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Conic Sections in Everyday Life

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Gisselle Saravia

on 2 February 2014

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Transcript of Conic Sections in Everyday Life

Conic Sections in Everyday Life
Automobile Headlights
"Car Headlights"- http://www.google.com
Circles
Intro to Conic Sections
There are four conics in the conics sections- Parabolas, Circles, Ellipses and Hyperbolas. We see them everyday, but we just don't notice them. They appear everywhere in the world and can be man-made or natural. The applications of conics can be seen everyday all around us. Conics are found in architecture, physics, astronomy and navigation. If you get lost, you can use a GPS and it will tell you where you are (a point) and it will lead you to your destination (another point). Bridges, buildings and statues use conics as support systems. Conics are also used to describe the orbits of planets, moons and satellites in our universe. Conics have also helped man kind. Conics are everywhere.
Parabolas
Parabolas are really common in our daily lives. Parabolas can be found in most things we encounter everyday. Parabolas are formed when a football is kicked, a baseball is hit, a basketball hoop is made, dolphins jump and much more. A parabola forms when a comet shoots across the sky. Parabolas have helped mankind in many ways. One example, is astronomy. Sometimes, parabolas are used to determine the distance of the rocket ship traveling up in the sky. The Eiffel Tower is known worldwide to be in the form of a parabola. Thousands of people see the Eiffel Tower everyday, yet they don't notice the significance of how the tower is formed. They do not realize that the parabola is actually really important in the structure of the tower. The middle of The tower can be seen as the "Axis of Symmetry" because that is where the middle of the tower is. The bottom part of the Eiffel Tower seems as if it is showing a "negative parabola". The Eiffel Tower was built and designed this way so it could support the wind and so it would be more stable. Another significant item that helps us everyday is Automobile Headlights. Without them, there would be tons of accidents daily and we wouldn't be able to commute safely. When the headlights are turned on, the light takes shape in a parabolic manner and it shines in front of the car while moving. The headlights are in the form of a parabola and they also have a vertex (the starting point) and the focus (the point of the light that leads the rest). Parabolas are found everywhere and the shape has truly helped mankind.
Eyes
The part of the eye that can be compared to a circle, is the iris because the iris is the overall part and the pupil is the center.
The Eiffel Tower
"The Eiffel Tower"- http://www.google.com
The bottom of the Eiffel Tower is a parabola and it can be interpreted as a negative parabola because it opens down.
"Eyes Tumblr" http://eyes.tumblr.com
Roller Coasters
"The parabola is the form taken by the path of any object thrown in the air, and is the mathematical curve used by engineers in designing some suspension bridges. The properties of the parabola make it the ideal shape for the reflector of an automobile headlight."
Have you ever wondered why the best roller coasters are parabolic? When on a roller coaster, it feels like you're defeating or going against the force of gravity. When a coaster falls from the peak of a parabola, it is rejecting air resistance. In America, there are hundreds of theme parks and thousands of roller coasters. People of all different ages ride roller coasters but only a few notice that most roller coasters are in the form of a parabola.
"Roller Coasters"- http://www.google.com
The cups we use, the CD's and DVD's we watch, the caps we take off of our juice and water bottles, the soccer balls we kick, the pizza we eat and the list goes on and on. All these little things are just some of the objects that take a circular shape. Parabolas and Circles are probably the two most common conics because you can see these two shapes everywhere. Pizza, as significant as it may seem, is actually a really great example of how a circle works in the conic sections. The center of pizza is like the center of a circle because thats the point where everything meets/starts. The slices of pizzas can kind of be visualized as the radius of the circle because they extend towards the edge of the circle. Another example is "eyes". Our eyes are really important because without them, we wouldnt be able to see. Our eyes take the shape of a circle and our pupils can be compared to the center of the circle.
Pizza
Pizza is not a really significant concept in the world, and thats why, it makes a great example. People nowadays, do not make an effort to relate math to the real world when really, math has changed the world in so many ways. The simple idea of a "pizza" taking the shape of a circle shows how important conics really are in our daily lives.
