a parabola was a single curve (created by
conic section slices).

What I didn't realize was that the "hyper" and "para" referred to the
"eccentricity" of the ellipse, specifically:
The eccentricity of a parabola is 1.
The eccentricity of a hyperbola is greater than 1.

That's the reason for the "hyper", and it uses the standard meaning
of "more" (which in this case, is more than 1 but not necessarily 2).

I'm a little disapointed in this ng though, as this is basic stuff,
that, even though "I" didn't know any of it, when I found out after
I had seen the totally off-base responses, I looked it up further
and realized that you guys were all just guessing.

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 18:23:13 +0000, Karlheinz Fenstermacher wrote:

> The verb from which "parabola" is derived is "paravallo" (the last letter
> actually being an "omega", more or less pronounced as an o. The v of
> ancient
> Greek is changed to a b, as often done when a word is borrowed in English,
> following the Erasmian pronunciation).

oooooooops. In my haste to respond, I had forgotten to supply the reference.
Sorry about that.

Here is that reference, but, having belatedly found a BETTER reference,
I wouldn't suggest you bother to read the one below.
http://mathforum.org/kb/thread.jspa?forumID=129&threadID=355682&messageID=1088169

I suggest you read this reference, instead:
http://english.stackexchange.com/questions/175756/rhetoric-vs-mathematics-ellipsis-ellipse-parable-parabola-hyperbole-hyperbol

In the end, the correct answer to the question turned out to be that I had
wrongly *assumed* that para and hyper meant the *number* of "bolas" (i.e.,
the number of curves).

But that assumption was incorrect.

The "para" and "hyper" refer to the "eccentricity" of the bolas:
Namely, the eccentricity of a parabola is 1.
While the eccentricity of a hyperbola is greater than 1.

Says so right here:
http://upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Eccentricity.svg/500px-Eccentricity.svg.png

[Bertel Lund Hansen]

Peter Duncanson [BrE] skrev:

> Parabolas and hyperbolas are what are known as "conic
> sections". They are the result of a "plane" (a flat surface)
> intersecting a "cone" (strictly one cone with an inverted one
> on top with the points together).

I say "parabola" and "hyperbola" about just one curve. The
function for a parabola produces only one curve.

--
Bertel, Kolt, Denmark

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 22:06:48 +0200, Bertel Lund Hansen wrote:

> I say "parabola" and "hyperbola" about just one curve. The
> function for a parabola produces only one curve.

I apologize for my earlier remarks, as you guys were just
trying to help (I was too snippy).

A parabola, by its very nature is a single unbounded symmetric
curve as shown by the ANGLE of the conic section:
http://math2.org/math/algebra/conics.htm

The hyperbola, by its very nature, MUST contain two curves.
You don't always *see* the second curve; but it's there.
http://www.coolmath.com/algebra/25-conic-sections/04-introduction-hyperbolas-01

Since we knew from the start that para = 1, bola = eccentricity
(yes, I called it a curve before, but it's really an eccentricity),
I had *assumed* (and you know what that means) that hyper = 2.

But, hyper turns out to merely mean "more eccentricity" than
that of the parabola.
http://www.softschools.com/math/algebra_2/conic_sections/

It's all about the ANGLE of the cut across the cone:

A slice at zero degrees results in a circle.
A larger angle results in an ellipse.
A still larger angle causes the slide to be parallel to one side
of the cone, and that results in an unbounded parabola
(i.e., 1 ellipse).

If the angle gets larger still, the slice also cuts into the
mirror cone, always resulting in TWO curves, which are together
known as a hyperbola.

Knowing that all hyperbolas contained two mirror curves, and in
knowing that there was only a single parabola possible given any
particular cone, my mistake was in *assuming* the "hyper" meant
two.

In reality, the para did mean one, and the bola did indicate the
curved shape, but the hyper meant that there were many such
shapes once the slice was greater than parallel to the cones'
sides.

Lesson learned. Thanks.

[Richard Tobin]

In article <mn402j$udj$2...@news.mixmin.net>,

Karlheinz Fenstermacher <karlh...@cordiallynetwork.com> wrote:

>Para = one
>Hyper = more than one
>Bola = curve
>
>Since parabolas are a single curve (resulting from a conic section),
>and since hyperbolas result in two curves (similar slice, but no longer
>parallel to the sides of the conic), I had (erroneously) *assumed*
>that the "hyper" in hyperbola indicated the number "2" (as in the
>number of curves which resulted).

I could see you might think this if "para" had something to do with
"one", but it doesn't.

