How many equilateral tetrahedra can be connected together without any empty space between them?

[Olga]

What evidence do you have for that?

I keep asking your for evidence that supports your claims. You keep neglecting to provide any. Why is that?

I'm sure that I must have read it, months ago. But I apparently didn't find it impressive enough to retain any of the details in my memory.

Did you read my posts that commented on the issues I had with your "equilibrium theory", months ago?

You disappeared from sciforums around the time when the discussion was getting a little heated, if I recall correctly. You struggled to have an honest discussion, if I recall correctly.

Ну раз моя теория не произвела на Вас впечатления, то я и повторяться не буду, незачем. В мире много людей, среди них есть те, на кого произвела. Просто забудьте о ней, и всё.

Не лицемерь, Джеймс. Я исчезла после того, как ты меня забанил. И вернулась сюда не ради тебя. Можешь забанить меня снова, мне всё равно.

 

[James R]

Olga:

Well, since my theory didn't impress you, then I won't repeat myself, there's no need.

Okay.

Don't be a hypocrite, James.

What? Please explain what I have done to be a hypocrite. That came out of nowhere.

I disappeared after you banned me.

Looking at the records, I see that you managed to accumulate 50 active warning points, which meant that you were automatically and temporarily banned for 1 day. That is all.

Have your read our published policy on warnings and bans? Do you know how the system works? If not, please view the Site Feedback subforum. There are two threads at the top of the thread list. One shows our posting guidelines, which you are expected to follow. Another explains the warnings and bans system.

And I didn't come back here for you. You can ban me again, I don't care.

All you have to do to avoid bans and warnings is to follow the posting guidelines that you agreed to follow when you signed up as member of sciforums.

Is that too much to expect from you?

 

[Olga]

Olga:

Okay.

What? Please explain what I have done to be a hypocrite. That came out of nowhere.

Looking at the records, I see that you managed to accumulate 50 active warning points, which meant that you were automatically and temporarily banned for 1 day. That is all.

Have your read our published policy on warnings and bans? Do you know how the system works? If not, please view the Site Feedback subforum. There are two threads at the top of the thread list. One shows our posting guidelines, which you are expected to follow. Another explains the warnings and bans system.

All you have to do to avoid bans and warnings is to follow the posting guidelines that you agreed to follow when you signed up as member of sciforums.

Is that too much to expect from you?

А за что ты меня забанил, Джеймс? Что конкретно я нарушила?

 

[James R]

Why did you ban me, James? What exactly did I violate?

You most recent warning was issued on 26 September, 2025. It was a warning for trolling.

You were sent two direct messages to your Conversations inbox at the time, explaining the warning in more detail.

Specifically, the text of the warning read:

When you make a scientific claim in those forums, you need to support your claim with appropriate arguments and evidence.

Merely claiming that establish scientific theories are nonsense, without making any argument for your position, appears to me to be an attempt to provoke an angry reaction from some of our members.

This is trolling. We do not tolerate trolling on sciforums.

Please back up your claims in future, Olga.

Hope this helps!

 

[Olga]

You most recent warning was issued on 26 September, 2025. It was a warning for trolling.

You were sent two direct messages to your Conversations inbox at the time, explaining the warning in more detail.

Specifically, the text of the warning read:

Hope this helps!

Охота на ведьм. Вечно вы на Западе неугодных сжигаете. А, ну да, теперь инквизиция стала гуманней - теперь просто банят.

 

[DaveC426913]

Witch hunts. You're always burning the unwanted in the West. Oh, right, now the Inquisition has become more humane—now they just ban people.

You flatter yourself immensely. Nobody's burning anything. We just don't want the site polluted with whatever fanciful stuff you pull out of your butt this week and pretend to call a "theory".

It might also help to read up on some basic greometry before makng your own assertions. There''s nothing wrong with asking questions if you don't know - but man! - admit you don't know!

Read the text of the warning again. Take it to heart.

 

[Olga]

You flatter yourself immensely. Nobody's burning anything. We just don't want the site polluted with whatever fanciful stuff you pull out of your butt this week and pretend to call a "theory".

It might also help to read up on some basic greometry before makng your own assertions. There''s nothing wrong with asking questions if you don't know - but man! - admit you don't know!

Read the text of the warning again. Take it to heart.

Самое главное в науке - это идея. А желающих создать под неё математический аппарат - пруд пруди.

 

[DaveC426913]

The most important thing in science is the idea.

No it isn't.

The most important thing in science is that an idea (AKA hypothesis) is based in evidence.
They don't waste time on hypotheses that are pulled out of someone's butt.

And there are plenty of people willing to create the mathematical apparatus for it.

Nobody is going to create a mathematical apparatus based on what you pulled out of your butt.

 

[James R]

Olga:

Witch hunt. You are always burning undesirables in the West. Oh, well, yes, now the Inquisition has become more humane - now they just ban.

Did you start this current thread as cover to complain about getting yourself banned for 1 day? Really?

The most important thing in science is the idea.

No. Ideas are just the starting point for useful science. Almost all of the hard scientific work remains ahead of you once you've come up with an idea.

