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Conic Sections: Real World Applications
Transcript of Conic Sections: Real World Applications
New Atlanta Falcons Stadium
Light shadow on a wall from a lamp
Lines on a basketball
An hour glass
Although most students think that conic sections can only be used in math, they can actually be found in every day life.
There are four basic conic sections. There are parabolas, hyperbolas, circles, and ellipses.
An example of a parabola in real life is a rainbow because it has one branch. Even though a rainbow can not be used, it can be a benefit by being an example of a parabola in order to help students learn the concept.
A parabola is a curve found on a point on a graph that is the same distance between its focus and directrix.
Roller coasters are a good example of parabolas because they curve in one direction. It is useful for roller coasters to have this conic shape because it gives the riders the anticipation of climbing up a hill, reaching the peak, and coasting down at high speeds.
Another example of parabolas in real life are suspension bridges. These are a good example because it shows that parabolas can point up or in a positive direction too. They are helpful because they keep the bridge from falling. Without the curve of the bridge, it would not be stable enough to be used for transportation.
At first glance, one might think that a basketball is an example of a circle, and they are correct. However, if looked at closely, one would see that the lines on the basketball form hyperbolas. These hyperbolic lines on the basketball are beneficial to players because it gives them an indication of where to put their hands on the ball.
A hyperbola is a conic section that can be described as a reflection of a parabola.
An hour glass is a great example of a hyperbola because in the middle of the glass on both sides, the glass comes in with an arch. The hyperbolas in an hour glass are useful because before we had clocks they were used to tell when an hour had passed.
Typically, lamps are not considered the best examples of hyperbolas, but when they are turned on and the light shines against the wall, the shape of the shade creates light hyperbolas on the wall. Although this can not be used, it is something that we use and see every day but do not think about relating to conic sections.
A circle is when all the points on the graph are the same distance from the center.
Although the sin might not be a perfect circle, it is still a great example of what a circle on a graph looks like. It is important that the sun is a circle because God made it that way to evenly distribute heat to the region of the earth that is facing the sun.
Car tires are a good example of a circular conic section because they have to be exactly round or the car will not run correctly. The tires and wheels being circles is useful and important because without that, car rides would be very bumpy and uncomfortable.
Although not all watch faces are perfectly round, the majority of the watches made do have a circular face. It is useful that the watch face is a circle because it can help us tell the time accurately when we are dealing with the big hand and the little hand.
An ellipse is similar to a circle in the aspect that it is cylindrical, but it is different because on a graph, there will be one axis where the points are more stretched than the other axis.
Although some football stadiums are circular, the new Atlanta Falcons stadium is going to be an elliptical shape. This is useful and important because it will allow the maximum amount of fans to be able to attend each home game as possible.
The Hyundai logo is an example of an ellipse because the oval shape that surrounds the "H" would stretch farther on the x-axis than it would on the y-axis. Although this can not be used in day to day life, the ellipse is a good way to make a product line stand out from others such as BMW or Mercedes.
Lemons are an example of an ellipse because if they are hanging from the branch, they would be stretched farther on the y-axis, but if they are laying on a counter top, they will be stretching farther on the x-axis. Lemons can be useful for many things throughout the day, and their elliptical shape allows them to be cut into more pieces in order for restaurants to save money.