In this problem we are faced with an apparently easy area problem,
but it has gone horribly wrong! What happened?
If you take two tests and get a marks out of a maximum b in the first and c marks out of d in the second, does the mediant (a+c)/(b+d)lie between the results for the two tests separately.
This problem in geometry has been solved in no less than EIGHT ways
by a pair of students. How would you solve it? How many of their
solutions can you follow? How are they the same or different? Which
do you like best?
A total solar eclipse is an amazing spectacle with the sun appearing to move exactly behind the moon for a few moments, with the view of the moon seeming to perfectly overlap the sun.
But how perfect is this coverage? Is the view of the moon slightly larger than that of the sun or vice versa? In other words, exactly how perfect is a total solar eclipse as viewed from earth?
To answer this question you will need to work out the apparent size or angular diameter of the sun and the moon as viewed from Earth, using the following astronomical data:
Radius of the sun: $695,500$ km
Radius of the moon: $1,737$ km
Radius of the earth: $6,371$ km
Smallest distance between Earth and Sun $147,098,074$ km
Largest distance between Earth and Sun $152,097,701$ km
Smallest distance between Moon and Earth $356,375$ km
Largest distance between Moon and Earth $406,720$ km
Here are some issues to consider:
Could other planets have perfect eclipses? To help you address this question you can consider the following data for the moons of other planets in the solar system.