Jobs That Use Geometry

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 
   should buy. She told me she had simply added all the numbers 
   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/