 Hyacinthos

 Restricted Group,
 3 members
Synthetic/Analytic Geometry
Expand Messages
 0 Attachment
 In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@...> wrote:>
I ask this question after reading "Geometric Construction of Reciprocal
> All,
>
> What are the differences between synthetic and analytic geometry?
>
> Sincerely, Jeff
>
Conjugations" by Keith Dean and Floor van Lamoen: see
Keith Dean and Floor van Lamoen, Geometric Construction of Reciprocal
Conjugations, pp.115120.
http://forumgeom.fau.edu/FG2001volume1/FG200116index.html
Proposition 1. under 2.1 has a proof but 2.2 construction does not have
a proof ... The answer seems analytic not synthetic in nature.
I want to understand this analysis better...
Friendly, Jeff 0 Attachment
Dear Jeff
I don't know the answer to your question. I think it's only a matter of
taste. In bygone days, there was a war between synthetic and analytic
geometers. I think now it's over!
As for KeithFloor's paper , I think their construction interesting but too
intricate.
To get the map:
f:(x:y:z) > (u/x:v/y:w/z)
I think, it's better to use f = g.s
where s:(x:y:z) > (1/x:1/y:1/z) is the isotomic conjugation
and g:(x:y:z) > (u.x:v.y:w.z) is the collineation with A, B, C
(vertices of the reference triengle) as fixed points, sending G(1:1:1) to
P(u:v:w).
Of course, we must have a simple construction for g. If you are interested,
I can send you a Cabrifile of this construction.
Friendly
François
[Nontext portions of this message have been removed] 0 Attachment
 In Hyacinthos@yahoogroups.com, "Francois Rideau"
<francois.rideau@...> wrote:>
matter of
> Dear Jeff
> I don't know the answer to your question. I think it's only a
> taste. In bygone days, there was a war between synthetic and
analytic
> geometers. I think now it's over!
but too
> As for KeithFloor's paper , I think their construction interesting
> intricate.
(1:1:1) to
> To get the map:
> f:(x:y:z) > (u/x:v/y:w/z)
> I think, it's better to use f = g.s
> where s:(x:y:z) > (1/x:1/y:1/z) is the isotomic conjugation
> and g:(x:y:z) > (u.x:v.y:w.z) is the collineation with A, B, C
> (vertices of the reference triengle) as fixed points, sending G
> P(u:v:w).
interested,
> Of course, we must have a simple construction for g. If you are
> I can send you a Cabrifile of this construction.
Thank you Francois once again,
> Friendly
> François
>
I wish to write A", B" and C" as Keith and Floor describe them in
some kind of a closed, easily understood and plausible, form. That
is, I wish to be able to duplicate it using basic math (examples
would provide a great deal of help.)
Sincerely, Jeff
P.S. I don't have Cabri so any examples you provide are all the more
appreciated. 0 Attachment
Stated in another way:
I want the coordinates for A" and cyclic given arbitrary P and Q.
More over, I want a proof of the result.
Sincerely, Jeff
 In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@...> wrote:
>
>  In Hyacinthos@yahoogroups.com, "Francois Rideau"
> <francois.rideau@> wrote:
> >
> > Dear Jeff
> > I don't know the answer to your question. I think it's only a
> matter of
> > taste. In bygone days, there was a war between synthetic and
> analytic
> > geometers. I think now it's over!
> > As for KeithFloor's paper , I think their construction
interesting
> but too
> > intricate.
> > To get the map:
> > f:(x:y:z) > (u/x:v/y:w/z)
> > I think, it's better to use f = g.s
> > where s:(x:y:z) > (1/x:1/y:1/z) is the isotomic conjugation
> > and g:(x:y:z) > (u.x:v.y:w.z) is the collineation with A, B,
C
> > (vertices of the reference triengle) as fixed points, sending G
> (1:1:1) to
> > P(u:v:w).
> > Of course, we must have a simple construction for g. If you are
> interested,
> > I can send you a Cabrifile of this construction.
