We give a confirmation that the Möbius ball of any real inner product space is a gyrovector space by using only elementary hand calculation. Some remarks to  will also be made.
This work is partly supported by Grant-in-Aid for Scientific Research (C) Number 23540190, Japan Society for the Promotion of Science.
"A confirmation by hand calculation that the Möbius ball is a gyrovector space." Nihonkai Math. J. 27 (1-2) 99 - 115, 2016.