who uses Geometry?
Algebryonic
Geometry in high school or junior college, you never really use much of it
again; you use algebra and trigonometry. Does any highschool Geometry get any
real world direct use?
Algebryonic
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Sky Rookie
"Algebryonic" <algeb...@cs.com> wrote in message
news:24r2p0ta0d0svs9ln...@4ax.com...
John
Most don't know the geometry behind it becasue we use speed squares
and what not, but what happens of I don't have my speed square?? Here
comes the geometry. also think about landscaping business.
Vladimir
>Euklidian Geometry in high school or junior college, you never
>really use much of it again; you use algebra and trigonometry. Does
>any highschool Geometry get any real world direct use?
>
>Algebryonic
>
The epicenter of an earthquake is determined by recording the start of
the primary (faster) and secondary (slower) waves at least at 3
seismographic stations. For simplicity, assume that the primary and
secondary waves travel at constant velocities vP and vS and neglect
the epicenter depth under the surface. Let the measured arrival times
of the primary waves to the points A, B, C (the 3 seismographic
stations) be tPA, tPB, tPC and let the measured arrival times of the
secondary waves to these points be tSA, tSB, tSC. The distances dA,
dB, dC of the epicenter from the 3 points A, B, C are in the ratio
dA : dB : dC = (tPA - tSA) : (tPB - tSB) : (tPC - tSC)
Construct the point E with a given ratio of distances from the
vertices A, B, C of a given triangle ABC.
Kevin Karplus
> On Wed, 10 Nov 2004 01:22:48 GMT, Algebryonic wrote:
>>Who really uses GEOMETRY in the real world? It seems like after
>>Euklidian Geometry in high school or junior college, you never
>>really use much of it again; you use algebra and trigonometry. Does
>>any highschool Geometry get any real world direct use?
>
> the primary (faster) and secondary (slower) waves at least at 3
> seismographic stations. For simplicity, assume that the primary and
> secondary waves travel at constant velocities vP and vS and neglect
> the epicenter depth under the surface. Let the measured arrival times
> of the primary waves to the points A, B, C (the 3 seismographic
> stations) be tPA, tPB, tPC and let the measured arrival times of the
> secondary waves to these points be tSA, tSB, tSC. The distances dA,
> dB, dC of the epicenter from the 3 points A, B, C are in the ratio
>
> dA : dB : dC = (tPA - tSA) : (tPB - tSB) : (tPC - tSC)
>
> Construct the point E with a given ratio of distances from the
> vertices A, B, C of a given triangle ABC.
It is true that few people use pure Euclidean geometry after high
school---almost all the applications use analytical geometry, which is
a combination of algebra, geometry, and trigonometry. Even the
example above is done numerically, not by straightedge-and-compass
construction.
I believe that the reason Euclidean geometry is still taught is
that it provides a good basis for explaining the concept of
mathematical proof. The proofs are less abstract and easier to
understand than proofs in other bransches of math, so provide a
relatively easy introduction. Also, a firm understanding of Euclidean
geometry probably makes trigonometry and analytical geometry easier to
learn.
------------------------------------------------------------
Kevin Karplus kar...@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus
Professor of Biomolecular Engineering, University of California, Santa Cruz
Undergraduate and Graduate Director, Bioinformatics
Senior member, IEEE Board of Directors, ISCB (starting Jan 2005)
life member (LAB, Adventure Cycling, American Youth Hostels)
Effective Cycling Instructor #218-ck (lapsed)
Affiliations for identification only.
Maurici Carbó
Are you asking about geometry? Who uses geometry?
We, the architects, use the geometry!
Carpenters, uses geometry!
Painters, use geometry!
Shutterers use geometry!
Any relation about 2D and 3D reality, needs the geometry!
If you make plans, maps or diagrams, you use geometry.
If you don't study geometry, later, you cannot understand the
Descriptive Geometry.
If you want to be a painter, you must understand Geometry. You must
know about perspective.