-- Richard

[Peter Duncanson [BrE]]

On Thu, 2 Jul 2015 18:31:49 +0000 (UTC), Karlheinz Fenstermacher
<karlh...@cordiallynetwork.com> wrote:

>On Thu, 02 Jul 2015 09:52:42 +0200, Athel Cornish-Bowden wrote:
>
>> +1. Who indeed (apart from Karlheinz Fenstermacher) said that "parabola
>> means 1 bola"? Maybe it's a sort of joke, but if so it isn't very funny.
>
>It's as obvious as the nose on your face that the mathematical wording
>is clear as day.
>
>Para = one
>Hyper = more than one
>Bola = curve
>
>Since parabolas are a single curve (resulting from a conic section),
>and since hyperbolas result in two curves (similar slice, but no longer
>parallel to the sides of the conic), I had (erroneously) *assumed*
>that the "hyper" in hyperbola indicated the number "2" (as in the
>number of curves which resulted).
>
>However, I was wrong.
>The "hyper" means exactly what it always means (which is "many" or
>"more"), which in this case, is "more than 1 but not necessarily only 2".
>
>That was the KEY epiphany for me to better understand the mathematical
>meaning of the two words.
>
>This article explains it more clearly than I can.
>http://english.stackexchange.com/questions/175756/rhetoric-vs-mathematics-ellipsis-ellipse-parable-parabola-hyperbole-hyperbol
>

Where does that say that "bola = curve"?

http://www.etymonline.com/index.php?term=parabola&allowed_in_frame=0

parabola (n.)
1570s, from Modern Latin parabola, from Greek parabole "parabola,
comparison, analogy; application" (see parable),

http://www.etymonline.com/index.php?term=parable&allowed_in_frame=0

parable (n.)
mid-13c., parabol, modern form from early 14c., "saying or story in
which something is expressed in terms of something else," from Old
French parable "parable, parabolic style in writing" (13c.), from
Latin parabola "comparison," from Greek parabole "a comparison,
parable," literally "a throwing beside," hence "a juxtaposition,"
from para- "alongside" (see para- (1)) + bole "a throwing, casting,
beam, ray," related to ballein "to throw" (see ballistics).

There's nothing specifically curved about "bola"/"bole".

>Specifically see this image:
>http://upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Eccentricity.svg/500px-Eccentricity.svg.png

[Peter Moylan]

On 03/07/15 04:23, Karlheinz Fenstermacher wrote:

> A very nice question, for the answer of which you have to look into
> ancient Greek. The verb from which "parabola" is derived is
> "paravallo" (the last letter actually being an "omega", more or less
> pronounced as an o. The v of ancient Greek is changed to a b, as
> often done when a word is borrowed in English, following the Erasmian
> pronunciation).

I see from your next message that you got this from a modern Greek. I
believe that he's wrong about the pronunciation.

Speaking about "the v of ancient Greek" is rubbish. Ancient Greek didn't
have a v. The reason why the beta (β) in words of ancient Greek origin
is pronounced as a "b" in English (and other languages) is that that's
the way the Greeks used to pronounce it. The pronunciation changed in
modern Greek.

For reasons that I've never understood, many Greeks today are absolutely
convinced that the ancient Greeks pronounced words the same way as
modern Greeks do. They didn't.

[Peter Moylan]

Or if "hyper" meant "more than one", but it doesn't.

Or if βολα meant curve, but it doesn't.

By the way, a hyperbola is only a single curve. It is true that the
equation describing a hyperbola has a second solution, but to get that
second solution as a conic section you have to balance a second cone on
top of the first, giving two hyperbolas, one from each cone.

For completeness, I should mention that an ellipse is one single curve.
If the above reasoning made sense, then an ellipse should consist of
less than one curve.

By the way, does anyone know whether the South American bola was known
in ancient Greece?

[Richard Tobin]

In article <mn52cg$nnd$1...@dont-email.me>,

Peter Moylan <pe...@pmoylan.org.invalid> wrote:

>By the way, a hyperbola is only a single curve. It is true that the
>equation describing a hyperbola has a second solution, but to get that
>second solution as a conic section you have to balance a second cone on
>top of the first, giving two hyperbolas, one from each cone.

When talking about conic sections, "cone" often means that double
cone, with the two parts sometimes referred to as "nappes".

One might also argue that a hyperbola is a single but discontinuous
curve.

-- Richard

[Karlheinz Fenstermacher]

On Fri, 03 Jul 2015 14:08:35 +1000, Peter Moylan wrote:

> Speaking about "the v of ancient Greek" is rubbish. Ancient Greek didn't
> have a v.

Interesting. I stand corrected. Thanks.

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 22:05:32 +0000, Richard Tobin wrote:

> I could see you might think this if "para" had something to do with
> "one", but it doesn't.

That's too bad because everything about a "parabola" is 1.

Look here for example:
http://www.mathsisfun.com/geometry/conic-sections.html

Verbatim:
"The curves can also be defined using a straight line and
a point (called the directrix and focus) When we measure
the distance from the focus to a point on the curve, and
perpendicularly from the directrix to that point the two
distances will always be the same ratio.

For a parabola, the ratio is 1, so the two distances are equal.
For a hyperbola, the ratio is greater than 1"

Notice how convenient it is to assume:
para indicates eccentricity = 1
hyper indicates eccentricity > 1
bola indicates the eccentricity

[Peter T. Daniels]

So "paranormal" is 'one normal'? "parapsychology" is 'one psychology'?
"paradox" is 'one dox'? "parallel" is 'one llel'?

