\magnification=\magstep1
\noindent
{\it Lucia Bostrom -- Why Study Geometry?}
\bigskip
Your paper is very well-written on the whole. I think the
first paragraph could do a better job of introducing the 
relations between the different ways of thinking about
the mathematics, though (and not just ``lay them out'' the
way you do.)  See the markings for
a few corrections and suggestions.  I think the conclusion is good
and, of course, I agree with what you are saying.  

\bigskip
\noindent
{\it Specific Comments}
\bigskip
\item{1.}  For the Greeks generally, and Proclus in particular,
the ``clearing the eye of the soul'' referred to ideas pretty
far outside of mathematics itself.  The study of Euclidean geometry was often
seen as the pathway to {\it philosophy}, so it was not just clearing the 
way for further ``mathematical endeavors.''
\item{2.}  The phrase ``knowledge of universals'' here seems also to hint at 
Plato's concept of eternal, unchanging ``ideas'' or ``forms'' behind
the objects and relationships in the physical world.
\item{3.}  As you point out later in the paragraph, Pascal is not
really agreeing with the idea that developing logical thinking
(at least of the sort used in Euclidean geometry) is that 
valuable.  So you should indicate somehow that Pascal's ideas
are going in a different direction here by saying ``however''
or something similar.  This would be a clearer signal what
the main point of this paragraph is going to be.  
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10 
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 13
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 13
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 13
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 15
\bigskip
Totals:  Content and Structure -- 94;  Style and English Usage -- 97.
\vfill\eject
\noindent
{\it Catherine Caracciolo}
\bigskip
Your essay is a good response to the basic question.  I have a question
about one thing you said in the first paragraph, though.  How
is doing mathematics ``for its own sake'' different from doing
mathematics ``as busywork.''  One might think that those two reasons
are almost the same thing, so it would be good to be clearer about
the distinction.
\bigskip
\item{1.}  The title was the {\it Elements} right from the beginning,
so it sounds a bit strange to say that that is the way people refer
to it today.
\item{2.}  I would disagree here.  I think Millay really does mean
beauty in the esthetic sense.  And it is ``beauty bare'' because
it is beauty in its simplest, purest form.  All externals and
temporary features are ``boiled away,'' so to speak, leaving
only the most basic ingredients of beauty, which are all the
more dazzling for that.   Also, be careful of the word
``simplistic.''  It has a pejorative connotation that I don't
think you mean here.  You say something is ``simplistic'' if
it is {\it too simple} and omits things that should be there
because they are important.
\item{3.}  Does ``having the worst circumstances'' mean ``with the weakest
possible assumptions (hypotheses)?''  This was not clear, and the
phrase ``worst circumstances'' has connotations that do not
really fit with this discussion.
\item{4.}  This is an excellent point!
\item{5.}  It would probably be good to identify the source
of this quotation.


\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 12
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 14
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 9
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 11
\bigskip
\noindent
Totals:  Content and Structure -- 96;  Style and English Usage -- 92
\vfill\eject
\noindent
{\it Sarah Cahn -- Why Study Geometry?}
\bigskip
This is a very good essay on the title question.  The only serious
criticism I have is that you have not really addressed any
of the quotations in the topic description.  I think that
would have added some interesting dimensions to what
you are saying here.  For instance, on the basis of
the Pascal quote, do think he would have agreed with
the idea that the kind of thinking one does in geometry
is really that useful in the law?  (I think not, for the
reason that he would argue it is too tied to clearly stated postulates,
and does not take into account the complexities of events
and situations in the real world.)
\bigskip
\item{1.}  Were these casual comments?  Or did you do some sort of
more formal survey of opinions about geometry as a part of this class
in high school?
The way you describe this makes it sound like a more formal survey,
and if so, it would have been good to mention the circumstances.
If not, it would be good to ``set up'' these comments by
saying that you had conversations at several points with classmates,
and they shared their opinions with you in this way.
\item{2.}  This is a good point, but I think it could even have
gone closer to the beginning of the paragraph.  I have the feeling
that this particular rationale for studying geometry is {\it very
specifically} Catholic and perhaps even specifically a part of
the tradition of Jesuit education, so it would be good to place
the whole discussion of this aspect of studying geometry in that
context.