> > Friendly
> > François
> >
>
>
> Thank you Francois once again,
>
> I wish to write A", B" and C" as Keith and Floor describe them in
> some kind of a closed, easily understood and plausible, form. That
> is, I wish to be able to duplicate it using basic math (examples
> would provide a great deal of help.)
>
>
> Sincerely, Jeff
>
> P.S. I don't have Cabri so any examples you provide are all the
more
> appreciated.
> 0 Attachment
Dear Jeff,
Francois is right but I want
to add my opinion.
I think that in our days synthetic in
mathematics is the effort, as in
computer scientists, for the use of known
compound tools, for detail encryption.
It is called in computer language
information hiding or data encapsulation.
Best regards
Nikos Dergiades
[FR]> > I don't know the answer to your question. I think
___________________________________________________________
> it's only a
> matter of
> > taste.
Χρησιμοποιείτε Yahoo!;
Βαρεθήκατε τα ενοχλητικά μηνύματα (spam); Το Yahoo! Mail
διαθέτει την καλύτερη δυνατή προστασία κατά των ενοχλητικών
μηνυμάτων http://login.yahoo.com/config/mail?.intl=gr 0 Attachment
Dear Nikolaos,
I have no idea what you are talking about...Could you please
elaborate?
Sincerely, Jeff
 In Hyacinthos@yahoogroups.com, Nikolaos Dergiades
<ndergiades@...> wrote:>
> Dear Jeff,
> Francois is right but I want
> to add my opinion.
>
> I think that in our days synthetic in
> mathematics is the effort, as in
> computer scientists, for the use of known
> compound tools, for detail encryption.
> It is called in computer language
> information hiding or data encapsulation.
>
> Best regards
> Nikos Dergiades
>
>
> [FR]
> > > I don't know the answer to your question. I think
> > it's only a
> > matter of
> > > taste.
>
>
>
>
>
>
>
> ___________________________________________________________
> ×ñçóéìïðïéåßôå Yahoo!;
> ÂáñåèÞêáôå ôá åíï÷ëçôéêÜ ìçíýìáôá (spam); Ôï Yahoo! Mail
> äéáèÝôåé ôçí êáëýôåñç äõíáôÞ ðñïóôáóßá êáôÜ ôùí åíï÷ëçôéêþí
> ìçíõìÜôùí http://login.yahoo.com/config/mail?.intl=gr
> 0 Attachment
By the way,
Francois is wrong, he is ignoring, I think, some very important
priciples.
Sincerely, Jeff
 In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@...> wrote:
>
> Dear Nikolaos,
>
> I have no idea what you are talking about...Could you please
> elaborate?
>
> Sincerely, Jeff
>
>  In Hyacinthos@yahoogroups.com, Nikolaos Dergiades
> <ndergiades@> wrote:
> >
> > Dear Jeff,
> > Francois is right but I want
> > to add my opinion.
> >
> > I think that in our days synthetic in
> > mathematics is the effort, as in
> > computer scientists, for the use of known
> > compound tools, for detail encryption.
> > It is called in computer language
> > information hiding or data encapsulation.
> >
> > Best regards
> > Nikos Dergiades
> >
> >
> > [FR]
> > > > I don't know the answer to your question. I think
> > > it's only a
> > > matter of
> > > > taste.
> >
> >
> >
> >
> >
> >
> >
> > ___________________________________________________________
> > ×ñçóéìïðïéåßôå Yahoo!;
> > ÂáñåèÞêáôå ôá åíï÷ëçôéêÜ ìçíýìáôá (spam); Ôï Yahoo! Mail
> > äéáèÝôåé ôçí êáëýôåñç äõíáôÞ ðñïóôáóßá êáôÜ ôùí åíï÷ëçôéêþí
> > ìçíõìÜôùí http://login.yahoo.com/config/mail?.intl=gr
> >
> 0 Attachment
I mean't "principles!"
