ELLIPSES!
- What is the mathematical definition of this conic section and how does that definition play a role in the properties of the conic section and how it is shaped or formed?
The mathematical definition of an ellipse can be determined by two points, each called a focus (plural: foci). An ellipse is considered an ellipse by taking any point on the ellipse, and seeing that the sum of the distances (from the point) to the focus points is CONSTANT.
The sum of these distances is equal to the length of the
major axis, which is 2a. The position of the foci determine how "skinny" or "fat" the ellipse will be.
- How does the focus (or foci) affect the shape of the conic section?The position of the foci determine how "skinny" or "fat" the ellipse will be. The position of the foci also attributes to the eccentricity of an ellipse. The eccentricity of an ellipse is between 0 and 1. So 0<e<1
http://www.mathopenref.com/ellipse.html
Click on the link above and move the focus around, notice what happens to the graph!
The trend here is that the closer the foci are to the center of the ellipse, the more round the ellipse will become (much like a circle) This means that the ECCENTRICITY of the ellipse is getting closer to zero. As the foci move further away from the center, the ellipse becomes more squished (like an oval). This means the ECCENTRICITY of the ellipse is getting closer to 1.
- How do the properties of this conic section apply in real life?
An example of an ellipse in real life is "The Whisper Chamber" at the United States capital. If you stand at one focus you can perfectly hear someone else whispering at the other focus. This is due to the reflective properties of ellipses regarding their focus points.
Another example is a lithotripter. It is a machine used in medicine to destroy kidney stones and gallstones. Shock waves are sent into a person's body to crush the stones into smaller pieces making them easier to pass.
The last example is orbital paths of planets. They orbit in an elliptical shape! Not circular.
This video will explain how Pluto's elliptical orbit around the sun works and is proven through an equation:
http://www.youtube.com/watch?v=YBbsb4N-KWM
CITATIONS:
First ellipse image: http://img.weburbanist.com/wp-content/uploads/2009/08/felice-varini-ellipse-rouge.jpg
Mathematical definition: http://www.mathopenref.com/ellipse.html
Website explaining position of foci: http://www.mathopenref.com/ellipse.html
Real life ellipse images: https://sites.google.com/site/arinsellipse/real-life-examples
http://illuminations.nctm.org/Lessons/MarsOrbit/2MarsOrbit-MarsEarth.jpg
Real life ellipses video: http://www.youtube.com/watch?v=YBbsb4N-KWM