[R H Draney]

"Peter T. Daniels" <gram...@verizon.net> wrote in
news:bd033279-4e1d-40af...@googlegroups.com:

One chute?...one keet?...one sol?...

(One university plus one university equals two diversity)....r

[Athel Cornish-Bowden]

On the other hand paramedic = no medic


--
athel

[Peter T. Daniels]

On Friday, July 3, 2015 at 12:09:37 PM UTC-4, R H Draney wrote:
> "Peter T. Daniels" <gram...@verizon.net> wrote in
> news:bd033279-4e1d-40af...@googlegroups.com:
> > On Friday, July 3, 2015 at 9:53:12 AM UTC-4, Karlheinz Fenstermacher
> > wrote:

> >> Notice how convenient it is to assume:
> >> para indicates eccentricity = 1
> >> hyper indicates eccentricity > 1
> >> bola indicates the eccentricity
> >
> > So "paranormal" is 'one normal'? "parapsychology" is 'one psychology'?
> > "paradox" is 'one dox'? "parallel" is 'one llel'?
>
> One chute?...one keet?...one sol?...

You missed one pet.

[Peter T. Daniels]

After you've been tended to by the paramedic, you might be a customer for
paratransit for a while.

[John Dawkins]

In article <XnsA4CC5CFFB7D0Fd...@74.209.136.92>,

R H Draney <dado...@spamcop.net> wrote:

> "Peter T. Daniels" <gram...@verizon.net> wrote in
> news:bd033279-4e1d-40af...@googlegroups.com:
>
> > On Friday, July 3, 2015 at 9:53:12 AM UTC-4, Karlheinz Fenstermacher
> > wrote:
> >
> >> Notice how convenient it is to assume:
> >> para indicates eccentricity = 1
> >> hyper indicates eccentricity > 1
> >> bola indicates the eccentricity
> >
> > So "paranormal" is 'one normal'? "parapsychology" is 'one psychology'?
> > "paradox" is 'one dox'? "parallel" is 'one llel'?
>
> One chute?...one keet?...one sol?...

And a paragon has but one side.

> (One university plus one university equals two diversity)....r

--
J.

[Oliver Cromm]

* Peter T. Daniels:

No, parapsychology is "one eccentric psychology". Sounds right.

--
Microsoft designed a user-friendly car:
instead of the oil, alternator, gas and engine
warning lights it has just one: "General Car Fault"

[Peter Duncanson [BrE]]

On Fri, 03 Jul 2015 10:50:33 -0700, John Dawkins <artfl...@aol.com>
wrote:

In some cases a paragon might be a paradigm.

[Karlheinz Fenstermacher]

On Fri, 03 Jul 2015 12:09:07 +0000, Richard Tobin wrote:

> When talking about conic sections, "cone" often means that double
> cone, with the two parts sometimes referred to as "nappes".
>
> One might also argue that a hyperbola is a single but discontinuous
> curve.

It does seem a little contrived that the nappes you speak of
are mirror image cones.

You only need the mirror image for the hyperbola, although one could
argue that the line and points might require the mirror image for
their full understanding.

[Karlheinz Fenstermacher]

On Fri, 03 Jul 2015 07:00:33 -0700, Peter T. Daniels wrote:

> So "paranormal" is 'one normal'? "parapsychology" is 'one psychology'?
> "paradox" is 'one dox'? "parallel" is 'one llel'?

I wasn't saying that.
I was agreeing that para doesn't mean "1".
At the same time, I was pointing out the "one'ness" of a parabola.

[Karlheinz Fenstermacher]

On Fri, 03 Jul 2015 16:08:29 +0000, R H Draney wrote:

> One chute?...one keet?...one sol?...
>
> (One university plus one university equals two diversity)....r

I guess I need to look up what 'para' means in these examples.

[Karlheinz Fenstermacher]

On Thu, 02 Jul 2015 23:39:46 +0100, Peter Duncanson [BrE] wrote:

> There's nothing specifically curved about "bola"/"bole".

Interestingly, if you look at a South American "bola":
https://en.wikipedia.org/wiki/Bolas

You'll see the origin of the *name" bola (i.e., two weights on a string)
is actually Latin and not South American (i.e., "ball").
http://dictionary.reference.com/browse/bola

Then, if you look at the definition of circle, ellipse, parabola, and
hyperbola, you'll see that they are mathematically modeled similarly
with the ratios of two segments, similar to how a string with two
balls on the ends could create the circle, ellipse, parabola, and
hyperbole, if you anchor the two points correspondingly.

Here is a discussion of how to draw conic sections with two pins,
a pencil, and a string (the two pins serving as the 'balls' in the
bola).
http://hollymath.com/2014/05/14/drawing-conic-sections-with-push-pin-and-string/
http://www.sciences.univ-nantes.fr/sites/genevieve_tulloue/conics/drawing/para_string.html

[Peter T. Daniels]

Thank you for your 20c worth!