\item{3.}  Say ``legal profession'' here -- ``Lawyer profession''
is not correct English.  Also, isn't it the logical reasoning skills
(and not the geometry itself) that is useful to lawyers?
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 8
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 8
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language  -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (15) Uses correct punctuation -- 10
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 12
\bigskip
\noindent
Totals -- Content and Structure: 91; Style and English Usage:  95.
\vfill\eject
\noindent
{\it Daniel Finn -- Why Do We Study Geometry?}
\bigskip
You are actually very right in saying that (another) reason
geometry is so important is that geometric ideas are used
all the way through calculus and other more advanced mathematics
courses.  This is not a reason for teaching geometry to
{\it all students}, of course, since many students (at least
traditionally in the U.S.) never get to those more advanced
courses.  But it is also a very important reason.  

I think your first paragraph is a bit too rushed.  It would be
good to take some more time to lay out the reasons you
will discuss in slightly more detail.

A minor technical point -- ordinarily, one would not capitalize
``geometry'' unless it was the title of a specific course or 
a book.  
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 15
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 13
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas  -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 8
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 14
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 14
\item{6.}  (15) Uses correct punctuation -- 14
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words 12
\bigskip
\noindent
Totals -- Content and Structure:  98; Style and English Usage:  92.
\vfill\eject
\bigskip
{\it Muhammad Javaid -- Why Study Geometry}
\bigskip
You have a lot of good ideas and examples here.  But the writing is a bit rough.
See the comments and the corrections on the paper.
\bigskip
\item{0.}  Usually, you don't capitalize the word geometry
unless it is the title of a course or a book.  
\item{1.}  Actually, I think the story is trying to make the point
that knowledge is good in and of itself and that one should not
need any prospect of reward to pursue it.  One can disagree
with this, of course, but the scornful way Euclid treats the
student comes across pretty clearly in the ``give the man
three obols since he must profit from what he learns.''
\item{2.}  These are all great examples of the ways the Greeks
used geometry to develop knowledge about the physical world and
new technologies.  I think it is questionable that Euclid could
have foreseen all of this.  And the quote seems to indicate that
he would not have agreed that this was the main reason to study
geometry in any case.
\item{3.}  I think I know what you mean here, but this is a
somewhat convoluted sentence (and {\it progress} is not a
transitive verb -- you cannot progress something).
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 13
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 13
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 8
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 16
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 10
\item{4.}  (10) Lacks incomplete sentences -- 9
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 13
\item{6.}  (15) Uses correct punctuation -- 13
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 11
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 94; Style and English Usage -- 82
\vfill\eject
\noindent
{\it Kyle Kadlick -- Why Study Geometry?}
\bigskip
Your paper is well written for the most part and has some good ideas.
However, I don't think you have really appreciated the main point
of the quote from Pascal (see comment 1 below).  The first 
paragraph could also say a bit more about the reasons for 
Euclid's point of view. I do not think the 
discussion of the quote from Stobaeus is completely correct
either.  It is not only a question of ignorance, but also a
question of incorrect motivation.  Finally I'm not sure about
how useful SAT-type problems are for real-world problem solving.
They seem pretty artificial to me!
\bigskip
\item{1.}  You are correct that Pascal is referring to the Euclidean
style of deductive mathematics with its apparatus of definitions and
postulates.  However, the main point that Pascal is trying to make
is that this style of thinking can be {\it quite limited} if it
is taken too far.  To paraphrase what Pascal is getting at:
This approach to problem-solving does not
take into account that situations in the real world humans must
deal with are rarely so clear-cut and orderly.  So mathematicians who
try to rely on this sort of thinking when it does not really apply are
frequently drawn into incorrect conclusions.  I have to say that
from my experience, Pascal is perfectly correct here!
\item{2.}  This is a good point.  It is also one of the main reasons
why the de-emphasis of geometry in high school mathematics is a real
problem!  However, the sentence at the start of the following
paragraph does not really fit with what you are saying the
rest of the way.  For Euclid, the reason to study geometry
was definitely not the practical applications.  (I'm not sure
if that is what you meant to say, but that's what the sentence
seems to be saying.)
\item{3.}  Sorry, but I have no idea what the ``rubber pencil trick''
you are referring to is!  Explain, please.
