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/
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