For to draw perspectives, you must know about the section of
cylinders, and cones.
Perspective is a knowledge obtained in the XV siecle. Is maybe too
early to forget this.
Perspective, needs a deep knowledge of a complex geometry, far from
the basic and simple 2D geometry that everybody usually learn in the
elementary school.
And many math problems, can be afforded with geometry.
You can solve algebra problems with geometry.
I stop here.
This letter can be endless.
Maurici Carbó
architect. (in Spain)
http://www.nummolt.org
On Wed, 10 Nov 2004 01:22:48 GMT, Algebryonic wrote:
Algebryonic
Most people who use geometry are using some intuitive sense of it or are using
geometry combined with trigonometry and analytic geometry. Original question
specified concepts + skills of the high school level course, without resort to
trigonometry. I have been weaned on the world of code and forming so many
expressions which often did not rely too much on geometry. During hard-core
education time, algebra and analytic geometry and trigonometry were usual
languages and methods of thinking. Most of high school geometry was not
needed. If I were an architect I would probably have a clearer idea how high
school geometry applies to architecture.
The painter situation uses 6th grade stuff; not high school level material.
Most painters I ever met did not study euclidean geometry.
The discussion of the earthquake epicenter was probably more along the lines
of what happens to most of geometry applications----- that trigonometry and
other parts of Mathematics take over, and that ordinary high school geometry is
not directly applied.
Algebryonic
m...@coac.net responds this way:
Guess who
>I work construction in the summer as a framer. There are many angles.
>Most don't know the geometry behind it becasue we use speed squares
>and what not, but what happens of I don't have my speed square?? Here
>comes the geometry. also think about landscaping business.
You'd be interested in an old woodworker's book, "The Carpenter's
Square", including even how to build a spiral staircase. It's all
about "layout", but there's a lot of math behind construcion
techniques making them valid, and a LOT of math in the carpenter's
square.
Guess who
wrote:
>Most of high school geometry was not
>needed.
It was, for two reasons at least:
1. Development. Theorems, and ideas are joined at the hip. They are
not distinct and separate but evolve one from another and complement
each other, and the study of that evolution is as important as the
subject itself as a training ground.
2. Completeness. Compare to the dictionary. Are all those words
really necessary?
If suggesting not all people use them, that's true of any study. Some
people spend their life on the end of a shovel.
Wendy
of beauty. I first began to love math in junior high when I found out
that 20 triangles could become an icosahedron, and I made and
decorated many icosahedra to give to my family as Christmas ornaments
(which are still hung on their trees over 30 years later). Now I turn
to geometric math art and crafts as one means of reaching out
mathematically to children around the world and turning them on to the
joy and beauty of math.
See the Math Crafts area of my Math Cats site:
http://www.mathcats.com/crafts.html
See "The Math Cats Visit Geometric Sculptor George Hart":
http://www.mathcats.com/explore/sculptor.html
See the Math Art Gallery at Math Cats:
http://www.mathcats.com/gallery.html
See a how-to website full of simple but beautiful geometric math art
and crafts at (the unfortunately-named) "William's Home Page" -
http://www.cyffredin.co.uk/
See the fascinating site of geometric sculptor George Hart:
http://www.georgehart.com
I purchased a geometric sculpture created by George Hart and it hangs
in our living room now. It is a truncated icosahedron (a buckyball
-or in more functional "real life" terms a soccerball) modeled after a
drawing by Leonard Da Vinci, and I believe George told me it is
constructed from 192 pieces of carefully-cut wood (with two angled
pieces forming each edge). Please agree with me that George used
geometry in designing and constructing it.
