皛（akira-ka） 60 Stars Astrology season holidays "An Extra 5" : Tanu-chan's concerns, Part 2 "71.777-4" ?

60 STARS ASTROLOGY
ENGLISH VERSION
SEASON HOLIDAYS "An Extra"

皛（akira-ka） 60 Stars Astrology 

Season holidays "An Extra 5 "  

Tanu-chan's concerns, Part 2   "71.777-4" ?

1.  Well, last time I shared my concerns with everyone, right?

...I guess it's not so much a concern as it is a question.

As I said last time, the volume of a cube with a base of 2 x 2 and a height of 2 is 8, or 24/3.

Two tetrahedrons with a base of 2 x 2 and a height of 1 (octahedron) is 8/3.

These are in the ratio 1:3.


So, what is a figure that has a volume of 16/3 in the middle of the two and is cool enough to fit into a cube?


That is the question.

.....Of course, if you make a rectangle with a 2x2 base and 4/3 height, it will be 16/3, but it's not cool.

People will boo you! Absolutely!

Well, what shall we do?




2.  When you are in trouble like this, let's use Φ !

Because Φ and "1" are twins and π is a good friend of "1".

Then what about 2 or 3 ?　It's a rival of "1" named “best friends" or "best partner"



The volume of cube A with base 2Φ×2Φ and height 2Φ is 8Φ³=24/3×Φ³

The volume of two square pyramids (octahedrons) C with base 2Φ×2Φ height is 4/3Φ³×2=8/3×Φ³

The ratio of C to A is 1:3


...Then we need to find a shape that is 16/3×Φ³ between them, right?




3.  Of course, if we make a sphere with radius ∛4Φ/(∛π), it would be 16/3×Φ³, but that would be a bit too large to fit well in cube A.

Because in this case, the diameter of the sphere would be 2×∛4Φ/(∛π)=3.50...

But it is larger than the length of one side of the base of the cube 2Φ(3.236...).


...I'm stumped.




4.  So, can't I get another cone like that?
　
Because the volume V of a cone with base area "S" and height "r"  is  1/3×Sr.

And now, V of B =1/3×16Φ³, right?


... So, Sr = 16Φ³ = 67.77708763999......


Hm? And this is?

4Φ⁶=71.77708763999........ in the definition of the length of the circumference, it's similar to ???


4Φ⁶-4= 67.77708763999... = 16Φ³ = ( ∛(2⁴Φ³))³

In other words, the definition of the length of the circumference minus 4 might have something with 2 to the 4th power multiplied by Φ³.



Apparently, it cannot be just a square pyramid or like that.

Maybe it's a little round?

What on earth could it be?




5.  By the way, I was looking at a website of someone who likes math and found this explanation.

About the figure when cylinders intersect, for the volume of the common part when two right circular cylinders with base radius of 1 intersect perpendicularly, the volume is 16/3 by Cavalieri's principle.

and there is a picture .....like this?

....Is this square or round?

Is it like a lunch box?


By the way, Cavalieri?　Who?

Tanu-chan is a humanities student, so I did not know his name.



6.  Then if there is also a cool shape 16/3? , which is halfway between the square column (cube) 24/3 and the two square pyramids (octahedron) 8/3?

Is it going to be like this shape of Mr. Cavalieri's, halfway between a cube and a sphere?

Will this shape fit neatly and perfectly into that 24/3 column?




......... So, Tanu-chan's question was not resolved because I still don't understand it!

Well, there are things we don't know in this world, aren't there?



Anyway, OK！

See you next time！

Tanu-chan💓  TOKYO-TANUKI💛