Abstract
The problem of determining the largest angular diameter
d
n
of
n
equal circles which can be packed on the surface of a sphere without overlapping is investigated. It is known that the best packing of 5 (11) circles on a sphere is obtained if one circle is removed from the best packing of 6 (12) circles. Robinson has suggested that perhaps there are some other cases also where this property holds, possibly
n
= 24, 48, 60, 120 are the circle numbers for which
d
n
–1
=
d
n
. In this paper it is proved that this property does not hold for
n
= 24, thus
d
23
>
d
24
, and it is conjectured that
d
n
–1
>
d
n
for
n
= 48, 60,120. A new packing construction is presented for 23 circles on a sphere with circle diameter 43.709964° and for 29 circles with circle diameter 38.677079°.
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