Square beehive radius and mound beds ?

[SiO2]

so if that's the case, how many beehives would it take to fully pollinate the entire radius in one day?

whatever number you will get, add 20% or something. Because pollination distribution is not intended to work efficiently. You can have overloaded hive on the one field side and underloaded on the other, so you should never use exact required number of hives.

[Sevenless]

but you are saying, in that radius only 50 tiles are pollinated a game day?

Nope. Alternative version.

"Each time a crop grows to the next stage, it checks if there's a beehive within range. If it finds beehive, the time before the next stage change is reduced, and the beehive receives a usage tick. Beehives can store up to 50 uses (and noting how jorb worded it, it's likely they start will a full 50 when first created), and will regenerate 6 uses per hour. Crops using a beehive will cause honey and wax production (exact mechanics unknown), but jorb has stated there is a low level of base production of honey/wax by a hive even if it has no crops nearby." -Sevenless

I touched on this in the post with pictures, but wasn't clear enough:

Yes, theoretically you can get 144 charges per day (6 charges per hour, 24 hours), but because the hive only stores 50 charges you're effectively limited to 50 tiles of a single crop since they all turn at roughly the same time. You could have 2x50 tiles of crops on different timers, or different species, but that's just not how players tend to farm so I handwave the specifics for simplicity.

The picture about the circle: Roughly 530 tiles in a 13 tile radius circle. 50 tiles per hive, so you'd need 11 hives to tap it fully.

You can have issues with hive overloading if you have large fields next to each other on different maturation cycles. Crops mature in a "wave" (probably to reduce server load). I think it starts in the northwest corner of the world and slowly radiates outwards. Rather than putting extra hives, I just keep my fields separated so the hives don't overlap. Also note: for the couple extremely fast maturing crops with multiple stages (like carrots) a speed node will make you need extra hives.