\item{4.}  It might be somewhat more correct to say that Plato's view
was studying
geometry can lead one to appreciate the existence of those
eternal forms, and hence to the study of philosophy.  (This is
the element of the {\it propaedeutic} in the study of geometry -- it
is a preparation for the even higher study of philosophy.)
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 11
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 13
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly identifiable main ideas -- 12
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 8
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 14
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 13
\bigskip
\noindent
{\it Totals:} Content and Structure -- 89;  Style and English Usage -- 97.
\vfill\eject
\noindent
{\it Matt Kasuba -- It's Hip To Be Square}
\bigskip
Your essay does a good job of addressing the issues
raised by the Stobaeus and Proclus quotations.  But I don't think that
it is the ``merit'' of studying geometry that is really the issue.
I would say it has more to do with the motivations or reasons
for doing that.   There are a
few minor corrections of writing issues that I have marked
on the paper itself -- please take a look, in particular
at the difference between ``its'' (possessive) and ``it's''
(contraction for ``it is'').  I would advise you to avoid
the contraction in formal writing like this.  It is fine
to use that if you are reporting everyday speech, but
spell out ``it is'' otherwise.

\item{1.}  Your examples of the ``barriers caused by the senses''
seem more like {\it errors of logic} in construction of mathematical
proofs to me.  When philosophers say this, they are usually thinking
of much more concrete examples, such as taking a mirage for an
actual object, or mistakenly interpreting the motion of the
Sun across the sky as a result of the Sun revolving around
a stationary Earth.
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 12
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 13
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 11
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 13
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 95;  Style and English Usage -- 94.
\vfill\eject
\noindent
{\it Astrid Ludwig -- Geometry: Our World}
\bigskip
You have certainly grasped most of the point of the story about Euclid and the
student from Stobaeus.  However, note that the person who asked the
question ``what shall I get from studying geometry?'' was not a slave.
He was presumably a reasonably well-to-do person in Alexandria
who could afford to spend the time to attend Euclid's lectures.
{\it There is} a slave in the story, though.  Namely, Euclid calls to
{\it his slave} and says to give the student who asked the question the
insultingly small amount of money.  Note that there is an added level of
scorn involved here, since it is not even Euclid himself who
``forks over'' the three obols.  It is Euclid's {\it slave} who is asked
to do the demeaning money transfer(!)
\bigskip
\item{1.}  Technical comment:  When identifying quotations like this, even
though you have only one item in your bibliography, it would still be
standard practice to
indicate the source of the quote by more than just the page number -- for instance,
say (Bloom, 206).
\item{2.}  Careful, cells have much too much complicated interior structure
to be represented by geometrical points.  Also, the other examples of
geometric shapes in nature are only {\it approximately} of the shapes you
are describing.  For example, a tree ring is never a perfect circle.
(See the next comment too.)
\item{3.}  This sounds more like ``comprehensive'' or
``inclusive'' than ``bare'' to me.  I think it is closer to Millay's intention
to say that it is ``beauty bare'' because beauty in geometry
is beauty in its {\it simplest, purest form}.  All externals and
temporary features are ``boiled away,'' so to speak, leaving
only the most basic ingredients of beauty, which are all the
more dazzling for that (the ``nothing, intricately drawn nowhere ... ''
also refers to the insubstantial but luminous geometrical 
relationships).   
\item{4.}  Careful here too -- {\it mathematical induction} is
a very different idea from the sort of {\it inductive reasoning} discussed
in philosophy or psychology (reasoning from the evidence seen in examples to
a general conclusion).  From the point of view of those
disciplines, in fact, mathematical induction is a purely
{\it deductive} form of reasoning.
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 11
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas --  15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 19
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 14
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 12
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 95;  Style and English Usage -- 93.
\vfill\eject
\bigskip
\noindent
{\it John Macomber -- Hidden Beauty}
\bigskip
In your first paragraph, I am somewhat doubtful that Euclid is
really a ``rubric for solving real life problems.'' Euclidean geometry
is much too abstract for that to be possible.  
Including an example to illustrate Pascal's point about the insufficiency of pure logic
to solve some practical problems was a good idea.  See point 2 below, though, for another
angle on the specific example you used.
\bigskip
\item{1.}  Picky comment -- while modern students certainly might ask why they need to
learn about degree measure of angles, recall that Euclid does not use that
idea at all.  Indeed, the only specific angles that he uses at all are
right angles and straight angles.