 In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@...> wrote:
>
> By the way,
>
> Francois is wrong, he is ignoring, I think, some very important
> priciples.
>
> Sincerely, Jeff
>
>
>  In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@> wrote:
> >
> > Dear Nikolaos,
> >
> > I have no idea what you are talking about...Could you please
> > elaborate?
> >
> > Sincerely, Jeff
> >
> >  In Hyacinthos@yahoogroups.com, Nikolaos Dergiades
> > <ndergiades@> wrote:
> > >
> > > Dear Jeff,
> > > Francois is right but I want
> > > to add my opinion.
> > >
> > > I think that in our days synthetic in
> > > mathematics is the effort, as in
> > > computer scientists, for the use of known
> > > compound tools, for detail encryption.
> > > It is called in computer language
> > > information hiding or data encapsulation.
> > >
> > > Best regards
> > > Nikos Dergiades
> > >
> > >
> > > [FR]
> > > > > I don't know the answer to your question. I think
> > > > it's only a
> > > > matter of
> > > > > taste.
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > > ___________________________________________________________
> > > ×ñçóéìïðïéåßôå Yahoo!;
> > > ÂáñåèÞêáôå ôá åíï÷ëçôéêÜ ìçíýìáôá (spam); Ôï Yahoo! Mail
> > > äéáèÝôåé ôçí êáëýôåñç äõíáôÞ ðñïóôáóßá êáôÜ ôùí åíï÷ëçôéêþí
> > > ìçíõìÜôùí http://login.yahoo.com/config/mail?.intl=gr
> > >
> >
> 0 Attachment
Good grief! Forget the spelling... let's get on with Triangle
Geometry!
jeff
 In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@...> wrote:
>
>
> I mean't "principles!"
>
>
>  In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@> wrote:
> >
> > By the way,
> >
> > Francois is wrong, he is ignoring, I think, some very important
> > priciples.
> >
> > Sincerely, Jeff
> >
> >
> >  In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@> wrote:
> > >
> > > Dear Nikolaos,
> > >
> > > I have no idea what you are talking about...Could you please
> > > elaborate?
> > >
> > > Sincerely, Jeff
> > >
> > >  In Hyacinthos@yahoogroups.com, Nikolaos Dergiades
> > > <ndergiades@> wrote:
> > > >
> > > > Dear Jeff,
> > > > Francois is right but I want
> > > > to add my opinion.
> > > >
> > > > I think that in our days synthetic in
> > > > mathematics is the effort, as in
> > > > computer scientists, for the use of known
> > > > compound tools, for detail encryption.
> > > > It is called in computer language
> > > > information hiding or data encapsulation.
> > > >
> > > > Best regards
> > > > Nikos Dergiades
> > > >
> > > >
> > > > [FR]
> > > > > > I don't know the answer to your question. I think
> > > > > it's only a
> > > > > matter of
> > > > > > taste.
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > ___________________________________________________________
> > > > ×ñçóéìïðïéåßôå Yahoo!;
> > > > ÂáñåèÞêáôå ôá åíï÷ëçôéêÜ ìçíýìáôá (spam); Ôï Yahoo! Mail
> > > > äéáèÝôåé ôçí êáëýôåñç äõíáôÞ ðñïóôáóßá êáôÜ ôùí åíï÷ëçôéêþí
> > > > ìçíõìÜôùí http://login.yahoo.com/config/mail?.intl=gr
> > > >
> > >
> >
> 0 Attachment
Dear Jeff
Given P(x:y:z), to compute barycentrics of A", B", C" is easy but rather
tedious and I am too lazy to do it.
But I don't understand your question.
Do you want a detailed computation of these barycentrics or another proof
that AP and AA" are isogonal lines?
I think KeithFloor's proof of this fact is not very satisfying for they
don't use signed distances (normal coordinates).
