Having just written an article about everyday use of geometry and another article about real-world applications of the principles of geometry, my head rotates with everything I found. Being asked what I consider the five most important concepts in a topic, “give me a pause.” I have taught Algebra almost all of my teaching career and avoided geometry like the plague, because I did not have gratitude for its importance that I have now. Teachers who specialize in this subject may not agree with my choice; but I managed to install only 5, and I did it by viewing these everyday and real-world applications. Some concepts suppress repetition; therefore, they are obviously important for real life.
5 The most important concepts in geometry:
(1) Measurement. This concept covers many areas. We measure distances both large and across the lake, and small, as the diagonal of a small square. For a linear (linear) measurement, 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, (Do not worry if you don’t know what radian is.Obviously, you don’t need this piece of knowledge, and now you don’t need it.) If you need to know, send me an email. measure weight - in ounces, pounds or grams; and we measure power: liquid, for example, quarts and gallons or liters, or dried using measuring glasses. For each of them, I just gave a few common units of measurement. There are many others, but you get the concept.
(2) Polygons. Here I mean shapes made with straight lines. The actual definition is more complex, but not necessarily for our purposes. The main examples are triangles, quadrilaterals and hexagons; and with each figure there are properties to study and additional things to measure: the length of individual sides, perimeter, medians, etc. Again, these are direct measures, but we use formulas and relations to determine measures. With the help of polygons, we can also measure the space of INSIDE shapes. This is called "area", measured effectively with small squares inside, although the actual measure is again found with formulas and denoted as square inches, or ft ^ 2 (square feet).
The study of polygons extends to three sizes, so we have the length, width and thickness. Boxes and books are good examples of two-dimensional rectangles from the third dimension. While the “inside” of a two-dimensional shape is called a “region,” inside a three-dimensional shape is called volume, and, in addition, there are formulas for it.
(3) Circles. Since the circles are not 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. The “perimeter” is actually called a circle, and both the circle and the area have formulas containing the number pi. With circles, we can talk about the radius, diameter, tangent line and various angles.
Note. There are purist mathematicians who think of a circle as consisting of straight lines. If you draw each of these figures in your mind as you read the words, you will find an important picture. Ready? Now that all the figures are equal, draw in your mind or draw a triangle, square, pentagon, hexagon, octagon and decagon on a piece of paper. What did you notice? Correctly! As the number of sides increases, the figure looks steeper. Thus, some people consider a circle as a regular (all equal sides) polygon with an infinite number of sides
(4) Methods. This is not the concept itself, but in each geometry, subject methods teach you to do different things. These methods are used in construction / landscaping and in many other areas. There are methods that allow us in real life to force lines to be parallel or perpendicular, to cause angles to be square and to find the exact center of a circular area or circular object — when folded, this is not an option. There are methods for dividing lengths into a third or seventh, which would be extremely difficult when measuring hands. All of these methods are practical applications that are covered in geometry, but rarely fully employed.
5 conic sections. Draw a spiky ice cream cone. The word "conic" means a cone, and the conic section means cuts of the cone. Cutting the cone in different ways produces cuts of various shapes. Cutting straight through gives us a circle. Cutting at an angle turns the circle into an oval or ellipse. The corner makes a parabola differently; and if the cone is double, the vertical cut causes a hyperbole. Circles are usually covered in their own chapter and are not taught as a piece of cone until the conic sections are studied.
The main focus is on the application of these figures - parabolic dishes for sending rays of light into the sky, hyperbolic dishes for receiving signals from space, hyperbolic curves for musical instruments such as pipes, and parabolic reflectors around a light bulb in a lantern. There are elliptical billiard tables and fitness equipment.
There is another concept that I personally think the most important thing is the study of logic The ability to use good mental abilities is so important and becoming more and more, as our life becomes more complex and more global. When two people hear the same words, understand the words, but make completely different conclusions, this is due to the fact that one of the parties does not know about the rules of logic. Do not put too thin a moment, but misunderstandings can start a war! Logic needs something to teach in each a year of study, and it should be a necessary course for all college students. Of course, there is a reason why this did not happen. In fact, our politicians and authorities depend on the uninformed population. They count on it for control. The educated population cannot control or manipulate.
Why do you think that there is a lot of talk about improving education but so little action ?
