# Math projects on conic sections

Written by errin reaume
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The study of conic sections is one of the oldest studies in mathematics. "Discovered" during the times of the ancient Greeks, they were conceived in a attempt to solve the three famous problems of trisecting the angle, duplicating the cube and squaring the circle. The four conic sections are a circle, ellipse, parabola and hyperbola. Use this information to create engaging math projects for students.

## History of Conic Sections

The history of conic sections and of mathematics in general is a very interesting subject. The Greeks were among the first to "discover" and implement the laws of mathematics to change how they viewed and understood the world around them. Have students write a paper on the purported discoverer of the conic sections and what they were used for. Explain the use of conic sections today in practical application.

## Find the Conic Sections

Ask students to go home and find at least five different items for each conic section in their home. Students can measure the item to define which conic section it is and take a picture or draw each the items to turn in later in class. Examples of household items that are also indicative of conic sections are pot lids, spoons or the reflection of a light bulb on a wall. Students can also go to the library, mall or other public places to find these images.

## Liquid Conic Sections

Fill a cone-shaped glass about half way with juice or another coloured liquid. This project works best in class when explaining conic sections in real world scenarios. Show the students what the liquid looks like when it's flat on a table. The top of the liquid forms a circle. When the liquid is tilted slightly it forms an ellipse. Tilt it more to form a parabola and tilt it heavily to form a hyperbola. Show the student what each conic section looks like and encourage them to repeat the conic sections in their minds whenever drinking.

## Conic Sections in Orbital Mechanics

Johannes Kepler provided the key to orbital mechanics when he figured out it was impossible for all the planets to move in perfect circles, and instead they must move on ellipses. Conic sections are the basis for today's orbital mechanics. Ask students to research the orbit of satellites moving around the Earth today and ask them in which conic section they are moving and how fast the satellite must be sent out from Earth to orbit.

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