If you call A1, B1, C1 to be symmetric points of P wrt sides BC, CA, AB,
then A"B"C" is the medial triangle of A1B1C1 and lines AA", BB", CC" are
respectively the perpendicular bissectors of the sides B1C1, C1A1, A1B1, so
it is known they are through Q isogonal conjugate of P wrt ABC.
Friendy
François
[Nontext portions of this message have been removed] 0 Attachment
Dear Nikolaos
Your opinion is very interesting.
Now we have computers, we can get rid of compasses and rules and we can
simulate all geometries on our screens.
Of course it will depend upon the software.
For example you can do affine geometry without compass using only rules,
translations, dilations and parallels or projective geometry using only
rules or circular geometry using only circles and so one.
Friendly
François
[Nontext portions of this message have been removed] 0 Attachment
Dear Jeff,
[JB]
http://forumgeom.fau.edu/FG2001volume1/FG200116index.html
Proposition 1. under 2.1 has a proof but 2.2 construction does not have
a proof ... The answer seems analytic not synthetic in nature.
[JB]
I want the coordinates for A" and cyclic given arbitrary P and Q.
More over, I want a proof of the result.
In Proposition 1, the point A'' is the reflection of P{p,q,r} in the
midpoint of B'C', which ends up as
A'' = {b^2 c^2 p + b^2 r SB + c^2 q SC, b^2 r SA, c^2 q SA}
A'B'C being the pedal of P
Seems that A''B''C'' is perspective to the medial triangle for P on the
Stammler hyperbola (= tangential Feuerbach)
To the Orthic for P on the Neuberg cubic.
Best regards,
Peter. 0 Attachment
On Feb 23, 2006, at 3:40 AM, Francois Rideau wrote:
> I don't know the answer to your question. I think it's only a
Jeff and François,
> matter of
> taste. In bygone days, there was a war between synthetic and analytic
> geometers. I think now it's over!
I too think this war is over and is a matter of taste. Many on
Hyacinthos seem to feel that synthetic proofs (which do no emphasize
algebra) are superior. But I often work next to a very good geometer
whose aims are more classical than most Hyacinthians but who uses
algebra almost all the time simply because you can always get an
answer with algebra).
The reason there is no argument anymore is that coordinates are
inherent in synthetic methods, so all one can do is state one's
preference). Coxeter's book on the projective plane has a nice
discussion of the role and inevitability of coordinatesl
I have also been writing on my web site that Euclid inevitably leads
to abstract algebra (From Euclid to Abstract Algebra, just revised),
which is more than, but includes, coordinates. (Euclid is very
interesting to read!).
Euclid is really the geometry of points and segments. If you use
lines rather than segments, then coordinate methods become very
effective and I think it was projective geometry that moved geometers
away from synthetic methods.
For me, I call myself a nonsynthetic geometer because the tasks I
set myself are takes far removed from the scope of synthetic
geometry, which is good at finding properties of particular geometric
objects. I am interested in groups (often very large groups) of
objects for which I am finding purely algebraic methods very successful.
Jeff, Enjoy your investigations into conjugates!
Steve
[Nontext portions of this message have been removed] 0 Attachment
I think cabri.com has a reader for both mac and pc for free.
Steve
On Feb 23, 2006, at 3:57 AM, Jeff Brooks wrote:
> P.S. I don't have Cabri so any examples you provide are all the more
> appreciated.
[Nontext portions of this message have been removed] 0 Attachment
Dear Steve
You are right. We cannot forget algebra, even if we enjoy synthetic
geometry, we know that a good analytic proof may be as fine as a synthetic
one.
And what is ETC, if not only repeated and tedious computations of
barycentric coordinates?
Besides even simple problems in triangle geometry are better solved by
higher dimensional tools as circulant determinants or some spaces of affine
maps and so one.
They are also other tools in triangle geometry, complex numbers for example
in Morley's books or June Lester's papers.
We know that Morley was very shrewd using complex numbers and I still don't
understand the ideas (as Galois theory) hidden behind some of his
computations. They is still some work to decipher his book!
