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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 admitting that there are far more visible and understandable applications for everyone of geometry than there are. for algebra. This is very hard to admit for a retired math teacher whose teaching preference has always been algebra! Algebra students constantly ask, “When are we going to use this?” Even when given believable answers to this question, they still believe that SOMEONE will use algebra, but it will never be them. Things are very different with geometry. There are some die-hards who feel it is 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 considering a description of some of the everyday uses of geometry, will virtually all agree that they do, indeed, use it every day.

So as not to repeat everything I said in the “Everyday Uses” article, I’m going to look at some specific industries and how geometry is critical to their success.

**3 real applications of the principles of geometry:**

**1. The construction industry.** Whether it’s building a storage building in your backyard, a single-family home, a new highway, a high-rise office complex, or the bridge around the Hoover Dam, the construction industry simply couldn’t not exist without the principles of Geometry. The entire industry relies on engineers first to design and plan the actual workflow of the work to be done. For example:

In Colorado Springs, we had two major intersections that were in serious need of redesign due to high accident/fatality rates and major traffic issues. One project was completed a few years ago and the second is nearing completion. In both cases, the solutions provided by each engineer planned to pass one road over the other. Once the designs were approved, the actual construction proceeded like a finely tuned machine. All work had to be done keeping the roads open to traffic. The project nearing completion is near my home, so I was able to observe every step of the construction plan and it was fascinating to see the math in action.

From initial surveying, to rough layout with earthmoving machinery, to drainage works, to paving temporary lanes for traffic adjustment, to pouring concrete, to removing the old road, working with local businesses to keep entrances accessible, constantly painting new lines as traffic needed to be rerouted, blocking nearby roads when ramps needed to be finalized, painting the new bridge (much of it hand painted main), setting up traffic lights with associated new lines to properly direct traffic, for what will be final cleanup and even landscaping – each step is an application of geometry. Linear measurements, area calculations for paint, volume calculations for concrete, strength calculations for vertical supports, angles, shapes, distances, curve calculations (they don’t believe in straight lines here – everything is curved), the perpendicular vertical support issues and parallel lane markings – pick any geometric subject and I can almost guarantee it was used at some point in the construction process.

**2. The medical field.** Because the construction is in front of us all the time, it’s easy to see the geometry happening. This is not true for the medical field. In medical research, microscopes are essential – the lenses are curves or more precisely conical sections. The cells and molecules studied have extremely important geometric properties. Calculating the quantities of drugs to be administered to patients requires knowledge of weight and mass. We now have a wide range of imaging machines – MRIs, CT scans, ECGs and even the modest x-rays. Transferring an image from one place to another involves geometry. The machines themselves are geometric applications. The field of robotics is becoming important in the performance of many surgeries. Admittedly, there are many other geometric applications in the medical field; and hopefully none of us will have to learn about medical applications unless we receive large sums of money to do so.

**3. The army.** Because Colorado Springs is home to Fort Carson, Shriver Air Force Base, The Air Force Academy – which is a working military base, and Peterson Air Force Base, and because Fort Carson was a primary source of troops for the Middle Wars. is, we again see the geometry used daily. A neighbor of mine was responsible for weight distribution when loading cargo and transport planes. The logistics of troop movements with all that will be needed for long periods of time is mind-boggling. And I for one don’t like to think about the huge amount of geometry involved in firing missiles, whether from the ground or from unmanned drones. And a particular irony for me is that after bombing everything, we go back and rebuild everything, and we’re back to building apps.

The more I write about geometry apps, the worse I feel about algebra. I know all of the apps I’ve mentioned here would also be impossible without algebra, but algebra just isn’t as tangible and visible. Suffice it to say that the real world requires both algebra and geometry.

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