Maths question

king_hellfire

king_hellfire

Well-known member
I was wondering if someone could help me with a maths problem. I want to be able to fit 50 people into the smallest area possible whilst keeping everyone 2 metres apart.
What I want to know is which layout would best achieve this, I’ve tried two options to see which would be the best but I’m wondering if there’s be a more space-saving way of doing it. Thanks.

I had a look at a square layout. 5460D172-53AB-4EFA-91B0-602DB0027203.jpeg
 
In the square 12m x12m gets you 49 people plus they will need room behind them to move or be seated .
so thats 13mx 13m for 49 for the extra person you will need another 2m either way ,in total 13mx 15m.
even so people need to be able to sit and move so to keep people 2m apart you would have to allow aprox 3m between them for body mass.
so now 19mx21m will keep them happily 2m apart.
 
turnoffsaysthestar said:
In the square 12m x12m gets you 49 people plus they will need room behind them to move or be seated .
so thats 13mx 13m for 49 for the extra person you will need another 2m either way ,in total 13mx 15m.
even so people need to be able to sit and move so to keep people 2m apart you would have to allow aprox 3m between them for body mass.
so now 19mx21m will keep them happily 2m apart.
Click to expand...

Thanks turnoffsaysthestar. I was thinking the squares would be the best way to go. 👍🏻
 
If no-one is allowed within two metres then as a starting point you are looking at everyone having a circular exclusion zone with a 1 metre diameter that touches but does not overlap anyone else's aren't you? If you lay fifty 10p coins flat, edge touching and see what area they cover, but cutting those at the edges in half. A square or hexagonal exclusion zone must surely be less efficient than a circular one as in places they exceed 1m distance from the centre.

You don't specify, so the overall space can be any shape?
 
Lefty said:
If no-one is allowed within two metres then as a starting point you are looking at everyone having a circular exclusion zone with a 1 metre diameter that touches but does not overlap anyone else's aren't you? If you lay fifty 10p coins flat, edge touching and see what area they cover, but cutting those at the edges in half. A square or hexagonal exclusion zone must surely be less efficient than a circular one as in places they exceed 1m distance from the centre.

You don't specify, so the overall space can be any shape?
Click to expand...

Do you mean something like this, Lefty, with the people in the centre and the circles having a diameter of 2 metres?

162C69DE-2FF3-4C87-A983-9255DBBCFF50.jpeg
 
To specify, the area is square and is roughly 15 metres by 15 metres, although it could be extended further by moving a few pallets out of the way 👍🏻
 
king_hellfire said:
Do you mean something like this, Lefty, with the people in the centre and the circles having a diameter of 2 metres?

I think your circles only need a diameter of 1m to maintain distance of 2m.

Sorry, ignore me. A radius of 1m would make a diameter of 2. I need to feed my brain before joining in.
Click to expand...
 
Your hexagon example can get 1 more person in the middle of each triangle - think of it as 6 equilateral triangles with seven vertices (people). I think a row of 24 equilateral triangles (sides = 2 m) alternating with 24 inverted triangles in between might do it. That's got 50 vertices and no wasted space

Edit: Sorry, thought it was just a maths problem. I've just seen your update
 
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