The name initially came from an acronym standing for  " Bionic Oscillatory Stabilization Unit (BOSU)" - a reference to the two ways a BOSU ball can be positioned. It is also referred to as the "blue half-ball", because it looks like a stability ball cut in half. The acronym now favored by the creators is "BOth Sides Utilised" 
The name initially came from an acronym standing for “Both Sides Up " - a reference to the two ways a BOSU ball can be positioned. It is also referred to as the "blue half-ball", because it looks like a stability ball cut in half. The acronym now favored by the creators is "BOth Sides Utilised" | URL | title=BOSU Balance Trainer Equipment Profile | publisher=Home Gym Equipment Hub | accessdate=April 13, 2015 | author=Home Gym Hub
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“Both Sides Up
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Bionic Oscillatory Stabilization Unit (BOSU)"
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| URL | title=BOSU Balance Trainer Equipment Profile | publisher=Home Gym Equipment Hub | accessdate=April 13, 2015 | author=Home Gym Hub