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### Jobs That Use Geometry

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Date: 12/18/2001 at 16:24:24
From: Keesha
Subject: Jobs related to Geometry

Dr. Math,

What are jobs that use geometry? I would like to learn how geometry
is used in real life. I am wondering what jobs involve geometry so
that I can know that I will some day use the information that I am
learning.

Thanks for your time and consideration.
Keesha
```

```
Date: 12/18/2001 at 17:45:41
From: Doctor Sarah
Subject: Re: Jobs related to Geometry

Hi Keesha - thanks for writing to Dr. Math.

Some contributions to the discussion group geometry-pre-college on
this topic may be helpful to you:

A few years ago, I attended a math teachers' conference.
The theme of this conference was applications of mathematics
in the workforce. The speaker who made the biggest impression
on me was a representative from a carpenters' union. He showed
us the entrance exam for their apprenticeship program. He said
that nearly of the rejected applicants were people who had
trouble with the math. This was not heavy stuff.  All of the
mathematics is introduced in or before eighth grade. A typical
geometry question would ask how much concrete is needed for a
footing with these dimensions, or how much fencing is needed
to enclose the region in this sketch. Carpentry generally does
not require much formal education, but some of their applicants
thought all they had to do was show up. - Paul Kunkel

I work in discrete applied geometry. Let me briefly describe
a few of the areas where I encounter geometry being used.
(a) Computer graphics is based on geometry - how images are
transformed when viewed in various ways.
(b) Computer-aided design, computer-aided geometric design.
Representing shapes in computers, and using these descriptions
to create images, to instruct people or machines to build the
shapes, etc. (e.g. the hood of a car, the overlay of parts in a
building construction, even parts of computer animation).
(c) Robotics. Robotic vision, planning how to grasp a shape with
a robot arm, or how to move a large shape without collission.
In (b) and (c) there is a field called 'computational geometry'
that involves algorithms for how to efficiently do these
calculations. There are many interesting issues and problems,
some of which can be understood in high school math.
(d) Medical imaging - how to reconstruct the shape of a tumor from
CAT scans, and other medical measurements.  Lots of new
geometry and other math was (and still is being) developed for
this.
(e) Structural engineering. What shapes are rigid or flexible,
how they respond to forces and stresses. Statics (resolution
of forces) is essentially geometry. This goes over into all
levels of design, form, and function of many things. I have
attended some interesting architecture and design conferences
where all of this flows together - sometimes (in North
American culture) with people knowing too little geometry to
do some of the things well.
(f) Protein modeling. Much of the function of a protein is
determined by  its shape and how the pieces move. Mad Cow
Disease is caused by the introduction of a 'shape' into the
brain (a shape carried by a protein). Many drugs are designed
to change the shape or motions of a protein - something that we
are just now working to model, even approximately, in
computers, using geometry and related areas (combinatorics,
topology).
(g) Physics, chemistry, biology, .... .  Symmetry is a central
concept of many studies in science - and also the central
concept of modern studies of geometry. Students struggle in
university science if they are not able to detect symmetries of
an object (molecule in stereo chemistry, systems of laws in
physics, ... ). the study of transfromations and related
symmetries has been, since 1870s the defining characteristic of
geometric studies. - Walter Whiteley

Here are a few professions that depend on geometry. First of all,
if you look at the derivation of the word, geo (earth) and metrics
(measurement) you have a description of what land surveyors do.
Two other occupations that have long depended on geometry are
navigation (figuring out how to get from point A to point B, and
knowing where one is at all times along the way) and astronomy.
Engineers who design all kinds of structures, from bridges to
airplanes to automobiles, use geometry to help determine the
stresses and strains of each part of a structure so that all
parts of the structure can be made strong enough. Try putting
the terms "finite element analysis" into your favorite search
engine and see what you find. NASA developed one of the best-known
packages of finite element analysis software, called NASTRAN.
The people who wrote the computer software to produce the animated
films "Monsters Inc." and "Toy Story" used geometry to make the
critters look real. - Tom Johnson

Last month I received a call from an acquaintance, a stock broker
at a major firm, that rather shocked me. She knew that I was a
geometry teacher and said she had come across a hard math question
for me to solve. I suppose I was expecting something along the
lines of a question on fractals and how they might be related to
chaotic behavior of the stock market. But no. Her question was
this:  a clerk at the paint store told her that a one gallon can
of paint would single coat 400 square feet, and she wanted to
paint the four rectangular walls of her bedroom, each of which was
12 feet long and 8 feet high. She wanted to know how many cans she
together to get 12 + 8 + 4 = 24 and then divided 400 by 24 to get
about 17, but intuitively knew that was too many cans to buy. She
also told me she knew the solution had something to do with
addition or subtraction or multiplication or division, but she
couldn't figure out the "right order" to do it in and thus was
calling upon my "expertise" for assistance. I must confess that I
was fairly stunned that a stock broker, whom one would assume uses
far more sophisticated mathematics than this on a daily basis in
the course of her work, would have so little number sense as to be
stymied by this relatively simple problem. - Steve Earth

My father was a tool and die maker for the Boeing Company in
Seattle for nearly 30 years. He created the tools that made the
parts that made the planes that you fly on. If the engineer asked
for a screw that was 6 inches long and would screw in with 4.5
twists, he would be the person to make the tool to create that
part... all with geometry and trigonometry. I have to admit that
when I was younger, I thought of his occupation as just a very
"blue collar" job. He hadn't finished high school (left school
during the depression). What could he possibly know about
mathematics?  The summer after my freshman year in college as a
mathematics major I went to work for the Boeing Company as a
mathematicians' assistant, and I had the opportunity one day to
wander down to his workstation and to see what he really did. Boy,
Oh Boy. Were my eyes opened. He knew more about the applications of
geometry and trigonometry than I will ever know. Unfortunately,
with the advent of computer technology, the need for this type of
skilled craftsman is declining. Too bad.... - Art Mabbott

We also have a number of questions and answers in what we call the
Practical Geometry area of the Dr. Math archives. They were sent to us
by people who were working on real problems. Take a look and see what
you can learn from them:

http://mathforum.org/library/drmath/sets/high_practical_geom.html

- Doctor Sarah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Higher-Dimensional Geometry
High School Practical Geometry
Middle School Geometry
Middle School Higher-Dimensional Geometry
Middle School Two-Dimensional Geometry

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