How are 9 Merlin 1D engines packed and able to fit in a Falcon 9 FT first stage?

It was proved by Pirl in 1969 the most optimal packing of 9 circles in a larger one https://en.wikipedia.org/wiki/Circle_packing_in_a_circle. The radius of the larger circle should be ≈ 3.613r (r is the radius of the smaller circle). The Merlin 1D has a radius of 1.25/2 = 0.625 meters (according to English Wikipedia figures). So the diameter of the larger circle should be at least 2 x (3.613 x 0.625) = 4.51625 meters. The Diameter of the Falcon 9 FT is 3.7 meters.

Additionally, how are they able to gimbal when they’re so close to each other? You can also add details on the gimbal range and direction and how it affects the diameter of the first stage.

Edit: English WP updated the diameter to 0.92 meters. So 0.46 meters radius.

Further edit: https://en.wikipedia.org/w/index.php?title=SpaceX_Merlin&oldid=966006133 shows the diameter to be 1.25 meters even in July of 2020

• The engines are not packed as close as possible, see wikipedia.
– Uwe
Mar 3 '19 at 18:51
• +1 for mathematics :-)
– uhoh
Nov 7 '20 at 6:33