Drawing Blanks

Premature Optimization is a Prerequisite for Success

Find the foci of an ellispe

leave a comment »

Find the foci of a given ellipse using a compass and a straight edge.

Trivial, but instructive. 

 Solution:

1. Find the center of the ellipse:

Construct 2 parallel chords of the ellipse. The straight line connecting their midpoints passes through the center. Repeat with another pair of chords, and we find the center. This works because the ellipse is a parallel projection of a circle.

2. Find the axes of the ellipse.

Construct a circle concentric with the ellipse that intersects it at 4 points. Connect the midpoints of the sides of the rectangle. This works because the axes of the ellipse are its axes of symmetry.

3. Find the foci.

Construct a circle with the center at the end of the minor axis with the radius equal to the major semi-axis. It intersects the major axis at the foci.

Advertisements

Written by bbzippo

05/09/2010 at 11:09 pm

Posted in math

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: