
SPACE SQUARED  Level 2
Joseph L. Lagrange was a French mathematician who lived from 1736 to
1813. He made many contributions to the field of mathematics, but the
most notable were the calculus of variations and the development of the
metric system. Lagrange was also an amateur astronomer. His two fields
of interest, mathematics and astronomy, have been combined in this
activity.
Joseph Lagrange proved conclusively that the Four Square Theorem was
indeed a valid theorem. This theorem states that every positive integer
is expressible as a sum of four or fewer square numbers. A square
number is attained when a number is multiplied times itself (example:
3 X 3 = 9; 9 is a square number).
Below you will find the distances between selected space objects. Your
mission is to take the underlined number and express it as a sum of four
or fewer square numbers. There may be more than one right answer. The
first one is done for you.
 Earth to Barnard's Star  6 lightyears
Solution: 1 + 1 + 4 = 6 (1x1 + 1x1 + 2x2)
 Earth to Ursa Major  7 lightyears
 Sun to Earth (average)  150 million kilometers
 Venus to Earth (average)  42 million kilometers
 Mercury to Mars (average)  170 million kilometers
 Earth to Pleiades Star Cluster  400 lightyears
 Uranus to Neptune (average)  1630 million kilometers
 Earth to the star Vega  27 lightyears
 Earth to M51: Whirlpool Galaxy  14 million lightyears
 Center of the Milky Way Galaxy to the Sun  30,000
lightyears
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