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## Real World Applications of the Principles of Geometry

I recently wrote an article about the everyday uses of Geometry and found myself having to admit that there are many more applications of Geometry that are visible and understandable to everyone than there are for Algebra. This is very hard for a retired math teacher whose teaching preference was always algebra to admit! Algebra students constantly ask themselves, “When are we going to use this?” Even when given credible answers to this question, they just believe that SOMEONE will use algebra, but it will never be them. Things are very different with geometry. There are a few who feel it their duty to ask “the question” in every math class they take, but for the most part, students can see that geometry is everywhere. Adults, after looking at a description of some of the everyday uses of Geometry, will almost all admit that they do, in fact, use it every day.

In order not to repeat everything I said in the “Everyday Uses” article, I will look at some specific industries and the ways in which geometry is critical to their success.

**3 Real-world applications of the principles of geometry:**

**1. The construction industry.** Whether the purpose is to build a backyard storage building, a single-family home, a new highway, a high-rise office complex, or the bridge over the Hoover Dam, the construction industry simply could not exist without the principles of Geometry. The entire industry depends first on engineers to design and plan the actual course of work at hand. For example:

In Colorado Springs, we have had two major intersections in serious need of redesign due to high accident/fatalities and major traffic issues. One project was finished a couple of years ago, and the second is nearing completion. In both cases, the solutions provided by each engineer called for one path to pass over the other. Once the designs were approved, the actual construction proceeded like a fine-tuned machine. All work had to be done while keeping the roads open to traffic. The project nearing completion is close to my home, so I’ve been able to observe every step of the construction plan and it’s been fascinating to see the math at work.

From the initial survey of the land, to a rough layout with earthworks, drainage work, paving temporary lanes for traffic adjustment, pouring concrete, removing the old road, working with local companies to keep inputs accessible, constantly paint new lines. as traffic needed to be re-routed, nearby roads blocked when the ramps were to be completed, the new bridge actually painted (much of it hand-painted), traffic signals put in with associated new lines to properly direct traffic, what will be final cleaning and even landscaping – every step is an application of geometry. Linear measurements, area calculations for paint, volume calculations for concrete, resistance calculations for vertical supports, angles, shapes, distances, curve calculations (here they don’t believe in straight lines, everything curves), the problems of Perpendicular Vertical Supports and Parallel Rail Markings – Pick any geometric theme and I can almost guarantee it was used at some point in the construction process.

**2. The medical field.** Since the construction is in front the whole time, it’s easy to see that the geometry is happening. This is not true for the medical field. In medical research, microscopes are essential: the lenses are curves or conical sections with greater precision. The cells and molecules that are studied have very important geometrical properties. Calculating the amounts of medication to give to patients requires knowledge of weight and mass. We now have a wide range of imaging machines: MRI, CT, EKG and even low X-ray. To transfer an image from one place to another involves Geometry. The machines themselves are geometric applications. The field of robotics is gaining importance in performing many surgeries. Certainly, there are many more geometric applications in the medical field; and hopefully none of us have to get too familiar with medical apps unless we’re being paid big bucks to do so.

**3. The military.** Because Colorado Springs is home to Fort Carson, Shriver Air Force Base, the Air Force Academy, which is an active military base, and Peterson Air Force Base, and because Fort Carson has been a major source of troops for the Middle Wars. in the east, we again see geometry being used daily. One of my neighbors was responsible for weight distribution when loading cargo and transport aircraft. The logistics of troop movements with everything that will be needed over long periods of time boggles the mind. And I, for one, don’t like to think about the sheer amount of geometry involved in firing missiles, either from the ground or from unmanned drones. And a particular irony for me is that after we bomb everything, we go back and rebuild everything, and we go back to building apps.

The more I write about geometry applications, the worse I feel about algebra. I know that all the applications I have mentioned here would also be impossible without Algebra, but Algebra is not as tangible and visible. Suffice it to say that the real world requires both algebra and geometry.

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