Perhaps I am reading too much into the question and follow-up by the
same questioner. The implied though unstated premise or question
seems to be that if Euclidean geometry cannot stand on its own with
real-world applications untainted by other branches of mathematics
then why do we ask students to study it? If this *is* the underlying
question, I think it is quite surprising. It is perfectly legitimate
for one body of knowledge to be applied within another body of
knowledge without negating the value of the first body of knowledge,
even if most people do not use the first body of knowledge in
isolation. Turning to another subject area by way of analogy, this
would be like saying: "Who uses grammar in the real world? Grammar
is only used in the context of composing or understanding or
appreciating sentences and paragraphs and essays and stories and
novels and nonfiction and PhD theses and [ .... ] and therefore a
basic knowledge of the structure of our language is of dubious value
in its own right." (If you agree with this statement, we can debate
it on another list!)
Highlighting a couple of the other statements made in support of
learning Euclidean geometry, my high school geometry teacher launched
our course by telling us that for most of us this would be the only
formal course in logic that we would ever take, and for this reason if
no other the course was important. If any of us or our students have
ever applied the principles of writing proofs to any other life
situation, then the exercise has been of value. And even if we've
never found a real-life application for this skill, the exposure to it
has been of value.
Taking it to an extreme, my older sister used to drive my mother crazy
by refusing to memorize anything in geometry except the few theorems
on which everything else was built. She would go into each test and
rebuild and reprove the whole course up to that point. My mother
would say, "Wouldn't it be a lot easier and safer if you just
memorized the new material?" and my sister would dismiss this notion
because she loved the intellectual challenge of starting over from
scratch in one class period. My sister is now a brilliant scholar in
international law. She doesn't reconstruct Euclidean geometry in her
daily work, but I'm quite sure she applies the same mental rigor in
everything she does.
I'd also like to point out that for many people, geometry makes sense
and algebra by comparison seems mysterious and abstract. My second
son struggled through algebra in high school but breezed through
geometry and finally (sort of) enjoyed a high school math course.
After that he had no problem with Algebra II with Analysis and
Calculus. The course in geometry had at given him a handle on
visualizing and understanding and appreciating and applying abstract
math concepts to (pretend) real-life situations. He never did learn
to love math but at least he felt comfortable with it after geometry
gave him a solid handle to grasp.
There are lots and lots of things we learn in school (and outside of
school) without an expectation that we will use them in our future
work. Did any of us play an instrument in a school band or orchestra,
and are any of us now professional musicians? Did we not find the
experience of playing an instrument to be of value all the same?
Didn't it enhance our appreciation of music as a spectator sport and
didn't it empower us as we experimented with little tunes not written
in the music books? And didn't we learn some self-discipline, and
didn't we learn that something that at first seems overwhelming can be
mastered with patience and perseverence and taking it one step at a
time? And didn't we apply some of this broader knowledge in other
aspects of our lives?
But to paraphrase a math teacher I know who wrote in answer to a
similar "who needs this" sort of question on a math teachers'
chatboard: No one knows your future. As you are learning in school,
it is not always clear if or how you will use this new knowledge. We
don't know yet what will capture your imagination and inspire you to
pursue a certain path in life. So what we as teachers are doing is
introducing you to a broad base of knowledge in a wide variety of
areas. It will all be of value to you as you become a well-rounded
person, and it will position you to be ready to pursue one path in
depth later on.
As Maurici writes: I'll stop now. This letter could be endless!
Wendy P.
Math Cats
www.mathcats.com
On Wed, 10 Nov 2004 01:22:48 GMT, Algebryonic wrote:
> Who really uses GEOMETRY in the real world?
> It seems like after Euklidian Geometry in high school
> or junior college, you never really use much of it
> again; you use algebra and trigonometry. Does any
> highschool Geometry get any real world direct use?
--
Algebryonic
art and beauty. I am slowly finding out about how architects use Geometry. I
saw a short description about using trapezoids and angles for part of a
building.
Algebryonic
--
Chergarj
how to make geometric constructions with a plain book.
Finding applications in the real world which ONLY use high school geometry is
difficult but for promoting some interesting techniques for learning high
school geometry, that site is interesting.
G C