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## The Five Most Important Concepts In Geometry

After writing another article about everyday uses of geometry and real world applications of geometry principles, my head is spinning with everything I’ve found. Asking what I consider to be the five most important concepts on the subject “gives me pause.” I spent almost my entire teaching career teaching algebra and avoiding geometry like the plague, because I didn’t have the current appreciation for its importance. Educators who specialize in the subject may not fully agree with my choices; But I’ve settled on just 5 and I’ve done that by considering everyday uses and real-world applications. Some concepts keep repeating, so they are obviously important to real life.

**5 Most Important Concepts in Geometry:**

**(1) Measurement.** This concept covers many areas. We measure distances large, like across a lake, and small, like the diagonal of a small square. For linear (straight line) measurements, we use the appropriate units of measurement: inches, feet, miles, meters, etc. We also measure the size of angles and we use a protractor to measure in degrees or we use formulas and measure angles in radians. . (Don’t worry if you don’t know what a radian is. You obviously didn’t need that piece of knowledge, and you’re unlikely to need it now. If you do, send me an email.) We measure weight—ounces, pounds, or grams. in; And we measure capacity: either liquid, such as quarts and gallons or liters, or dry with measuring cups. For each of these I have given some common units of measurement. There are many more, but you get the concept.

**(2) Polygons.** Here, I am referring to shapes made with straight lines, the actual definition is more complicated but not necessary for our purposes. Triangles, quadrilaterals, and hexagons are primary examples; And with each figure there are additional things to learn and measure: length of individual sides, perimeter, median, etc. Again, these are straight line measurements but we use formulas and relationships to determine measurements. With polygons, we can measure the space within the figure. This is called “area”, actually measured with small squares inside, although actual measurements, again, are found with formulas and labeled as square inches, or ft^2 (feet squared).

The study of polygons extends to three dimensions, so that we have length, width, and thickness. Boxes and books are good examples of 2-dimensional rectangles given a third dimension. While the interior of a 2-dimensional figure is called “area,” the interior of a 3-dimensional figure is called volume, and there are of course formulas for that as well.

**(3) Circles.** Since circles are made with straight lines, our ability to measure the distance around the space inside is limited and requires the introduction of a new number: pi. “Perimeter” is actually called perimeter, and both perimeter and area have formulas involving the number pi. With circles, we can talk about radii, diameters, tangents and different angles.

Note: There are math purists who think of circles as being made of straight lines. If you picture each of these shapes in your mind as you read the words, you will discover an important pattern. are you ready Now, if all the sides in the picture are equal, make a picture in your mind or draw on a piece of paper a triangle, a square, a pentagon, a hexagon, an octagon, and a decagon. Do you remember what’s going on? Right! As the number of sides increases, the image appears more and more circular. Therefore, some people consider a circle to be a regular (all equal sides) polygon with an infinite number of sides.

**(4) Techniques. **It is not a concept in itself, but different things are learned in each geometry subject techniques. These techniques are used in all construction/landscaping and many other fields as well. There are techniques that allow us to make lines parallel or perpendicular in real life, force corners to be square, and find the exact center of a circular area or spherical object–this is not an option when folding. There are techniques for dividing lengths into thirds or sevenths that would be extremely difficult with hand measurements. All of these techniques are practical applications that are covered in geometry but are rarely embraced to their full potential.

**(5) Conic Sections.** Picture a pointed ice cream cone. The word “conic” means cone, and conic section means the pieces of a cone. Cutting the cone in different ways results in different shapes. A straight slice gives us a circle. Slicing at an angle turns a circle into an oval, or ellipse. A different angle produces a parabola; And if the cone is double, the vertical segment produces a hyperbola. Circles are usually covered in their own chapter and are not taught as conic sections unless conic sections are taught.

The main emphasis is on the applications of these figures – parabolic dishes for sending light rays into the sky, hyperbolic dishes for receiving signals from space, hyperbolic curves for musical instruments such as trumpets, and parabolic reflectors around light bulbs in flashlights. There are elliptical pool tables and exercise machines.

There is another concept that I personally consider **The most important and this is the study of logic**. The ability to use good reasoning skills is very important and is increasing as our lives become more complex and more global. When two people hear the same words, understand the words, but come to completely different conclusions, it is because one party is ignorant of the rules of logic. Not to put too fine a point on it, but a misunderstanding can start a war! Reasoning needs to be taught in some way **every** school year, and it should be a required course for all college students. Of course, there’s a reason why it doesn’t happen. In fact, our politicians, and power people depend on an ignorant public. They rely on it for control. An educated public cannot be controlled or manipulated.

Why do you think this is so? *many things *About education reform, however *Such a small task*?

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