\item{2.}  I think it might be more accurate to say that President Bush
and his advisers were arguing that we had to invade Iraq to stop
Saddam Hussein from continuing to develop his weapons programs and to eliminate
the repressive features of his regime.  But of course they were also misinterpreting
(or fabricating) a lot of the evidence for the existence of those weapons programs.
So it is not clear that they were really doing the sort of reasoning Pascal
was talking about.  The thing that comes closest to that sort of thinking
to me was Defence Secretary Donald Rumsfeld's approach to the military issues -- superior
air power, ``shock and awe,'' and the rest were supposed to eliminate
Saddam's military and then the Iraqi people would welcome us with open arms.  Needless
to say, it didn't quite work out that way.
\item{3.}  I am not sure exactly what you mean by ``dynamic'' here.  Are you
thinking of statements that are more involved (or less ``obvious'')?
\item{4.}  Yes, Euclid might have said that you should have just been happy to
learn Latin for its own sake, or for the intellectual challenge of learning
a differently-structured language.
\item{5.}  This sentence does not really make sense.  You have the connection
to the real world in both ``places'' here.   I also suggested a rearrangement
of this sentence because the way you have it, ``{\it The Elements}'' should
be the possessive ``{\it The Elements'}.''  That would be correct, but awkward.
(The same construction also occurs in the last paragraph.)
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 13
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 13
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 14
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 12
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 12
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 95; Style and English Usage -- 91.
\vfill\eject
\noindent
{\it Andrew Marzo -- Why Study Geometry}
\bigskip
Your essay goes into a lot of very detailed discussion of
some of the philosophical implications of studying geometry
and also the way that study supposedly prepares one to
think logically in other settings.  The discussion of
the role of logical thinking on the SAT and other
standardized tests seemed to be a bit ``off topic''
to me, although I grant that there is a connection.

My main commen is that I don't think you
have really appreciated Pascal's objection to these ideas,
though.  See comment 2 below for what I mean about this.
\bigskip
\item{1.}  You are using ``math'' here in the restricted sense that
often comes up in colloquial phrases such as ``do the math.''  This
refers, of course, mostly to simple arithmetic.  There is much
more to mathematics as an intellectual discipline!  So 
I do not really agree with what you are saying here.
\item{2.}  You are correct that Pascal is referring to the Euclidean
style of deductive mathematics with its apparatus of definitions and
postulates.  However, the main point that Pascal is trying to make
is that this style of thinking can be {\it quite limited} if it
is taken too far.  To paraphrase what Pascal is getting at:
This approach to problem-solving does not
take into account that situations in the real world humans must
deal with are rarely so clear-cut and orderly.  So mathematicians
and others who
try to rely on this sort of ``strictly Euclidean''
thinking when it does not really apply are
frequently drawn into incorrect conclusions.  I have to say that
from my experience, Pascal is perfectly correct here!
\item{3.}  Really, there is no question of trying to prove them
false.  The postulates are to be taken as the starting point
for the process of deducing new propositions.
\item{4.}  This is the idea of the {\it propaedeutic} that
I mentioned in the paper topic description.  For Proclus and
other Greek thinkers, the study of
geometry can lead the student to the study of deeper issues
in philosophy by introducing him or her to the idea
of pure forms.
\item{5.}  But see point 2 above.  Isn't this training ground
really much different from the real world that the training
is supposed to prepare students for?
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 12
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 13
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 8
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 12
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 11
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 93; Style and English Usage -- 90
\vfill\eject
\noindent
{\it Xuan Ha Nghiem -- Why Study Geometry?}
\bigskip
Good essay on the ``why study geometry question!''   There are still
a few places where minor rewordings would improve the readability.
But I am impressed at how hard you worked to revise and polish
this essay.  Good work.

\bigskip
\noindent
{\it A Comment}
\item{1.}  I like this interpretation of what Proclus was getting
at in the quotation I put in the paper assignment very much.
It was really {\it not just pure intellectual curiosity} that
led the Greeks to study this subject.  There was another
side to it as you say -- the motivation was to study mathematics
because it could provide insight about the natural world.

