Indded, in the hexagonal packing, adding a row increases the height by R*sqrt(3).
In case of n rows:
The height is 2*R + ( n - 1 )*sqrt(3)*R.
This is why, I looked at multiples of sqrt(3) a tad under an even integer.
So, got interested in 15*sqrt(3) that happens to be 25.98. That gives 16 rows in a 14 x 14 squares. 8 pairs of rows with 14 and 13 barrels for a total of 216 barrels. Which is better than 14*14 = 196 barrels. You jam 20 more barrels hexagonaly.
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I notice, Steve, that your balls are "HI BOUNCE!".
You'll be able to stoat them off the wall! 😀
P.S. "Stoat" is Scottish for "bounce". 😉
This is the answer to stv's question:
pack circles of radius 0.5 in a square of side 8 - Wolfram|Alpha
I used to buy hard rubbery "Superballs" when I was a kid. Claimed to have a 96% "Coefficient of Restitution" or something. Perfect for establishing Newton's Laws of motion. I think these current ones are similar.
You could do tricks with them like spinning them, and they bounced most strangely. This pack of 8 is a nightmare. They prove "Sod's Law". They all roll off the table together and leap across the room and hide under anything where you can't be bothered to look.
But I do know you always find things in the last place you look.
I have sussed them out. I dropped a pound coin today. Couldn't find it anywhere. Then I asked myself what a cunning pound coin would hide under. Lifted the weedburner and there it was! 😀
pack circles of radius 0.5 in a square of side 8 - Wolfram|Alpha
I used to buy hard rubbery "Superballs" when I was a kid. Claimed to have a 96% "Coefficient of Restitution" or something. Perfect for establishing Newton's Laws of motion. I think these current ones are similar.
You could do tricks with them like spinning them, and they bounced most strangely. This pack of 8 is a nightmare. They prove "Sod's Law". They all roll off the table together and leap across the room and hide under anything where you can't be bothered to look.
But I do know you always find things in the last place you look.
I have sussed them out. I dropped a pound coin today. Couldn't find it anywhere. Then I asked myself what a cunning pound coin would hide under. Lifted the weedburner and there it was! 😀
Superballs were big in the 70s!
Physicists love them: Why Physicists Love Super Balls | Inside Science
Physicists love them: Why Physicists Love Super Balls | Inside Science
I had a washer gone for a week, that came back.
Must be extraterrestrial trickery.
And car keys, they never gave back.
I always look first at the last place.
Must be extraterrestrial trickery.
And car keys, they never gave back.
I always look first at the last place.
I have analysed the Lithium 7 nucleus. 😎
Maybe one reason I am a "Confirmed Bachelor" is women are always tidying up. AND I CAN'T FIND ANYTHING! 😡
Maison "Le System7" was looking particularly disreputable this afternoon. I decided a tidy up was regrettable, but essential, since I have a date next week with the woman "Joy".
I ended up covering my freshly laundered jeans in brown dust. 😕
Downside was I couldn't find my pocket calculator. But it eventually turned up. Last place I looked.
But I did solve "The Mystery of the Christmas Cactus". Some old flame of mine had given me this thing. Reliably flowers on December 26th. St. Stephen's Day. But lately has struggled. It's a Cactus, right? So why do I have to water it every 2 days, if I remember.
And has been very poor for 2 years. Scarcely raising more than 2 flowers?
THIS IS YOUR NEW PUZZLE! 🙂
Maybe one reason I am a "Confirmed Bachelor" is women are always tidying up. AND I CAN'T FIND ANYTHING! 😡
Maison "Le System7" was looking particularly disreputable this afternoon. I decided a tidy up was regrettable, but essential, since I have a date next week with the woman "Joy".
I ended up covering my freshly laundered jeans in brown dust. 😕
Downside was I couldn't find my pocket calculator. But it eventually turned up. Last place I looked.
But I did solve "The Mystery of the Christmas Cactus". Some old flame of mine had given me this thing. Reliably flowers on December 26th. St. Stephen's Day. But lately has struggled. It's a Cactus, right? So why do I have to water it every 2 days, if I remember.
And has been very poor for 2 years. Scarcely raising more than 2 flowers?
THIS IS YOUR NEW PUZZLE! 🙂
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Monsieur AllenB, I find your Mathematical explorations deeply disturbing and suggestive of criminal activity...
WHY would you be exploring the nature of 69! = 1.711224524×10^98?
Deeply Suspicious Behaviour, IMO. Arrests are imminent. 😎
WHY would you be exploring the nature of 69! = 1.711224524×10^98?
Deeply Suspicious Behaviour, IMO. Arrests are imminent. 😎
Three posts above yours, I had that plus a lovely drone fly-over.
Whiskey is not math. An added constraint is that fine makers move the barrels around the warehouse to expose a variety of temperatures and keep the sediment moving. Also the barrels should not be exposed to side-stress such as six more barrels on top.
This seems to lead to aisles where barrels suffer only their own weight plus a trivial side touch-load, may be easily rolled out into the hall and to a lift for vertical transposition. So the bulk lattice is square plus a finger worth of tolerance, AND huge set-asides for transport hallways.
There's also a lot of air-control involved. Those windows (49 per end all) are not for the whiskey's viewing pleasure, a little about light, and a lot about airflow. Which a really-tight packing might not allow.
I think I know the real reason you are single Steve. You don’t recognize the value of stress. That includes your succulent, the one you want to call a cactus.
Create a situation whereby the object of your desire requires a return in order to show its survival skills and you will be rewarded.
Create a situation whereby the object of your desire requires a return in order to show its survival skills and you will be rewarded.