And those who want to create a mathematical apparatus for it are a dime a dozen.

That's not true. People who are skilled in mathematics are generally not going to waste their time on just any old idea, because most ideas that come out of nowhere are going to turn out to be wrong. It is more often up to the person who has the idea to show that they understand the state of the field they are hoping to advance, and it is that person who needs to make a convincing case for why other people should invest their time and effort into trying to progress the idea towards something that is quantitatively testable.

 

[Olga]

Olga:

Did you start this current thread as cover to complain about getting yourself banned for 1 day? Really?

No. Ideas are just the starting point for useful science. Almost all of the hard scientific work remains ahead of you once you've come up with an idea.

That's not true. People who are skilled in mathematics are generally not going to waste their time on just any old idea, because most ideas that come out of nowhere are going to turn out to be wrong. It is more often up to the person who has the idea to show that they understand the state of the field they are hoping to advance, and it is that person who needs to make a convincing case for why other people should invest their time and effort into trying to progress the idea towards something that is quantitatively testable.

Угу. Эйнштейну невероятно повезло, что его жена оказалась математиком, потому что все остальные его идею просто высмеяли. И не потому, что идея была старая, а потому, что она не укладывалась в рамки тогдашних представлений.

 

[Olga]

No it isn't.

The most important thing in science is that an idea (AKA hypothesis) is based in evidence.
They don't waste time on hypotheses that are pulled out of someone's butt.


Nobody is going to create a mathematical apparatus based on what you pulled out of your butt.

Дэйв, ты уже 2 раза применил выражение:"вытащить из задницы". Это "оговорка по Фрейду"? У тебя там что то застряло? Будь аккуратнее с игрушками в постели...

 

[DaveC426913]

Dave, you've already used the expression "pull out of your ass" twice.

It is an accurate descripton of what you are doing. No slip about it.

That's why this is in pseudoscience.

everyone else simply ridiculed his idea.

No they didn't. Some thought it was brash and bold. But his math was indusputable. His model matched observations, solving a number of mysteries, which is what won them over.

 

[TheVat]

They don't waste time on hypotheses that are pulled out of someone's butt.

We just don't want the site polluted with whatever fanciful stuff you pull out of your butt this week

Nobody is going to create a mathematical apparatus based on what you pulled out of your butt.

don't know why you think we'd want to entertain stuff you're just pulling out of your butt for fun.

Is someone a little obsessed with Olga's butt?

 

[DaveC426913]

Is someone a little obsessed with Olga's butt?

Olga is. She is fascinated with everything she pulls out of it, waves it under everyone's nose, polishes it, and then wonders why the rest of us aren't likewise fascinated. I just keep saying 'flush that!'

 

[Olga]

Is someone a little obsessed with Olga's butt?

Olga is. She is fascinated with everything she pulls out of it, waves it under everyone's nose, polishes it, and then wonders why the rest of us aren't likewise fascinated. I just keep saying 'flush that!'

Olga is. She is fascinated with everything she pulls out of it, waves it under everyone's nose, polishes it, and then wonders why the rest of us aren't likewise fascinated. I just keep saying 'flush that!'

Анекдот:
Идёт мужик по улице, весь побитый и порватый, несёт в руках бумеранг. Навстречу ему идёт его приятель. Останавливается, и между ними происходит диалог:
"Гиви, что с тобой"?
"Не знаю".
"А куда идёшь"?
"Не знаю".
"А что несёшь"?
"Не знаю".
"Ну выброси".
Тот протягивает ему предмет- "на, сам выброси"!

 

[James R]

Einstein was incredibly lucky that his wife turned out to be a mathematician, because everyone else just ridiculed his idea.

That doesn't sound right.

Who ridiculed his idea? Be specific. Name names. (Which idea?)

And not because the idea was old, but because it did not fit into the framework of the ideas of the time.

What does Einstein have to do with tetrahedra?

 

[James R]

Looking at the title of this thread now, I notice that the question in the title is, bizarrely, different from the question in the opening post.

The question in the thread title doesn't seem to have been addressed, so I'll answer it here:

Mathematically, an infinite number of equilateral tetrahedron can be connected together without any empty space between them.

To put it another way: identical equilateral tetrahedra can tile three dimensional space without leaving any gaps.

 

[DaveC426913]

Mathematically, an infinite number of equilateral tetrahedron can be connected together without any empty space between them.

To put it another way: identical equilateral tetrahedra can tile three dimensional space without leaving any gaps.

Had to look this up.

Apparently, no.

"In geometry, tetrahedron packing is the problem of arranging identical regular tetrahedra throughout three-dimensional space so as to fill the maximum possible fraction of space.

The currently densest known packing structure for regular tetrahedra is a double lattice of triangular bipyramids and fills 85.63% of space
Currently, the best lower bound achieved on the optimal packing fraction of regular tetrahedra is 85.63%."

Tetrahedron packing - Wikipedia

en.wikipedia.org

 

[James R]

My bad. Thanks for the correction.

 

[DaveC426913]

My bad. Thanks for the correction.

Surprised me too.