Changing Miller-family integers changes the checked reciprocal spacing. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The one-zero-zero family leaves six metres between planes

Cell side 6 metres and index family 1, 0, 0 gives square sum 1 and spacing 6 metres.

d=6/1=6d=6/\sqrt{1}=6
Reciprocal mapInteger reciprocal spots sit at checked grid positions.spotspotspotspacing

The two-one-two family compresses spacing to two metres

Keeping cell side 6 but using family 2, 1, 2 gives square sum 9 and spacing 2 metres.

d=6/9=2d=6/\sqrt{9}=2
Reciprocal mapInteger reciprocal spots sit at checked grid positions.spotspotspotspacing

The four-zero-three family makes a six-fifths spacing

The family 4, 0, 3 gives square sum 25 and spacing 6/5 metres.

d=6/25=65d=6/\sqrt{25}=\frac{6}{5}
Reciprocal mapInteger reciprocal spots sit at checked grid positions.spotspotspotspacing