Friendly
François
[Nontext portions of this message have been removed] 0 Attachment
Dear Jeff, Francois,Steve (and everyone else)
We seem to be agreed that syntheic = analytic.
As to the details of Floor's paper :
Jeff, I do not think it is worth the effort to work through A",B",C".
Floor uses this result to motivate a construction for the image of a
point Z under the reciprocal conjugation which swaps X and Y.
In itself, it is simply a bad way to find K.
If X = x1:x2:x3, Y = y1:y2:y3, Z = z1:z2:z3, then the image we want
has barycentrics x1y1/z1 and so on.
Floor's construction is not particularly simple, and fails when X = Y.
My way of constructing this image is no simpler, but covers all cases.
Notation :
U.V denotes the line joining points U and V
For a point W = w1:w2:w3
Wa = 0:w2:w3, the intersection of B.C and A.W, and similarly Wb, Wc
aW = 0:w2:w3, the intersection of B.C and Wb.Wc, and similarly bW, cW
Construction :
cZYa = intersection of C.A and cZ.Ya
bZXa = intersection of B.A and bZ.Xa
Abc = intersection of B.cZYa and C.bZXa
Then define Bca, Cab similarly
The lines A.Abc, B.Bca, C.Cab meet in a point
This has coordinates x1y1/z1:x2y2/z2:x3y3/z3
Obviously you need only construct two of the lines.
The barycentric calculations are very easy.
It is enough to check that Abc has the form *:x2y2/z2:x3y3/z3,
where * is irrelevant.
This gives the reciprocal conjugate, as intended. Also
With Z = G, it gives the barycentric product of X and Y
With Y = G, it gives the barycentric quotient of X by Z
Note: When Z = G, the points aZ, bZ, cZ are infinite.
To construct, say, the line aZ.W, we simply draw the line
at W which is parallel to BC.
Regards
Wilson
 In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@...> wrote:
>
>  In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@> wrote:
> >
> > All,
> >
> > What are the differences between synthetic and analytic geometry?
> >
> > Sincerely, Jeff
> >
>
> I ask this question after reading "Geometric Construction of
Reciprocal
> Conjugations" by Keith Dean and Floor van Lamoen: see
>
> Keith Dean and Floor van Lamoen, Geometric Construction of
Reciprocal
> Conjugations, pp.115120.
>
> http://forumgeom.fau.edu/FG2001volume1/FG200116index.html
>
> Proposition 1. under 2.1 has a proof but 2.2 construction does not
have
> a proof ... The answer seems analytic not synthetic in nature.
>
>
> I want to understand this analysis better...
>
> Friendly, Jeff
> 0 Attachment
Yes,
I cannot see the forest for the trees. I wish to see someone
overcome the tedious nature of this type of problem and develop a
solution.
Sincerely, Jeff
 In Hyacinthos@yahoogroups.com, "Francois Rideau"
<francois.rideau@...> wrote:>
rather
> Dear Jeff
> Given P(x:y:z), to compute barycentrics of A", B", C" is easy but
> tedious and I am too lazy to do it.
proof
> But I don't understand your question.
> Do you want a detailed computation of these barycentrics or another
> that AP and AA" are isogonal lines?
they
>
> I think KeithFloor's proof of this fact is not very satisfying for
> don't use signed distances (normal coordinates).
CA, AB,
> If you call A1, B1, C1 to be symmetric points of P wrt sides BC,
> then A"B"C" is the medial triangle of A1B1C1 and lines AA", BB",
CC" are
> respectively the perpendicular bissectors of the sides B1C1, C1A1,
A1B1, so
> it is known they are through Q isogonal conjugate of P wrt ABC.
>
> Friendy
> François
>
>
> [Nontext portions of this message have been removed]
> 0 Attachment
Dear Wilson,
I am not in agreement here. If I understand the definitions correctly,
it's much easier to move from given synthetic constructions to unknown
analytic ones.
The development of synthetic methods seems more difficult.
