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Wizard
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Wizard
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April 20th, 2019 at 8:05:50 PM permalink
This is a follow-up to my math puzzle SPHERE INSCRIBED IN A TETRAHEDRON.


Click on image for larger version.

Imagine a stack of cannonballs arranged like a tetrahedron, as shown in the image above. What is the limit of the ratio of the volume of the entire pyramid to the volume of the cannonballs in the pyramid, as the size of the pyramid reaches infinity? In other words, what ratio of space in the pyramid isn't wasted with empty space?

Hint: See the previous math puzzle linked to above.

I know you can easily search on this one, so I want to see a full solution for the beer, not just a copy and paste of the answer from another site.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
Ayecarumba
Ayecarumba
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April 20th, 2019 at 10:41:43 PM permalink
Is the stack always 5 layers?
If not, it is possible for very tiny spheres to fill 100% of the pyramid.
Simplicity is the ultimate sophistication - Leonardo da Vinci
RS
RS
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April 20th, 2019 at 10:46:11 PM permalink
Quote: Ayecarumba

Is the stack always 5 layers?
If not, it is possible for very tiny spheres to fill 100% of the pyramid.


They would all be the same size. Infinite layers.


Is that picture on your ping pong table tennis table, Wizard?
Wizard
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Wizard
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April 21st, 2019 at 2:47:30 AM permalink
Quote: RS

They would all be the same size. Infinite layers.



Correct!

Quote:

Is that picture on your ping pong table tennis table, Wizard?



No, it's a ping pong table! Only snobs say "table tennis."
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
Wizard
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Wizard
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April 22nd, 2019 at 8:01:34 AM permalink
Since this is a thread about cannonballs, let's have some pirate jokes until somebody submits a real answer.

Q: Why is pirating so addictive?
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
DJTeddyBear
DJTeddyBear
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April 22nd, 2019 at 8:20:11 AM permalink
Most of your math puzzles are beyond me.

However....
Quote: Wizard

Since this is a thread about cannonballs, let's have some pirate jokes ...

You’ve opened a can of worms here.



What’s a pirate’s favorite restaurant?
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
onenickelmiracle
onenickelmiracle
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April 22nd, 2019 at 8:44:25 AM permalink
Quote: Wizard

Since this is a thread about cannonballs, let's have some pirate jokes until somebody submits a real answer.

Q: Why is pirating so addictive?

But Pirate, you should not talk about Axelwolf, he got married to cover that up.
I am a robot.
Ayecarumba
Ayecarumba
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Thanks for this post from:
onenickelmiracle
April 22nd, 2019 at 9:28:00 AM permalink
Quote: DJTeddyBear

Most of your math puzzles are beyond me.

However....You’ve opened a can of worms here.



What’s a pirate’s favorite restaurant?




Arrrrr by's
Simplicity is the ultimate sophistication - Leonardo da Vinci
Ayecarumba
Ayecarumba
Joined: Nov 17, 2009
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Thanks for this post from:
beachbumbabs
April 22nd, 2019 at 9:31:35 AM permalink

"Yo, Ho's hoeing"
Last edited by: Ayecarumba on Apr 22, 2019
Simplicity is the ultimate sophistication - Leonardo da Vinci
Dalex64
Dalex64
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April 22nd, 2019 at 10:23:15 AM permalink
This will be a question and an answer.

What is a pirate's favorite letter?

RRRRRRRRRRR

and that used to be the end of the joke

but wait, that's not all!

No, the pirate's true love is the C!

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