Commander

Yes TY all for answers !

Pi/6 is the Fraction and 3xSqr Rt 3 times is the Volume of the Bigger Sphere to that of the Smaller one !

Quite Straight forward !

If *C* is a Cube and *S1* is the Sphere Inscribed and *S2* is the Sphere Superscribed then 
(1) What is the fraction of the volume of *C* is contained in *S1*
(2) How many times the volume of *S2* is that of *S1*

E = M C ²

^{That is :}

^{E >>> Energy | Ego | Eminence}

^{M >>> Mind | Mobility | Maturity}

^{C >>> Creativity | Conscience | Courage}

Need to cut like that !

5 hours ago, Genady said:

ChatGPT asked me to tell you this:

  Reveal hidden contents

It's not possible to cut a cube into four identical pieces, each with 9 edges and triangular faces. A cube has 12 edges and 6 square faces. In order to create pieces with triangular faces, you would need to further subdivide the cube's faces. However, doing so will result in more than 9 edges on each piece.

If you're looking to create four identical pieces with triangular faces and 9 edges, you would need a different shape or object that meets these criteria, as it cannot be achieved with a cube.

Just passing the message 😉

You need to chop of four corners with an equilateral triangle as the base with sides of diagonals
Four of them 

That leaves a tetrahedron in the middle 
We need to cut it in four equal parts with each equilateral triangular base (four of them) and apex meeting at the center of the cube

The four earlier cut pieces (cut for the sake of explanation) are merged with equal area bases of the four pieces of the tetrahedron

Also all the faces of the pieces must be TRIANGLES  !

Sorry I forgot to mention this !

3 hours ago, Commander said:

Cut a Cube into four identical pieces each having nine edges !

Please note it is four pieces and not six ! Error regretted !!

Cut a Cube into six identical pieces each having nine edges !

On 8/12/2023 at 7:00 AM, TheVat said:

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The white portion is one half of a rectangle that is 4/9 of the square.  So the triangle is 2/9, ergo green portion is 7/9.  

 

Correct

On 8/11/2023 at 4:54 PM, Genady said:

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Pi/8

 

Yes Right well done !

15 hours ago, Genady said:

I don't know why to hide it, but just for consistency:

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Pi*r² = Pi

r = 1

 

Correct ! Well done !!

Not a wordplay

The area of the circle

If the area of a square is Pi what is the radius of a circle of the same area ?

15 hours ago, Genady said:

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7/9

 

Just now, Commander said:

 

Just now, Commander said:

Very Right ! Well done !!

DING LIREN the CHESS WORLD CHAMPION !

22 hours ago, Intoscience said:

Is there a question in there??

It's not true that all the research is focussed on migrating to another planetary body. Protecting and making the Earth sustainable for all life for as long as possible is a bigger priority. The resource & technology to enable humans to spread out even within our own solar system is still way off, let alone any nearby habitable planets within other systems.    

Dear Sir, I agree that currently all Research are not in this direction and rather in Specializing at How to compete with each other, how to make better weapns to Kill and Destroy etc which are a Waste of Time against the Enemy Environment and extra-terrestrial attacks ! We need to think as a Global Human Community before embarking on my suggested venture ! I also agree with your statement that right now this appears impossible !

15 hours ago, Phi for All said:

!

Moderator Note

Moved from The Sandbox (which is for testing LaTex) to The Lounge.

 

I don't think evolution has a goal, but I've often thought humans were special because we came up with a way to leave the planet if necessary. Not sure we're going to find a safer world, or a more long-lasting one (how many billions of years do you need?), but I think we're the only species that could take other species with us when colonizing.

Dear Sir, I agree with you 100 %

All the Research and Aim of Human Beings are to evolve into a Long-living and Long-lasting Species all the time looking to migrate to a Safer, more suited and Long-lasting Planet !

A shape like this 

What comrs next inthe Series 1 , 6 , 39 , 340 , 3905 , _

Oh yes it turned out to be easy

Though it is
X(n) = n^2 + 4n - 1 being the formula

Correction 
Sry error regretted

What comes in the Series ?

4 , 11 , 20 , 31 , _ , 59 , 76 , 95 , 116 , _ , ?

And Why ?

Walker's Series ?

What comes in the Series ?

4 , 9 , 20 , 31 , _ , 59 , 76 , 95 , 116 , _ , ?

And Why

I thought it shouldn't envelope like this

3 hours ago, TheVat said:

English is my second language (I don't have a first one).  And I can't quite figure out what the puzzle wants.  Anagram, Sator Square, acrostic, what?  Hint is....steps?  chest?  cheat?  

CHESS