This page explains how NASA and other scientists predict the path of the total eclipses. They use 19th century methods to predict the path of the eclipse. People use NASA´s Shuttle Radar Topography Mission, which measures the elavation of 1,200 points between each line of latitude or longitude.
This page explains why solar eclipses occur. The moons umbra casts a shadow upon a part of Earth. They get in line about every 18 months. The area of a total eclipses is never more than 167 miles wide.
This website explains why the sun's corona can be seen during a total solar eclipse. It happens because the sun´s corona is so thin you can only see it during an eclipse.
This website explains the magnitude or the fraction of the suns diameter covered by the moon. Higher magnitude=longer totality. Annular Eclipse that have magnitude close to 1 tend to look more like total eclipses.