\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 15
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 14
\bigskip
\noindent
{\it Totals:} Content and Structure -- 100; Style and English Usage -- 97
\vfill\eject
\noindent
{\it Kaitlin O'Hagan -- Why Study Euclidian Geometry?}
\bigskip
Good essay on the way Euclid embodies the pure, logical form
of beauty that Millay was getting at in her poem.  The first paragraph
really only addresses part of what you say later, though, so that 
could do a better job of setting up the rest of the essay.
Your writing is
generally very good.  I have marked a few corrections and
comments on the paper.    (Very minor comment -- I know the spelling ``Euclidian'' you use is correct
too, but I think ``Euclidean'' is more common.)
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 15
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 13
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 15
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 19
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 12
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 98;  Style and English Usage -- 96.
\vfill\eject
\noindent
{\it Max Pettinelli -- No Title}
\bigskip
I like the fact that you were (I think) pretty honest about
your opinions of mathematics here.  Your writing is also generally
good.  See the paper for a few corrections and suggestions for
smoothing things out.
\bigskip
\item{1.}  I don't quite understand what you meant here.  Did you mean
something like ``process of argumentation?''  I agree that there is
an element of truth to this.  But as a prospective lawyer you should
be aware (and you will certainly learn) that there is much more to
being a good lawyer than this.  As either a prosecutor or a defence
attorney, you also have to understand the psychology of jurors, and
that is something that is often far from logical.  (My brother is
a lawyer who worked for years as a DA and he and I have had a lot of
interesting conversations about this point.)  Many prosecutors, in
fact, {\it do not want mathematicians} on the juries they have to
deal with because they don't really ``get'' the idea of ``beyond
reasonable doubt.''  This is, of course, a part of what the
Pascal quotation is getting at.   The strict Euclidean
style of thinking can be {\it quite limited} if it
is taken too far.  To paraphrase what Pascal is getting at:
This approach to problem-solving does not
take into account that situations in the real world humans must
deal with are rarely so clear-cut and orderly.  So people who
try to rely on this sort of thinking when it does not really apply are
frequently drawn into incorrect conclusions.  I have to say that
from my experience, Pascal is perfectly correct here!
\item{2.}  Actually, almost all engineers need to use calculus
in one way or another.
\item{3.}  See comment 1 above.  I think there is an aspect
of Pascal's ideas that you are not appreciating completely.
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 13
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 12
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 10
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 12
\bigskip
\noindent
{\it Totals: } Content and Structure -- 98;  Style and English Usage -- 94.
\vfill\eject
\noindent
{\it Tom Santa Maria -- Why Study Geometry?}
\bigskip
Very strong essay on the reasons for studying geometry.  There are a few minor
punctuation issues that I have marked on the paper, but overall your writing
is also very good.
\item{1.}  Don't capitalize ``honesty'' here since it is not the start of
a new sentence.
\item{2.}  Yes, this is the key idea that Pascal is trying to express.
The strict Euclidean style of thinking can be {\it quite limited} if it
is taken too far.  To paraphrase what Pascal is getting at:
This approach to problem-solving does not take into account that situations
in the real world humans must deal with are rarely so clear-cut and orderly.
So people (especially mathematicians) who try to rely on this sort of thinking
when it does not really apply are frequently drawn into incorrect conclusions.
I have to say that from my experience, Pascal is perfectly correct here!
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 15
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas  -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 15
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 15
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 13
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 15
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 100; Style and English Usage -- 98.
\vfill\eject
\noindent
{\it Kylee Sullivan -- Studying Geometry: The Key to Human Survival}
\bigskip
Your essay is very good.  I'm not entirely sure about the title, though.
I think this is overstating (and overdramatizing) things a bit.  You are
right that we need to understand the environment we live in in order to
survive.  However, it is not obvious that geometry is the
best or most important way to derive that sort of knowledge.
\bigskip
\item{1.}  You should be aware that the emphasis on philosophy here
is probably not all that common.  It is a reflection of the traditional
structure of education in Jesuit schools.  (Up until the late 1960's,
in fact, every student here had effectively to do a double major in
a subject like the ones we have now, together with a second collection of
required courses in philosophy and theology.)
\item{2.}  These shapes appear only {\it approximately} in the physical
world of course.  And it is only the trunk of a tree that is
approximately cylindrical.  If you take the crown (leaves) and the
roots into account, the shape is much more ``interesting(!)''
\item{3.}  I am not entirely sure why you said ``abstract emotions''
here.  How did you mean the ``abstract?''  It would have been
good to make the connection here with the quotation from Pascal
because, of course, that is exactly what he is saying too.  The strict Euclidean
style of thinking can be {\it quite limited} if it
is taken too far.  To paraphrase what Pascal is getting at:
This approach to problem-solving does not
take into account that situations in the real world humans must
deal with are rarely so clear-cut and orderly.  So people who
try to rely on this sort of thinking when it does not really apply are
frequently drawn into incorrect conclusions.  I have to say that
from my experience, Pascal is perfectly correct here!
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 12
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 14
\bigskip
\noindent
{\it Totals:} -- Content and Structure -- 97;  Style and English Usage -- 97.
\vfill\eject
\noindent
{\it Kevin Sutman -- Why Study Geometry?}
\bigskip
Your essay on the title question is very good.  I like that you
have drawn on your own experiences (struggles?) with mathematics
for this.  The writing is also generally very good, although
there are a few places where I have marked some corrections
and suggestions for rewordings.  There is also a place toward
the bottom of page 4 where I think that something got mistakenly
erased or truncated.  

\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 15
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 10
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 13
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 14
\bigskip
\noindent
{\it Totals:} Content and Structure -- 100; Style and English Usage -- 97.
\vfill\eject
{\it Peter Zona -- The Importance of Geometry}
\bigskip
\item{1.}  This is somewhat repetitive since you have already 
repeated the quote.  It is not necessary to go through
the story again in this way.
\item{2.}  This was certainly true in the past.  But I think it is 
becoming less true today.  Or, at least, it is becoming more
common to mix geometric topics into the high school mathematics
curriculum each year without devoting a whole year to geometry
as was done in the past.  This has the unfortunate effect that
students who take this sort of ``integrated mathematics curriculum''
in high school are not introduced to the idea of proof in mathematics
to the same extent as was true in the past.
\item{3.}  Careful here -- Eratosthenes' calculation gave an estimate
for the {\it circumference} of the Earth (essentially assuming that
it had a spherical shape).  This is not actually a proof that the 
Earth has that shape, though.  

I think you could also have said a bit more about the meaning of the
Pascal quotation.  You are on the right track there, but there is
another aspect of this.    Pascal is also saying that the strict Euclidean
style of thinking can be {\it quite limited} if it
is taken too far.  To paraphrase what Pascal is getting at:
This approach to problem-solving does not
take into account that situations in the real world humans must
deal with are rarely so clear-cut and orderly because they involve
things like feelings and attitudes that may not be logical.  So people who
try to rely on this sort of thinking when it does not really apply are
frequently drawn into incorrect conclusions.  I have to say that
from my experience, Pascal is perfectly correct here!  
\bigskip
\noindent {\it Content and Structure -- The paper:}
\bigskip
\item{1.}  (10) Has a clearly stated topic or question that it will address -- 10
\item{2.}  (10) Does address the stated topic or question -- 10
\item{3.}  (15) Presents a good understanding of the issues raised in the quotations -- 13
\item{4.}  Has a clearly articulated and logical structure:
\bigskip
\itemitem{a.}  (15) First paragraph lays out the topic or question -- 15
\itemitem{b.}  (15) Later paragraphs have topic sentences and clearly
identifiable main ideas -- 15
\itemitem{c.}  (10) Transitions between paragraphs are logical -- 10
\bigskip
\item{4.}  (10) Is concise, clear, and not too repetitive -- 8
\item{5.}  (15) Has a clearly identifiable conclusion that draws together the ideas presented -- 15
\bigskip
\noindent {\it Style and English Usage -- The paper:}
\bigskip
\item{1.}  (20) Is clear and direct in its use of language -- 20
\item{2.}  (10) Is free of misspellings -- 10
\item{3.}  (15) Is free of grammatical mistakes (e.g. subject/verb agreement, proper use of pronouns) -- 14
\item{4.}  (10) Lacks incomplete sentences -- 10
\item{5.}  (15) Lacks run-on or overly complicated sentences -- 15
\item{6.}  (15) Uses correct punctuation -- 15
\item{7.}  (15) Is free of colloquialisms, cliches, and misused words -- 15
\bigskip
\noindent
{\it Totals:}  Content and Structure -- 96; Style and English Usage -- 99.
\bye
