## Life Cycles of Stars (Grade K-8) - Page 10

## 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