[Robin Bignall]

Well (just to be serious for a moment), a paramedic is what you get here
if you dial 999, ask for an ambulance, and the 999 operator judges that
you're ill enough to be *assessed* for the ambulance service. If so,
the operator sends a paramedic, who then calls for an ambulance if
he/she considers it necessary after examining you. There are even
different sorts of "emergency" ambulances these days. Some of them rush
through traffic lights with blues and twos running at full blast, while
others are more sedate, depending on the patient's condition. It's all
quite different from 20 or 30 years ago, when, if you asked 999 for an
ambulance, you got one without quibble. I wonder if your pompiers are
better trained than our paramedics.
--
Robin Bignall
Herts, England (BrE)

[Peter T. Daniels]

Over Here we have EMTs, Emergency Medical Technicians, who come with an
ambulance (not _before_ an ambulance) and often are based at firehouses.

We don't have distinct emergency and "sedate" ambulances. In a non-emergency
transport situation, the ambulance can proceed without siren and flashers.
(But why would it? There always might be a serious condition that wasn't
immediately obvious to the EMTs.)

[tonyco...@gmail.com]

On Fri, 3 Jul 2015 20:09:41 -0700 (PDT), "Peter T. Daniels"
<gram...@verizon.net> wrote:

>On Friday, July 3, 2015 at 5:35:06 PM UTC-4, Robin Bignall wrote:
>> On Fri, 3 Jul 2015 18:19:09 +0200, Athel Cornish-Bowden
>> <athe...@yahoo.co.uk> wrote:
>
>> >On the other hand paramedic = no medic
>>
>> Well (just to be serious for a moment), a paramedic is what you get here
>> if you dial 999, ask for an ambulance, and the 999 operator judges that
>> you're ill enough to be *assessed* for the ambulance service. If so,
>> the operator sends a paramedic, who then calls for an ambulance if
>> he/she considers it necessary after examining you. There are even
>> different sorts of "emergency" ambulances these days. Some of them rush
>> through traffic lights with blues and twos running at full blast, while
>> others are more sedate, depending on the patient's condition. It's all
>> quite different from 20 or 30 years ago, when, if you asked 999 for an
>> ambulance, you got one without quibble. I wonder if your pompiers are
>> better trained than our paramedics.
>
>Over Here we have EMTs, Emergency Medical Technicians, who come with an
>ambulance (not _before_ an ambulance) and often are based at firehouses.

"Over here" is not "down here".

We have both EMTs and Paramedics. My son, who is a firefighter, is
certified as both. It varies by state, but firefighters are the first
responders to emergency ambulance calls (911 calls) in Florida. Every
fire station has what you would call an ambulance and either an EMT or
a paramedic on duty on every shift.

Most cities and county fire departments in Florida either require a
paramedic on each shift in each station or have a plan in place to
make this a requirement in the next few years.

The other type of ambulance - the ones operated by a hospital or a
private ambulance company - are used to transport patients. Patients
are transferred from one hospital to another, from jail to hospital,
from private homes to hospitals, and from care facilities to a
hospital.


--
Tony Cooper - Orlando, Florida

[Peter Moylan]

Tombola was named after an eccentric man called Tom.

My university used to have two professors who were brothers. One was the
head of psychology, the other the head of mathematics, so you didn't
often see them together. Their surname was Keats, so collectively they
were ....

[Peter Moylan]

On 04/07/15 06:12, Karlheinz Fenstermacher wrote:
> Here is a discussion of how to draw conic sections with two pins,
> a pencil, and a string (the two pins serving as the 'balls' in the
> bola).
> http://hollymath.com/2014/05/14/drawing-conic-sections-with-push-pin-and-string/
> http://www.sciences.univ-nantes.fr/sites/genevieve_tulloue/conics/drawing/para_string.html

<quote>
This creates a parabola – the conic section with one foci at infinity.
</quote>

What's the plural of foci?

[R H Draney]

Peter Moylan <pe...@pmoylan.org.invalid> wrote in
news:mn7rvc$9n7$1...@dont-email.me:

> <quote>
> This creates a parabola – the conic section with one foci at infinity.
> </quote>
>
> What's the plural of foci?

foc2....r

[Richard Tobin]

In article <mn7rvc$9n7$1...@dont-email.me>,

Peter Moylan <pe...@pmoylan.org.invalid> wrote:
>What's the plural of foci?

Hyperfoci of course.

-- Richard

[Athel Cornish-Bowden]

That would be a good start, but it's not the only thing you need to look up.


--
athel

[Athel Cornish-Bowden]

On 2015-07-03 20:12:12 +0000, Karlheinz Fenstermacher said:

> On Thu, 02 Jul 2015 23:39:46 +0100, Peter Duncanson [BrE] wrote:
>
>> There's nothing specifically curved about "bola"/"bole".
>
> Interestingly, if you look at a South American "bola":
> https://en.wikipedia.org/wiki/Bolas
>
> You'll see the origin of the *name" bola (i.e., two weights on a string)
> is actually Latin and not South American (i.e., "ball").
> http://dictionary.reference.com/browse/bola

That's not what the Dictionary of the Royal Spanish Academy says. It
says the word come from Provençal "bola", (which surprises me a
little), itself from Latin "bulla". It then gives more than half a
column of definitions, none of which resembles "curve". In any case,
what distinction are you trying to make between "South American" and
"Latin"? Latin (in modern forms, of course) is what educated people
speak in most of South America, all except Surinam and Guyana.