Sincerely, Jeff
P.S. I'm still working all the wonderful information I received.
 In Hyacinthos@yahoogroups.com, "Wilson Stothers" <wws@...> wrote:
>
> Dear Jeff, Francois,Steve (and everyone else)
>
> We seem to be agreed that syntheic = analytic.
> 0 Attachment
There is nothing in my repertoire to suggest that analytic =
synthetic.
Jeff
 In Hyacinthos@yahoogroups.com, "Jeff Brooks" <trigeom@...> wrote:
>
> Dear Wilson,
>
> I am not in agreement here. If I understand the definitions
correctly,
> it's much easier to move from given synthetic constructions to
unknown
> analytic ones.
>
> The development of synthetic methods seems more difficult.
>
> Sincerely, Jeff
>
> P.S. I'm still working all the wonderful information I received.
>
>
>
>  In Hyacinthos@yahoogroups.com, "Wilson Stothers" <wws@> wrote:
> >
> > Dear Jeff, Francois,Steve (and everyone else)
> >
> > We seem to be agreed that syntheic = analytic.
> >
> 0 Attachment
On Feb 28, 2006, at 10:48 PM, Jeff Brooks wrote:
> The development of synthetic methods seems more difficult.
I had a long discussion about this with Conway a few years ago. He
uses coordinate methods almost all the time, but of course he had to
invent many of those methods to make them effective. I have often
thought that he wills the mathematics to work simply because he
believes so strongly that it will work.
I asked him why he did not do more proofs in the old geometric style.
He said that each synthetic proof was unique, that the path from
givens to conclusion was different for every proof and consequently
often difficult to find, and not very generalizable when you do. He
said that coordinates always work, although sometimes they are not
pretty.
I thought "yes, they always work when you are John Conway."
I then remarked that I thought that one leans more from algebra
because, just be being algebra, it often applies for a whole class of
things.
A great example of this last is simply to realize that if you write
ETC in barycentrics, all the affine information of the plane is
contained there in. Just replace a,b,c with l, m, n.
Steve
[Nontext portions of this message have been removed] 0 Attachment
 In Hyacinthos@yahoogroups.com, Steve Sigur <s.sigur@...> wrote:>
to
>
> On Feb 28, 2006, at 10:48 PM, Jeff Brooks wrote:
>
> > The development of synthetic methods seems more difficult.
>
>
>
> I had a long discussion about this with Conway a few years ago. He
> uses coordinate methods almost all the time, but of course he had
> invent many of those methods to make them effective. I have often
style.
> thought that he wills the mathematics to work simply because he
> believes so strongly that it will work.
>
> I asked him why he did not do more proofs in the old geometric
> He said that each synthetic proof was unique, that the path from
consequently
> givens to conclusion was different for every proof and
> often difficult to find, and not very generalizable when you do.
He
> said that coordinates always work, although sometimes they are not
of
> pretty.
>
> I thought "yes, they always work when you are John Conway."
>
> I then remarked that I thought that one leans more from algebra
> because, just be being algebra, it often applies for a whole class
> things.
write
>
> A great example of this last is simply to realize that if you
> ETC in barycentrics, all the affine information of the plane is
hmmn well, there is certainly a lot to be said about willpower.
> contained there in. Just replace a,b,c with l, m, n.
>
> Steve
>
Jeff 0 Attachment
Hola, (hi) to all of you!
About synthethic/ analityc methods I just wish to add a teacher´s point of view: I've been teaching the Modern Geometry course for a loooooong time, and as result of the lack of interest in geometry in the pre university years curricula, students can "rely" on analityc methods without any idea of what is going on geometrically. Once they get the geometric flavour even analytic methods work better.
As fot the synthetic demonstrations students tend to look at them as "magic" without any method....but eventually they can actually work on demonstrations of their own.
Now, don't even think this happens with most of the students: as a matter of fact, this course has the greatest reprobation average in our Science School over any course in physics, biology and mathematics.
