   Lucky match  This is an image taken from the Mir space
station showing the Moon's shadow during a Solar Eclipse.  Moon
casting shadow on Earth during Solar Eclipse  Why do you think a
total solar eclipse is important in terms of geometry?  When the
Moon passes perfectly in line with the Sun it blocks it out
completely. This means they have the same angular size in the
sky. This geometric relationship allows us to apply the
properties of similar triangles.  10th century CE Greek copy of
Aristarchus of Samos's 2nd century BCE calculations of the
relative sizes of the Sun, Moon and the Earth.  Thanks to
similar triangles we know the ratio of distances from earth to
sun and earth to moon must equal the ratio of sun’s diameter
to moon’s diameter.    Setting up the proportions between width
and distance  distance to sun / distance to moon = sun diameter
/ moon diameter  We’ve already determined these values so we can
simply plug them in!  149 600 000 / 384 400 = sun diameter /
3474  sun diameter = 1 352 004 km