--
athel

[Athel Cornish-Bowden]

On 2015-07-04 05:47:41 +0000, Peter Moylan said:

> On 04/07/15 06:12, Karlheinz Fenstermacher wrote:
>> Here is a discussion of how to draw conic sections with two pins,
>> a pencil, and a string (the two pins serving as the 'balls' in the
>> bola).
>> http://hollymath.com/2014/05/14/drawing-conic-sections-with-push-pin-and-string/
>>
>> http://www.sciences.univ-nantes.fr/sites/genevieve_tulloue/conics/drawing/para_string.html
>>
>
> <quote>
> This creates a parabola – the conic section with one foci at infinity.
> </quote>
>
> What's the plural of foci?

hyperfoci


--
athel

[Athel Cornish-Bowden]

Oh dear. You got there before me.


--
athel

[Peter Duncanson [BrE]]

Here we have two physical types of ambulance operated by ambulance
services. There are the familiar emergency ambulances crewed by
paramedics and EMTs, and carrying life-saving and treatment equipment
and materials.

Emergency Ambulance:
http://www.nias.hscni.net/calling-999/who-will-treat-you/ambulance-crew/

There are also Patient Transport Ambulances. Those can be thought of as
specialised buses. They are used to transport people between their homes
and hospitals for outpatient treament, planned admission to hospital,
discharge from hospital, etc. The patients are seated.

Patient Transport Service (non-emergency):
http://www.nias.hscni.net/our-services/patient-transport-service/

A Patient Transport ambulance in Wales:
http://careersmatch.careerswales.com/media/resources/foto/joc1-a.jpg

We also have RRVs, Rapid Response Vehicles. An RRV is a car/SUV with a
single paramedic. It carries all the equipment that an emergency
ambulance does except for a means of transporting a recumbent patient to
hospital. RRVs can typically get to a patient faster than an ambulance
can and can start treating a patient sooner.

RRV:
http://www.nias.hscni.net/calling-999/who-will-treat-you/rapid-response-vehicle/

Before we had RRVs here in Northern Ireland we had paramedics on
motorbikes. They had the advantage of getting to patients faster but the
disadvantage of not being able to carry a full set of equipment. So a
paramedic on a motorbike might arrive promptly and discover that he
couldn't do what was necessary for the patient.


A few years ago one of my near neighbours (whom I didn't know)
collapsed. A paramedic in an RRV arrived. A little later another RRV
arrived. A standard emergency ambulance came quite a bit later, and
waited in case it was needed. The paramedics from the RRVs and the
ambulance worked on the patient but were unable to save her life. The
patient had not been in a suitable condition to be taken to hospital in
the ambulance. I heard a suggestion later that moving her would probably
have been instantly fatal.

Police arrived to record details of the death. Once those formalities
were complete the RRVs and ambulance departed.

The body of the deceased was later collected by an undertaker (funeral
director).

[Peter Duncanson [BrE]]

On Fri, 3 Jul 2015 20:01:22 +0000 (UTC), Karlheinz Fenstermacher
<karlh...@cordiallynetwork.com> wrote:

>On Fri, 03 Jul 2015 12:09:07 +0000, Richard Tobin wrote:
>
>> When talking about conic sections, "cone" often means that double
>> cone, with the two parts sometimes referred to as "nappes".
>>
>> One might also argue that a hyperbola is a single but discontinuous
>> curve.
>
>It does seem a little contrived that the nappes you speak of
>are mirror image cones.
>

To a mathematician that thing with mirror images is a "doubly infinite
cone, or double cone":
http://math.wikia.com/wiki/Cone

[which] is the union of any set of straight lines that pass through
a common apex point, and therefore extends symmetrically on both
sides of the apex.

The boundary of an infinite or doubly infinite cone is a conical
surface, and the intersection of a plane with this surface is a
conic section. For infinite cones, the word axis again usually
refers to the axis of rotational symmetry (if any). 1/2 of a double
cone is called a nappe.

http://math.wikia.com/wiki/Conic_section

The possible conic sections are:

circle
ellipse
parabola
hyperbola
point (degenerate)
two intersecting lines (degenerate)
two parallel lines (degenerate)
nothing (degenerate)

Parabolas and hyperbolas go to infinity. The cones of which they are
sections must also be infinite, not truncated.

[Peter T. Daniels]

This seems like a devaluation of the term "ambulance." We just call those
"paratransit" vans. They're little buses for people of limited mobility but
no particularly acute medical condition requiring attention from, say, a
nurse. They're usually also equipped with a wheelchair lift.

