172 60stars astrology Season 7 Appendix 5 Divisions of Figures 1 About 2-gon

60stars astrology

English version

By Tokyo-Tanuki

60stars Astrology Season 7

60stars astrology Season 7 Appendix 5  

Divisions of Figures 1 -

About the digon (2-gon)

1.  Today we are going to talk about 2-gon.

....Well, before you call an ambulance, please listen to me for a moment.

In Season 6, we talked about how a circle and a rectangle can be divided by 60 constellations around them, but a triangle is divided by 36 constellations around it.

"Why can't we divide a triangle into 60 zodiacal divisions? "

I know some of you may wonder, so today, I will explain very briefly how polygons are divided.

Or rather, I will just write the conclusion.

2.  A 2-gon has two points AB and a line segment between them, but zero angles. 

Well, it looks like two lines overlap, but no angle can be obtained.

But a 2-gon is also a polygon. 

Because the overlap means that the position of the two line segments is fixed, and the sum of the interior angles is 0° while the sum of the exterior angles is 360°.

Since the lines are overlapping, the interior angle between them is zero degrees because there is no way to expand it, but since they are fixed to each other, we can conceive of them as planes. 

The shape of the two faces is unknown.

It is a dihedron because it has two sides. 

Since its area is zero, its volume is also zero.

In space, creating vertex C at the extension of line segment AB creates line segment ABC.

Line ABC is a straight line segment, but in the end, it is still a 2-gon and a dihedron because no angle can be created.


If we create vertex C in a place that is not an extension of the line segment, the 2-gon AB may become a triangle ABC, which is also a dihedron, if we connect AC and BC.

But as it is, it is an inflection line ABC.

Well, this is where things get a little tricky.
I would explain it again when I have a chance.

3.  Now, then, how is the circumference of the 2-gon segmented?

Let's put aside the detailed reasons,

The number of divisions of an n-gon,

 T(n) is,  Tn=3n(n+1).



Well, then, in the case of a 2-gon,

T2 = 3 x 2 x (2 + 1) = 18

That is, it is divided into 18 constellations ( segments).



In addition, using this formula, for example, if it is a pentagon, the circumference of the pentagon is,

T5 = 3 x 5 x (5 + 1) = 90

This means that it is divided into 90 constellations ( segments).

And if it is a triangle,

T3 = 3 x 3 x (3 + 1) = 36

This means that there are 36 constellations.

I wrote a bit about this in Season 6.

4. .... Since I know everyone will think that Tanu-chan is finally going to be hospitalized, I will skip the explanation and only show the results in the figure.
(Fig)

I think the Aliens are also saying "the heptagon is 168!". 

Maybe⇓
(Photo).

5.  Now, if you look at the figure I drew above, you will notice that there is a 1-gon and a zero-gon.

Since Tanu-chan does not want to go to the hospital, I will explain a little bit.

First of all, a 1-gon is a straight line, not a line segment. 

It is different from a curve.

I will explain about curves when I have a chance.

There is a starting point (vertex) A, but there is no end point.

 And it extends in one direction forever. 

Therefore, there is no distinction of edges.

The line is also not fixed and extends without surface or backside.

Since a 1-gon has only one line, it is impossible to conceive of an interior angle and an exterior angle. 

Therefore, it is not a polygon.

It is not a dihedron because there is no distinction between inside and outside even if they are in space.

Whether we call it a mono-hedron or not depends on how we define it.

If we create and connect another vertex B where there is a 1-gon, the line is doubly fixed between AB, resulting in a line segment AB (2-gon and dihedral).

.....By the way, if we apply the formula for a 1-gon,

T1 = 3 x 1 x (1 + 1) = 6 constellations (segments).

Well, it is very hard to imagine.

6.  Next, a zero-gon is a "point" .　

It has no lines, no corners, no faces. 

There is no direction either.

A zero-gon has no number of constellations, i.e., it cannot divide its circumference, since T0 = (3 + 0) x 0 = 0.




.......Now, before everyone calls an ambulance for Tanu-chan, let me tell you a little more about the story in the next article.



That's all for today.

Tanu-chan💓 TOKYO-TANUKI💛