On the second course , which is optative and is mainly over modern geometry of the circle (Shively and Altshiller's books), we even have been able to work on hyperbolic synthetic geometry thus preparing students for complex variable methods.
So yes, I see (I live actually) the difference between these two methods.
Just to finish a quote from three students of this semester which are taking at the same time Modern Geometry II and Analytic Geometry II: talking about a problem in the analytic geometry course they said:
"it's so simple to see it synthetically and so tiresome to work it analytically"
Best wishes
María de la Paz
PS I hope my spelling was not too bad......sorry!

Do You Yahoo!? La mejor conexión a Internet y 2GB extra a tu correo por $100 al mes. http://net.yahoo.com.mx
[Nontext portions of this message have been removed] 0 Attachment
 In Hyacinthos@yahoogroups.com, "Ma. de la Paz Alvarez"
<madelapaix@...> wrote:>
point of view: I've been teaching the Modern Geometry course for a
> Hola, (hi) to all of you!
>
> About synthethic/ analityc methods I just wish to add a teacher´s
loooooong time, and as result of the lack of interest in geometry in
the pre university years curricula, students can "rely" on analityc
methods without any idea of what is going on geometrically. Once they
get the geometric flavour even analytic methods work better.>
as "magic" without any method....but eventually they can actually
> As fot the synthetic demonstrations students tend to look at them
work on demonstrations of their own.>
matter of fact, this course has the greatest reprobation average in
> Now, don't even think this happens with most of the students: as a
our Science School over any course in physics, biology and
mathematics.>
geometry of the circle (Shively and Altshiller's books), we even have
> On the second course , which is optative and is mainly over modern
been able to work on hyperbolic synthetic geometry thus preparing
students for complex variable methods.>
methods.
> So yes, I see (I live actually) the difference between these two
>
are taking at the same time Modern Geometry II and Analytic Geometry
> Just to finish a quote from three students of this semester which
II: talking about a problem in the analytic geometry course they said:> "it's so simple to see it synthetically and so tiresome to work it
analytically"
>
Dear María,
> Best wishes
> María de la Paz
> PS I hope my spelling was not too bad......sorry!
>
>
Thank you very much for these comments; I am definitely in agreement
with your student's quote! At times I am even more frustrated, as
I'm sure others might be, with the enormous amount of information
available to us in this digital world. With computers, we can obtain
tons of data but I tend to get lost in trying to decipher meaning
from it and neither synthetic nor analytic methods alone seem to
suffice. Seems the best is to work from both sides toward a common
middle ground where hopefully better understanding is found.
Sincerely,
Jeff Brooks
Tulsa, OK 0 Attachment
Dear François,
Is KeithFloor's paper really so intricate after all?
Jeff
>
matter of
> Dear Jeff
> I don't know the answer to your question. I think it's only a
> taste. In bygone days, there was a war between synthetic and
analytic
> geometers. I think now it's over!
but too
> As for KeithFloor's paper , I think their construction interesting
> intricate.
(1:1:1) to
> To get the map:
> f:(x:y:z) > (u/x:v/y:w/z)
> I think, it's better to use f = g.s
> where s:(x:y:z) > (1/x:1/y:1/z) is the isotomic conjugation
> and g:(x:y:z) > (u.x:v.y:w.z) is the collineation with A, B, C
> (vertices of the reference triengle) as fixed points, sending G
> P(u:v:w).
interested,
> Of course, we must have a simple construction for g. If you are
> I can send you a Cabrifile of this construction.
> Friendly
> François
>
>
> [Nontext portions of this message have been removed]
> 0 Attachment
Dear Jeff
Yes I read this paper and as I have said it, I am not quite satisfied with
some proofs.
I have to draw many Cabri pictures of myself to understand what they were
talking about.
I hope now you are satisfied with my explanation of the chuffchuffs?
Friendly
François
PS
Fred Lang send me a Cuppens's Cabri macro drawing cubic knowing 9 points and
it works properly!