> We also have RRVs, Rapid Response Vehicles. An RRV is a car/SUV with a
> single paramedic. It carries all the equipment that an emergency
> ambulance does except for a means of transporting a recumbent patient to
> hospital. RRVs can typically get to a patient faster than an ambulance
> can and can start treating a patient sooner.

Again, at least several minutes of delay.

[Peter Duncanson [BrE]]

On Sat, 4 Jul 2015 10:27:34 -0700 (PDT), "Peter T. Daniels"

They seem to be called "ambulances" because they are operated by the
ambulance services and are used for conveying people with various
medical conditions.

> We just call those
>"paratransit" vans. They're little buses for people of limited mobility but
>no particularly acute medical condition requiring attention from, say, a
>nurse. They're usually also equipped with a wheelchair lift.
>
>> We also have RRVs, Rapid Response Vehicles. An RRV is a car/SUV with a
>> single paramedic. It carries all the equipment that an emergency
>> ambulance does except for a means of transporting a recumbent patient to
>> hospital. RRVs can typically get to a patient faster than an ambulance
>> can and can start treating a patient sooner.
>
>Again, at least several minutes of delay.

Of course. The shorter the delay the better.

When, or if, Star Trek style teleportation becomes available it will be
possible to get a paramedic with equipment to a patient in just a few
seconds.

[Charles Hope]

In article <520f6478-52d9-46e9...@googlegroups.com>, Peter

in a copy of Punch from the early 1940s, there is a cartoon of two soldiers
trying to get a lift from a passing vehicle. The driver says "This an
ambulance - from the latin 'ambulo' - to walk. No lifts."

[Peter T. Daniels]

Why wouldn't they be called firetrucks, if they operate (like ours) out of
firehouses and in conjunction with fire rescue squads? One name for every
type of vehicle operated by one service is quite strange.

> > We just call those
> >"paratransit" vans. They're little buses for people of limited mobility but
> >no particularly acute medical condition requiring attention from, say, a
> >nurse. They're usually also equipped with a wheelchair lift.
> >> We also have RRVs, Rapid Response Vehicles. An RRV is a car/SUV with a
> >> single paramedic. It carries all the equipment that an emergency
> >> ambulance does except for a means of transporting a recumbent patient to
> >> hospital. RRVs can typically get to a patient faster than an ambulance
> >> can and can start treating a patient sooner.
> >Again, at least several minutes of delay.
>
> Of course. The shorter the delay the better.
>
> When, or if, Star Trek style teleportation becomes available it will be
> possible to get a paramedic with equipment to a patient in just a few
> seconds.

And hopefully (s)he'll arrive with a fully equipped ambulance and not what
little can be carried on a motorcycle or car. SUVs are notoriously unmaneuverable
so unsuited for rapid travel, especially on the cowpaths that pass for streets
in your cities.

[Peter T. Daniels]

Of course not. It's low to the ground.

Oh, look, AHD5 knows why it's called that. It's from Fr. _hôpital ambulant_
'mobile hospital'.

[Peter Moylan]

The "two parallel lines" case is doubly degenerate, in that it requires
a cone whose apex is at infinity. Or, in common language, a cylinder.

[R H Draney]

Peter Moylan <pe...@pmoylan.org.invalid> wrote in news:mna339$k0e$1
@dont-email.me:

Someone has screwed up...I can't find any way of cutting a cone
(consisting of both nappes) with a plane to produce either "two parallel
lines" or "nothing", and the list of conic sections above doesn't
include the "one straight line" degenerate case....r

[Peter T. Daniels]

If the plane is tangent to the surface of the cone, don't you get a straight line?

You could get "nothing" either if the cone isn't infinite (so the plane simply
doesn't touch it, or if the diameter of its base is 0.

[R H Draney]

"Peter T. Daniels" <gram...@verizon.net> wrote in
news:d3a59b1d-da03-4fb4...@googlegroups.com:

Yes, and that's the missing case I mentioned....

> You could get "nothing" either if the cone isn't infinite (so the
> plane simply doesn't touch it, or if the diameter of its base is 0.

The cone is infinite by definition, and therefore doesn't have a
"base"...if the cone itself is degenerate, it's a straight line, and the
plane then either does not intersect that line (which would indeed result
in "nothing" as the conic section) or it does (which makes the section a
single point)....r

[Peter Moylan]

You can also get a single point with a non-degenerate cone, of course. I
think of that case as an ellipse or circle with zero radius.

[Peter T. Daniels]

That's inevitable: it happens where the tips of the two nappes meet. Which
point, AHD5 s.v. "nappe" tells me, is the vertex of the cone.

And "nappe" mostly means 'sheet of water flowing over a dam or spillway', from
Fr. for 'tablecloth'. Someone was being rather imaginative the day they applied
that word to a cone-half.

[Janet]

In article <1sbgpa168khbtaupp...@4ax.com>,
ma...@peterduncanson.net says...

> When, or if, Star Trek style teleportation becomes available it will be
> possible to get a paramedic with equipment to a patient in just a few
> seconds.

