If you are a teacher, chances are high that you are always looking for new and innovative methods to teach children challenging mathematics concepts. Don’t you? Mathematics, at times, can be a challenging and difficult subject to study and understand.
If concepts are not introduced properly, children suffer to learn and understand the concept accurately. Although, there are always some fun ways to make mathematics interesting and easy to understand. One such method is introducing the real-life applications of the concept to the students.
It will help children better relate to the concept, resulting in better understanding. In this article, we have discussed some real-life applications of tangents and normals for making the concept easy and interesting.
First, let’s begin by decoding what tangents and normals are.
Decoding tangents and normal
Tangents and normals are the features of curves. They are the straight lines used to represent the characteristic features of curves and other related geometrical figures. Examples of geometrical figures, important for tangent and normal, involve circles, parabolas, hyperbolas, ellipses, ovals, etc.
Tangents and normals are two different lines that are applied together to identify the speed and direction of moving objects. Let’s decode both of the terms individually to get a better idea of the concept.
What are tangents?
A Tangent is any straight line that externally touches a curve at any specific point, and the tangent goes in the same direction as the curve. In other words, only one tangent will touch a specific point of the curve at one time and will move in the direction of the curve itself. The point where the tangent touches the curve is known as the point of tangency.
For instance, you are riding your bike on a curvy hill, which is an example of a parabola, at full speed. The curvy hill is the curve required for applying the concept. The tangent line is the direction where the bike is going, and any point that your bike is touching the hill is the point of tangency. Your direction is tangent to the hill, which is in the same direction you are riding your bike since tangents move in the direction of the curve.
What are normals?
Normal to the curve is any straight line that will pass through the curve and be perpendicular to the tangent, passing through the point of tangency.
For instance, continuing with a bike example, you wish to know in which direction you are turning your bike on the curvy hill at that specific point. The perpendicular line to your tangent (the direction you are going) will represent the normal. Here, normal will help you understand the change in direction concerning tangents on the hilly road.
Characteristics of tangents and normal
Now that you have a clear idea of tangent and normal (we hope you have!) Let’s understand some of its important characteristics for better comprehending its applications. The characteristics of tangents and normals are-
- Tangents and normals are always perpendicular to each other.
- The straight line will only be called a tangent if there is a normal present perpendicular to it.
- Tangents and normals are straight lines. Hence they will always be represented using linear equations.
- Generally, normal passes through the center of the curve, but it can vary according to the situation.
- There is no limit to points of tangent on the curve. They can be endless.
Tangents and normal: Some real-life applications
Tangents and Normals have their application more in the real world than in books. If you are trying to spread the pipelines underground or swinging a merry-round, tangents and normal are profoundly applied there. Some real-life applications of tangent and normal are-
The field of architecture relies heavily on tangents and normals. Designing and creating architectural pieces requires knowledge of intersections, joinery of different parts of buildings, interior designing, spacious layout, sense of lighting, etc. All these elements work best if tangent and normal are applied to them and then designed into the architectural piece.
2. Force and motion of objects
Tangents and normals are applied to various areas of physics, such as identifying the force applied and the motion of different objects. Tangent and normal help to identify which direction an object is moving and predict its direction if there is any change in velocity or motion.
3. Illustrations and computer graphics
Arts & crafts, portraits, and illustrations require tangent and normal for highlighting different aspects of art, adding lighting and shadowing to bring a real look to the illustrations, bringing contrast in different elements of the illustrations, and so on. Tangents and normals are also used to represent the detailing on the surface, creating realistic models or portraits by highlighting correct angles and making background and foreground appealing and easy to differentiate. Computer graphics also use tangent and normal to make the graphics more realistic.
Tangents and normal play a crucial role in the field of aerodynamics. From designing the aircraft and its wings to flying the aircraft, considering the concept of tangent and normal is important. The direction air is moving can impact the movement of aircraft or pressure distribution in the aircraft, hence, to deal with these situations, knowledge and application of tangents and normals are important.
5. Studying sound waves or water waves
Tangents and normal are used to study the sound proportion and the direction where the sound wave will travel. They are also useful in assessing the reflection of sound waves and the path it will take to reach the surface. The same concept is applied to water waves. The direction in which waves move and the concept of wave crust or wave trough is studied using tangent and normal.
6. Medical field
Another major area where tangent and normal are applied is the medical field. Knowledge of the orientation and structure of different anatomical parts is necessary to conduct and study medical tests such as MRI, CT Scans, etc. Tangents and normal ensures that imaging is done from the right angle and the distortions are minimum in the scans obtained. Additionally, studying cellular samples or different species under a microscope requires proper alignment of the samples for accurate results, which can be done through tangent and normal.
Tangent and normals are applied to the field of optics to study the processes like reflection, refraction, deviation of light from the surface, etc. The passing of light through the prism and the angle it will form, and in which direction is also determined through tangent and normal. Lens or optic fibers are also designed and applied based on tangent and normal.
Astronomy is another domain that relies heavily on the application of tangent and normal. To determine the orbital mechanics or celestial coordination, tangent and normal are handy. Additionally, studying how different celestial bodies are organized, their position in space relative to other celestial bodies, and how light travels between different celestial bodies also requires the application of tangent and normal.
Cartography, or the art of making maps, is another important application of tangent and normal. Maps are of different types, such as some representing countries, some representing counties, localities, or even specific streets to reach some specific location. To accurately design the map, organizing and positioning different locations, tangents and normal are important.
A rapidly growing field called robotics also involves the application of tangent and normal. Robots or AI machines require preset programs of orientations, positions, directions, motions, speed, distance, etc. Though to preset these elements, they need to be extensively tested and then applied, which can require the use of tangent and normal. Also, fixing or joining different parts of the robot requires the application of tangent and normal for its accurate functioning and movement.
Tangents and normals is a widely used mathematical concept applied in various domains. Understanding the real-life application of the concept will help children better comprehend the concept. Children can also engage in online games and math activities to enhance their knowledge of the mathematical concept. Additionally, the right tips and strategies for studying mathematics alone or with peers can help students get a better hang of the concept.
I am Sehjal Goel, a psychology student, and a writer. I am currently pursuing my Masters’s from Banaras Hindu University, Varanasi. Child psychology has always fascinated me and I have a deep interest in learning about disabilities in children and spreading awareness regarding the same. My other areas of interest are neuropsychology and cognitive psychology. Connect me on Linkedin