In particular, I was able to draw the Neuberg cubic very easily!
I only have some difficulty to choose 9 points among all knwn ETC on it!
Thanks Fred!
[Nontext portions of this message have been removed] 0 Attachment
Thank you François for answering my posts. Thank you more for
allowing me to answer in the order I choose. This one is easier!
>
satisfied with
> Dear Jeff
> Yes I read this paper and as I have said it, I am not quite
> some proofs.
Neither am I!
> I have to draw many Cabri pictures of myself to understand what
they were
> talking about.
chuffs?
> I hope now you are satisfied with my explanation of the chuff
I'll get there eventually...
> Friendly
points and
> François
> PS
> Fred Lang send me a Cuppens's Cabri macro drawing cubic knowing 9
> it works properly!
on it!
> In particular, I was able to draw the Neuberg cubic very easily!
> I only have some difficulty to choose 9 points among all knwn ETC
> Thanks Fred!
>
>
> [Nontext portions of this message have been removed]
> 0 Attachment
Dear Francois et al,
Could you or Fred possibly put the macro in the file area?
Come to think of it, it might be nice to have an archive of
Cabri macros for the group. Any thoughts
Wilson
 In Hyacinthos@yahoogroups.com, "Francois Rideau"
<francois.rideau@...> wrote:
> Fred Lang send me a Cuppens's Cabri macro drawing cubic knowing 9
points and
> it works properly!
on it!
> In particular, I was able to draw the Neuberg cubic very easily!
> I only have some difficulty to choose 9 points among all knwn ETC
> Thanks Fred!
>
> 0 Attachment
Dear hyacinthers
I finally success to join Mr Roger Cuppens and he agree
i can put its 235 macros on conics and cubics for Cabri in the group.
Does Antreas agree ?
If yes, how can I send it?
Regards.
Fred
 In Hyacinthos@yahoogroups.com, "Wilson Stothers" <wws@...> wrote:
>
> Dear Francois et al,
>
> Could you or Fred possibly put the macro in the file area?
>
> Come to think of it, it might be nice to have an archive of
> Cabri macros for the group. Any thoughts
>
> Wilson
>
>  In Hyacinthos@yahoogroups.com, "Francois Rideau"
> <francois.rideau@> wrote:
>
> > Fred Lang send me a Cuppens's Cabri macro drawing cubic knowing 9
> points and
> > it works properly!
> > In particular, I was able to draw the Neuberg cubic very easily!
> > I only have some difficulty to choose 9 points among all knwn ETC
> on it!
> > Thanks Fred!
> >
> >
> 0 Attachment
Dear Nikos and Francois,
This is an update to an old post:
I think I just now found what you guys were describing:
Here, Ian Stewart writes "Bourbakism was an example of what computer
scientists now call data compression."
http://links.jstor.org/sici?sici=00255572%28199511%292%3A79%3A486%
3C496%3ABBPSIM%3E2.0.CO%3B2E&size=LARGE&origin=JSTORenlargePage
OFF SUBJECT:
Antreas, I posted another message I think on Friday still pending
approval  Could you please delete it  Thank you,
Sincerely, Jeff
> Dear Nikolaos,
>
> I have no idea what you are talking about...Could you please
> elaborate?
>
> Sincerely, Jeff
>
>  In Hyacinthos@yahoogroups.com, Nikolaos Dergiades
> <ndergiades@> wrote:
> >
> > Dear Jeff,
> > Francois is right but I want
> > to add my opinion.
> >
> > I think that in our days synthetic in
> > mathematics is the effort, as in
> > computer scientists, for the use of known
> > compound tools, for detail encryption.
> > It is called in computer language
> > information hiding or data encapsulation.
> >
> > Best regards
> > Nikos Dergiades
> >
> >
> > [FR]
> > > > I don't know the answer to your question. I think
> > > > it's only a matter of taste.
Your message has been successfully submitted and would be delivered to recipients shortly.