No need; just teleport the patient to the sickbay on the Enterprise.

Janet.

[Karlheinz Fenstermacher]

On Sat, 04 Jul 2015 13:28:34 +0100, Peter Duncanson [BrE] wrote:

> Parabolas and hyperbolas go to infinity.

What's interesting as they approach infinity is that the parabola becomes
essentially two parallel lines on either side of the Y axis, while the
hyperbola becomes the shape of an X.

This is because the parabola (y=x^2) moves more in the y direction for
every step in the x direction, so it's like spreading your arms at out in
a U-shape above your head and then clasping your palms together as y
approaches infinity.

The hyperbola is different [y=sqrt(1+x2)] because as y approaches
infinity, x approaches y, such that eventually x almost equals y, so for
every step of x, you have an equal step of y. Hence a parabola approaches
a huge X (or a V in the positive y quadrants).

So, notice this, if I have the words to describe it.

1. Stand up and make a circle with your arms.
2. Then lengthen that circle until it's an ellipse.
3. Then open that ellipse until it's a parabola (a U'ish shape).
4. Then open further to the all the angles of the hyperbola.
5. Then open even further until your arms are akimbo to form a line.

Notice the "eccentricity" is what changes there:
1. The eccentricity of the circle is 0.
2. The eccentricity of the ellipse is greater than 0 but less than 1.
3. The eccentricity of the parabola is exactly 1.
4. The eccentricity of the hyperbola is greater than 1.
5. The eccentricity of the line is infinity.

What's interesting is that there is only one circle and only one
parabola, but many ellipses and even more hyperbolas.

Since gravity is curving of space, just as a conic section is, it's no
wonder that it's rare to see perfect circular orbits or parabolic
trajectories as objects follow the conic sections of gravity. There is
only one eccentricity for each.

That's why there are plenty of elliptical orbits and hyperbolic
trajectories because almost every object moving straight in a line along
the cone of gravity will be curved by the conic distortion of space.

Just don't ask me what the latus rectum has to do with it all.

[Karlheinz Fenstermacher]

On Sun, 05 Jul 2015 06:59:53 -0700, Peter T. Daniels wrote:

> And "nappe" mostly means 'sheet of water flowing over a dam or
> spillway', from Fr. for 'tablecloth'. Someone was being rather
> imaginative the day they applied that word to a cone-half.

And the "latus rectum" is the all-important line through a focus that is
parallel to the directrix.

http://mathworld.wolfram.com/LatusRectum.html

latus === side
rectum === straight

[Peter Moylan]

On 07/07/15 16:02, Karlheinz Fenstermacher wrote:
> On Sat, 04 Jul 2015 13:28:34 +0100, Peter Duncanson [BrE] wrote:
>
>> Parabolas and hyperbolas go to infinity.
>
> What's interesting as they approach infinity is that the parabola becomes
> essentially two parallel lines on either side of the Y axis, while the
> hyperbola becomes the shape of an X.
>
> This is because the parabola (y=x^2) moves more in the y direction for
> every step in the x direction, so it's like spreading your arms at out in
> a U-shape above your head and then clasping your palms together as y
> approaches infinity.

You're trying to describe two "parallel" lines that are getting further
and further apart. Not very parallel.

Try plotting it on log-log paper and you'll get a very different answer.

[Richard Yates]

On Tue, 7 Jul 2015 06:05:30 +0000 (UTC), Karlheinz Fenstermacher
<karlh...@cordiallynetwork.com> wrote:

>On Sun, 05 Jul 2015 06:59:53 -0700, Peter T. Daniels wrote:
>
>> And "nappe" mostly means 'sheet of water flowing over a dam or
>> spillway', from Fr. for 'tablecloth'. Someone was being rather
>> imaginative the day they applied that word to a cone-half.
>
>And the "latus rectum" is the all-important line through a focus that is
>parallel to the directrix.

For a split second I read that as "flatus rectum." Never mind.

[Peter T. Daniels]

On Tuesday, July 7, 2015 at 2:02:07 AM UTC-4, Karlheinz Fenstermacher wrote:

> 5. Then open even further until your arms are akimbo to form a line.

How does putting your hands on your hips make your arms "form a line"?

[Karlheinz Fenstermacher]

On Tue, 07 Jul 2015 05:32:18 -0700, Richard Yates wrote:

> For a split second I read that as "flatus rectum." Never mind.

I'm surprised that "rectum" means "straight".
I would have thought hole or tube.
But I would have been wrong.

[Karlheinz Fenstermacher]

On Tue, 07 Jul 2015 20:27:40 +1000, Peter Moylan wrote:

> You're trying to describe two "parallel" lines that are getting further
> and further apart. Not very parallel.
>
> Try plotting it on log-log paper and you'll get a very different answer.

Actually, you're making a very common mistake, if, you are talking about
a parabola, which I "think" you were.

Parabolas are not asymptotic.

Just type y=x^2 into this graphic calculator, and then zoom out as far as
you feel comfortable.
https://www.desmos.com/calculator

Do you see that the ends of the parabola approach parallel lines?

