鱻（se-n）60 stars astrology Season holidays " An Extra 4 " Tanu-chan's concerns, part 1 Archimedes' "1:2:3"

60 STARS ASTROLOGY

ENGLISH VERSION

SEASON HOLIDAYS "An Extra"

鱻（se-n）60 stars astrology 

Season holidays "An Extra 4" 

Tanu-chan's concerns, part 1 

 Archimedes' "1:2:3"

1.　 Well, as I wrote last time, Tanu-chan is going to give a detailed explanation of the article I wrote on Twitter (X) in this blog.

But first, I have something on my mind, so please listen.



2.  Thinking on the commuter train, as usual.

Of course, I am not thinking about work.
If I do, it's for about 10 seconds.

Tanu-chan doesn't like labor so much.

Also, it is still hot in Japan!
Japan is now in the leisure season called “Shoku-yoku no AKI

 Season”.

...By the way, I am now struggling with the story of Mr. Archimedes.

As I wrote in the top picture,

A cylinder with a base radius of 1 and a height of 2,
A cone with a base radius of 1 and a height of 1, and 
Two cones combined and joined at the base.

If a sphere of radius 1,

the volume of the cylinder is 2π, or 6/3π.
The volume of the sphere is 4/3×π.　　　
The volume of the two cones is 2/3×π.

The total volume of the sphere and the two cones is equal to that of the cylinder.

A sphere and two cones fit perfectly in a cylinder, and yet the beautiful 1:2:3 ratio is still there.

........ Archimedes is indeed a great teacher!

3.  Well, since this is a well-known story, some say that Archimedes was not the first to notice it in the first place, and that it was known much earlier.

But I am not interested in who was the first.

What Tanu-chan is having concerns about is the case of a square column.

Now, let us consider a square column (cube) with a base of square, a side length of 2, and a height of 2.

Then the volume of this cube is 8 = 24/3

Next,

What happens when two square pyramids with a square base, a side length of 2, and a height of 1 are put together, i.e. when an octahedron of such a shape is made.

...The volume of this solid (an octahedron) may be 1/3 x4× 2 = 8/3.

Compared to the cube, the ratio of the volumes of these two solids would be 3:1.



.....By the way, then, is there a smart figure which is in the middle of the ratio “2”, i.e., 16/3 ?

Of course, if we made a rectangle with a square base, length of one side 2, and height of 4/3, the volume would be 16/3 and the ratio would be 1:2:3.

But that is not very cool.


Tanu-chan wants to make something like Archimedes' sphere, something that fits into a larger object and still looks cool!

4.  That's why I'm thinking about it every day. It's hard to find...

“Oh! I found something cool here...”

If you have a cool idea, please tell Tanu-chan in secret!

That's all for today!

Tanu-chan💓  TOKYO-TANUKI💛