"Pizza"- http://www.google.com
Clocks
Clocks are really useful and important because they help us keep time. Before, we used a sun dial to tell time but now we have the clock. But the clock has always taken the form of a circle. The middle of the clock is the "center" of the circle and the hands are the "radius".
"Clocks"- http://www.google.com
Ellipses
Ellipses are seen everyday and all around the world. We don't notice the importance of this conic, but it really has an impact on the world. There are many items that are used daily that take the form of a parabola. There's buildings, supplies, toys, foods and much more. Ellipses are actually really important because planets take an elliptical path. This occurs in our universe. Some foods that look like ellipses are lemons and eggs. Most of us eat eggs everyday but we don't realize that the egg actually takes the form of an ellipse. For example, an ellipse is formed when you tilt a glass of water. When the cup is tilted, the water all goes to one side, making the water uneven, forming an ellipse. Conics are really important because they help us daily.
Football
Many people play football...on a team or just for fun. The thing is that nobody notices the importance of why the football is shaped this way. Because the football is in the shape of an ellipse, it rotates and moves quicker. This makes it easier and much more convenient when throwing the ball long distance.
http://www.eteamz.com/ncyfl/
Tycho Brahe Planetarium
The Tycho Brahe Planetarium is located in Copenhagen, Denmark. It is in honor of Tycho Brahe, Danish astronomer. It was opened on November 1st, 1989. The building takes the form of an ellipse and it is clearly shown. Any cylinder sliced at an angle will reveal an ellipse.
"Tycho Brahe Planetarium"- http://www.google.com
The Planets
The early Greek astronomers thought the planets moved in circular orbits around an unmoving Earth. In the 17th century, Johannes Kepler eventually discovered that each planet moves in an elliptical pattern around the sun. The sun is the center of the "ellipse". Many people don't realize that we literally travel in an ellipse.
"Elliptical Orbit of the Planets"- http://www.google.com
Hyperbolas
A hyperbola is the mathematical shape that you obtain when vertically cutting a double cone. The hyperbola has a few properties that allow it to play its part in the real world. Many fields use this conic to help in design. Hyperbolas are the least common conics in daily life. They aren't seen as much or as often as the other 3 conics. Some examples are radios and satellites. Both of these use hyperbolic functions. When scientists launch a satellite into space, they must first use various mathematical equations to predict its path. By using hyperbolas, scientists can make sure that the satellite gets to its proper destination. There are many hyperbolic structures in real life.
Beyonce's Figure
Conics can even be seen in humans! Beyonce is known for having an hourglass figure, otherwise known as a hyperbola. A hyperbola is clearly seen in her body. The "asymptotes" can be seen going up and down. As mentioned before, conics are everywhere. They appear everywhere and most people don't notice.
"Beyonce's Figure"- http://www.google.com
The James S Mcdonnell Planetarium
The James S Mcdonnell Planetarium is part of the Saint Louis Science Center in St. Louis, Missouri. In the field of architecture, there are many buildings and statues that take the form of conics. In the architecture of the James S Mcdonnell Planetarium, a hyperbola is formed. In the middle, you can clearly see the "box" that is formed when the points are created. The asymptotes extend to the sides. Perhaps many people see this building but don't know that it is in the form of a hyperbola.
"James S Mcdonnell Planetarium"- http://www.google.com
Lamp Shade
When you turn on a lamp, you get a hyperbola. If the lamp is open from the top and the bottom, the light comes out and form a hyperbola. The asymptotes can be seen coming out from the top and the bottom.
"Lamp Shade Light"- http://www.google.com
Conclusion
Conics are really important in the real world. The main problem is that people don't notice that conics are everywhere and all around us. Circles and Parabolas are the two most common conics in the real world. Conics are so significant that we even find them in the food we eat and in even the people we meet. Not only do conics appear in our world but they also help us as well. Hyperbolas have really helped us in the the field of astronomy. There are four types of conics and they are parabolas, circles, ellipses and hyperbolas. Conics are so significant that we see them where ever we go, all around the world no matter where you are. You are always going to find conics in your surroundings.
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