Efficiency of space in stack of cannonballs with triangular base
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| | 2 votes (16.66%) | ||
| | 1 vote (8.33%) | ||
| | 7 votes (58.33%) | ||
| | 2 votes (16.66%) | ||
| | 3 votes (25%) | ||
| | 2 votes (16.66%) |
12 members have voted
April 20th, 2019 at 8:05:50 PM
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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.
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
April 20th, 2019 at 10:41:43 PM
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Is the stack always 5 layers?
If not, it is possible for very tiny spheres to fill 100% of the pyramid.
If not, it is possible for very tiny spheres to fill 100% of the pyramid.
Simplicity is the ultimate sophistication - Leonardo da Vinci
April 20th, 2019 at 10:46:11 PM
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Quote: AyecarumbaIs 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?
April 21st, 2019 at 2:47:30 AM
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Quote: RSThey 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
April 22nd, 2019 at 8:01:34 AM
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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?
Q: Why is pirating so addictive?
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
April 22nd, 2019 at 8:20:11 AM
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Most of your math puzzles are beyond me.
However....
What’s a pirate’s favorite restaurant?
However....
You’ve opened a can of worms here.Quote: WizardSince this is a thread about cannonballs, let's have some pirate jokes ...
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? 😁
April 22nd, 2019 at 8:44:25 AM
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But Pirate, you should not talk about Axelwolf, he got married to cover that up.Quote: WizardSince this is a thread about cannonballs, let's have some pirate jokes until somebody submits a real answer.
Q: Why is pirating so addictive?
I am a robot.
April 22nd, 2019 at 9:28:00 AM
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Quote: DJTeddyBearMost 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
April 22nd, 2019 at 9:31:35 AM
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"Yo, Ho's hoeing"
Last edited by: Ayecarumba on Apr 22, 2019
Simplicity is the ultimate sophistication - Leonardo da Vinci
