Archimedes created an invention called the Archimedes screw, which is effectively one of the earliest types of pumps used to move water from a low lying area to a higher plane.
(Picture from http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0002929.html)
You can see the bottom of the screw dips into water, and as you turn the screw by the handle at the top, water is picked up. The 45˚ inclination of the cylinder allows the water to raise to the next thread, while the bottom of the screw picks up more water. As you turn, the water is moved to the top with relatively easy effort.
It is a simple invention to the modern eye but it solved many problems in antiquity. Where did Archimedes get his idea? The screw-pump arose from his work on the geometry of spirals. He, continued the work of his fellow Greek Conon, in the description of the below spiral, now called Archimedes spiral.
(Picture from
http://www.daviddarling.info/encyclopedia/A/Archimedean_spiral.html)
Imagine travelling along this spiral. You start at
the center of the spiral and move
at a constant speed along a path which is itself rotating with a constant
angular velocity. Sound dizzy
doesn’t it. This is only one arm of
the spiral, if you flip this arm over the y-axis you see the other arm. One arm for θ > 0 and one for θ
< 0 and they connect at the origin.
(r, θ) are the polar
coordinates (distance, angle). a is the parameter that will turn the
spiral and b controls the distance
between turnings.
(http://en.wikipedia.org/wiki/Archimedes_spiral)
With modern caluclus finding the area and tangents
of a point moving in a curve with uniform speed along a straight line revolving
with a set angular velocity seems straightforward. But you have to remember that Archimedes
was just beginning to invent calculus with his fellow greek mathematicians.
But what is the use of
this?
Well today we use archimedes spiral for a number
of things.
--Scroll compressors are made from two intertwined spirals. One if fixed normally and the
other rotates around it, and are used for compressing liquids and gases.
These are found in air-conditioners.
--The grooves
of the first music records were in the shape of archimedes spirals.
-- Doctors
ask neurologically damaged patients to draw the spiral as a means of diagnosing
amount of tremor. (http://en.wikipedia.org/wiki/Archimedes_spiral)
Archimedes spiral can be found in nature but not as often as the logarithimic spiral. The archimedes spiral described growth that just adds, whereas logarithimic spiral growth is related to its size. (http://www.2dcurves.com/spiral/spiralaa.html)
Archimedes Spiral -- very close to Pinecone
http://www.2dcurves.com/spiral/spiralaa.html)