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Copy of Polynomials and Roller Coasters

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Ricky Payne

on 29 March 2014

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Transcript of Copy of Polynomials and Roller Coasters

Roller Coasters
Why Polynomials?
Brief Intro
History of Roller Coasters
Some Examples
History of Polynomials
The End
What is it?
I was interested in figuring out where
and how math effects the making
of roller coasters, and how much of an importance it is when constructing it. I then realized, that probably the biggest factor in the making of roller coasters, would be polynomials.
Once I found my topic, polynomials, I found an immediate connection to roller coasters.
Roller coasters imitate the shape of
a polynomial functions
For example, it's quite common for roller coasters to take the shape of a parabola. These shapes can only be made by polynomials. Therefore, you need polynomials to get these shapes needed for roller coasters.
The word “algebra” was derived from the Arabic word for restoration, AL-jabru
The origin of the Roller Coaster dates back to the Russian Ice Slides built in the 17th century. They began in the "Russian Mountains" in St. Petersburg Russia.
The shape of a roller coaster can be formed by using the equation:
An expression of more than two algebraic terms
Polynomial functions are expressed in the form :
the coefficient of the
greatest power of x,
is the leading coefficient
a = a real #
n = a whole #
x = variable
the coefficient with a 0, is
the constant term
~Solve basic algebra of polynomials
~Discuss the importance of the unknown variable x
~Multiply, divide, and find the roots of polynomials
~And started to put together binomial theorems during he Medieval times
Islamic mathematicians were able to :
Carl Friedrich Gauss
Hero of Alexandria
Leonardo Fibonacci
Lodovico Ferrari
Omar Khayyam
The structures were built out of lumber with a sheet of ice several inches thick covering the surface. Riders climbed the stairs attached to the back of the slide, sped down the 50 degree drop and ascend the stairs of the slide that laid parallel to the first one. The slides were very popular with the Russian upper class, and some were elegantly decorated to provide entertainment "fit for royalty."
The first looping coaster was located in Frascati Gardens in Paris, France. The hill was 43 feet high, had a 13 foot-wide loop and was tested with everything under the sun before humans were allowed on. The layout was simple: the rider rode down the gentle slope on a small cart and through a small metal circle.
For example, let's take the equation :
If we were to graph it, it would look something like this
I went ahead and tried doing some of my own graphs with this equation, trying to imitate the forms a roller coaster would have. Here are some graphs I came up with
For this example, I used the equation:
-(x )+(3.5x )-(2.5x )-(12.5x )+1.5x+9
The equation I used to form this graph was:
x +4x - 4x -26x -7x +28x +20x
The last equation I used for this graph:
-2x -13x +26x -7x +28x +20x
Looking at these
3 graphs; if they
were all made into
roller coasters,
which would you ride?
Full transcript