What formula can I use to workout...

[believer]

I need to work out how many circles with a diameter of 45mm will fit inside a lager circle or square?
Can anyone help?

[beer4life]

I need to work out how many circles with a diameter of 45mm will fit inside a lager circle or square?
Can anyone help?

G'Day Cobber,
For a square, hexagonal packing as in a Bees' honeycomb gives more than square packing.

For a circle,

Smoothed Octagon A plane shape constructed by Reinhardt (1934) that is conjectured to be the "worst" packer of all centrally-symmetric plane regions. It has a packing density of

(Sloane's ), significantly less than the density of

(Sloane's ). The smoothed octagon is constructed from a regular octagon by smoothing the edges using a that is tangent to adjacent edges of the octagon and has the edges adjacent to these as asymptotes.

[believer]

Thanks for the reply, but I am using a design that will have about 100 circles 45mm diameter into a larger circle about 1500mm diameter.
I need to know how many pieces to get laser cut.

[beer4life]

Thanks for the reply, but I am using a design that will have about 100 circles 45mm diameter into a larger circle about 1500mm diameter.
I need to know how many pieces to get laser cut.

All care but no responsibility accepted.

797 circles 45 mm diameter will fit precisely into a circle 1485 mm diameter with square packing.

939 will fit in same outer circle in hexagonal packing. (honeycomb.)

Please provide address to send account Proximo.

Kindest Regards, " The Druid ".

[fandtm666]

if you are using a 1500 sheet to cut the big circle may as well use the lot and have no wastage

1500 x 1500 sheet now taking into consideration the circles you want are
45mm and allowing a few mill for the laser cut you can fit roughly
30 per line that is 45mm for the piece and allowing 2.5mm for the laser
this will give you around the 900 odd