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# Spiral of Archimedes

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## Julian Cullumber

on 18 April 2014

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#### Transcript of Spiral of Archimedes

General Information
The spiral was first studied in Archimedes' novel,
On Spirals
.
The linear relation between the radius and the angle means the distance between each winding is the same, no matter how the
a
value changes.
If used as a cam, the spiral converts uniform angular motion into uniform linear motion.
In nature the curve can be seen in pine cones.

References
Spiral of Archimedes Polar Equation
Polar Equation: r = aθ±
k
Application
Archimedean spirals are used in digital light processing (DLP) to lessen the "rainbow effect", making televisions, computers, and phones look as if multiple colors are being displayed at the same time, when in actuality red, green, and blue are being cycled rapidly.
The coils in a watch are also in the form of an Archimedes spiral.
Who Was Archimedes?
Spiral of Archimedes
The Spiral of Archimedes
Application (con.)
Archimedes screws are used in third world countries use to transport water from low area to canals and irrigation ditches.
http://mathworld.wolfram.com/ArchimedesSpiral.html
http://www.mathematische-basteleien.de/spiral.htm
By:Julian Cullumber, Kaitlyn Quirk, Elena Bishop,Jaegan Lawrence
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. He is known for the invention of the screw and the principle of water displacement which allows the measurement of volume with irregularly shaped objects.
Who was Archimedes? (con.)
Archimedes also participated in the advancement and understanding of levers and why they work. Although he was an inventor we owe credit to Archimedes for integral calculus, which allows the measurement of area around geometric shapes.
Mother Function: r=θ
Eureka!
Varying Constants and Windows
As a increases the spacing between the lines also increases. As a decreases the spacing between the lines decreases.

Regarding k as you increase or decrease it moves the graph longitudinally and latitudinal
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