In fact linear, quadratic and cubic functions do not have asymptotes
http://www.dummies.com/how-to/content/how-to-find-the-equation-of-
asymptotes.html
https://www.physicsforums.com/threads/what-is-an-asymptote-and-why-doesnt-
parabola-have-one.188318/

Just think about the equation y=x^2 and try to visualize it, out at the
very ends of space. Do you see it yet? Keep looking? Think. Think. Notice
that y increments faster than x?

Therefore, it can't possibly do what you describe. It just *looks* (to
you) that it does what you describe. The two lines do *not* get further
apart; and, in fact, they actually do the opposite of what you think.

The two lines are getting closer and closer and closer together, until
they are almost parallel.

But, don't feel badly. Many people make the same mistake. They don't
carry with them enough paper to draw the parabola out far enough to see
its true character.

[Karlheinz Fenstermacher]

On Tue, 07 Jul 2015 20:27:40 +1000, Peter Moylan wrote:

> Try plotting it on log-log paper and you'll get a very different answer.

BTW, log paper *changes* the shape of the curve, so, you need to plot, as
I noted, on linear paper, such as plotting y=x^2 on this calculator:

https://www.desmos.com/calculator

The arms of a parabola approach parallel lines, while the hyperbola does
what you think it does (but maybe not).

Most people *think* a hyperbola gets wider and wider and wider, and, it
does, but it actually approaches an X shape because, unlike a quadratic
it *does* have a denominator, which makes it asymptotic.

Try graphing, for example, this top half of a hyperbola y=sqrt(1+x^2),
for example. You should get a V shape (i.e., the top half of an X), as x
approaches infinity.

One thing to note is that the flyby scheduled for Pluto will 'zing' the
satellite into a hyperbolic orbit, never to return, but to approach a
straight line at infinity due to the conic curvature of space by the
gravity of Pluto.

Since the satellite is moving quickly, it won't be captured by Pluto's
conic curvature of space, so it won't become an ellipse (a circle would
be nearly impossible since there is only 1 circle possible, and a
parabola is just as unlikely.

[Karlheinz Fenstermacher]

On Tue, 07 Jul 2015 06:27:08 -0700, Peter T. Daniels wrote:

> How does putting your hands on your hips make your arms "form a line"?

Aha! Now it is my turn to be wrong!
Thank you!

You are correct. I was wrong.

I just looked up the meaning of akimbo, which is:

1375-1425; late Middle English in kenebowe
Old Norse *i keng boginn bent into a crook
(i in, keng accusative of kengr hook,
boginn past participle of bjūga to bend)
http://dictionary.reference.com/browse/akimbo?s=t

So what one-word term do I use to describe the arm position from U-ish:
http://s1185.photobucket.com/user/JohnDuke1/media/jesus_bigger-sm.jpg.html
throughout the range, to finally becoming outstretched?
http://inspiringthealtruisticmoment.com/blog/wp-content/uploads/2010/12/arms_stretched.jpg

[Peter T. Daniels]

Now you're going in the corRECT diRECTion.

[Peter T. Daniels]

If they were getting "closer and closer and closer," they would make an
ellipse (not parallel lines).

> But, don't feel badly. Many people make the same mistake. They don't
> carry with them enough paper to draw the parabola out far enough to see
> its true character.

Geometers don't generally rely on paper and pencil to draw their conclusions.

[Peter Moylan]

I left all of this intact because I didn't know where to snip. I am
flabbergasted by the enormity of your misconceptions.

Try taking my suggestion of using log-log paper for your parabola.
You'll see that both x and y increase without bound. You'll also see
that the graph is asymptotic to a straight line.

At my school quadratics were covered in year 9. (In fact the mathematics
teacher got me to teach that topic, to give me some teaching
experience.) You must surely have gone that far in school.

But perhaps you're just trolling.

[Richard Tobin]

In article <mnfq79$rj7$2...@news.mixmin.net>,

Karlheinz Fenstermacher <karlh...@cordiallynetwork.com> wrote:

>And the "latus rectum" is the all-important line through a focus that is
>parallel to the directrix.

More precisely, the segment of that line between its intersections with
the curve.

-- Richard

[Athel Cornish-Bowden]

On 2015-07-08 06:22:06 +0200, Peter Moylan <pe...@pmoylan.org.invalid> said:

> On 08/07/15 02:19, Karlheinz Fenstermacher wrote:

>> [ ... ]

> But perhaps you're just trolling.

I think that interpretation has become inevitable.



--
athel

[Athel Cornish-Bowden]

On 2015-07-07 18:33:50 +0200, Karlheinz Fenstermacher

<karlh...@cordiallynetwork.com> said:

> On Tue, 07 Jul 2015 06:27:08 -0700, Peter T. Daniels wrote:
>
>> How does putting your hands on your hips make your arms "form a line"?
>
> Aha! Now it is my turn to be wrong!

You've had so many such turns that I wonder why you single this one out.


--
athel