|
|
|
Technical Graphics - Plane Figures - The Ellipse
What is an Ellipse ?
 In the world today we are surrounded by Ellipses or partial
Ellipses. From company logos to special engine parts Ellipses
play an important part in our lives. Some bridges incorporate
the Ellipse shape as it is a very strong structure. The
planets revolve around the sun following elliptical paths. In
this case the Sun is at one of the Foci of the Ellipse.
(You will learn more about the Focal Points later.) You can
see this to the right.
The Ellipse and the Cone
 The Ellipse like the Parabola,
the Circle and the Hyperbola, is a Conic Section. This
means that if a cone is cut in a certain way then you
get one of the four curves mentioned above.
A cone cut by a simply inclined plane which cuts all
of the cone's Generators results in an Ellipse. Below you can see a diagram.
If we take an Orthographic
Projection of the cone, which has a simply inclined
plane cutting it we can see from an auxillary plan of
the cone the true shape of the resulting surface which
turns out to be an Ellipse. You can see this below.
Earlier we said that an Ellipse and a Circle were
closly linked. A Circle can be generated or created if
you cut a cone with a plane that is perpendicular to its
axis and which cuts all of the cone's generators.
The Ellipse and the Cylinder
 Just as it is true that if you cut a cone in a
certain way you will get an Ellipse, you can also
cut a Cylinder to get an Ellipse. To the right you
can see a Cylinder cut by a simply inclined plane
and the result is an ellipse.
|
|
|
You might not think it but the Ellipse and the Circle
are very closly linked.
A Circle is a special type of Ellipse, just like
a Square is a special type of Rectangle, but the
connection goes further than that. If you look at a
circle obliquely, (that is not straight on), you will
see an Ellipse. Take the picture of the satellite to the
left. You know that the shape of a satellite when you
look straight at it is a circle but you can see from the
picture that when you look at it at a different angle
you get an Ellipse. Now look at the picture of Big Ben
in Londan to the right, you can see two clock faces and
both of them look like Ellipses. Again this is because
you are not looking at then straight on. If you still
don't believe us, put your mouse oven the red circle
below. This will cause the circle to rotate, therefore
changing the angle at which you are looking at the
Circle. Have a look and see what happens...