- Get link
- X
- Other Apps
60 Stars Astrology Season ▲
English Version
By TOKYOｰTANUKI
麤(a-ra-i) Season ▲ mini-appendix
" What is b-squared = C＋１? " Part 2
1. Well, I will continue with what I said last time.
I thought it might need a little more explanation.
For a regular polygon with side length “a” = 1, let the shortest diagonal be “b” and the second shortest diagonal be “c”,
For a regular polygon with side length “a” = 1, let the shortest diagonal be “b” and the second shortest diagonal be “c”,
b squared = c + 1
I explained in the previous article that there is a relationship between the lengths of the two diagonals: b-squared = c + 1.
2. In the previous article, I wrote “when there are two or more diagonals,” but this is for the sake of clarity.
2. In the previous article, I wrote “when there are two or more diagonals,” but this is for the sake of clarity.
In short, to put it in a more general way
The line from one corner (vertex) of a regular polygon is “a” for the shorter one (usually the side of the polygon), “b” for the one next to it, and “c” for the one next to it,
The line from one corner (vertex) of a regular polygon is “a” for the shorter one (usually the side of the polygon), “b” for the one next to it, and “c” for the one next to it,
... "b squared = a + c" holds.
This is what I mean by “b squared = a + c”.
In the previous article, we discussed regular hexagons and regular heptagons.
In the previous article, we discussed regular hexagons and regular heptagons.
For example,
In the case of a quadrilateral, if side a = 1, diagonal b = √2 and c is its neighbor, so side c = 1
b squared = a + c = 2.
( the illustration of this post ⇑)
In the case of a triangle, if a = 1, then b = neighboring side = 1 because there is no diagonal, and c does not exist.
Then b squared = a + 0 = a = 1.
............So the equation holds for all polygons.
............And also for the dihedral, too!
3. So, in the previous story, for a circle, if points P and Q are taken on the circumference, and these two points are connected by a circumferential curve “ P" Q" ” of another circle of the same size (P and P", Q and Q" are in the same position),
In the case of a quadrilateral, if side a = 1, diagonal b = √2 and c is its neighbor, so side c = 1
b squared = a + c = 2.
( the illustration of this post ⇑)
In the case of a triangle, if a = 1, then b = neighboring side = 1 because there is no diagonal, and c does not exist.
Then b squared = a + 0 = a = 1.
............So the equation holds for all polygons.
............And also for the dihedral, too!
3. So, in the previous story, for a circle, if points P and Q are taken on the circumference, and these two points are connected by a circumferential curve “ P" Q" ” of another circle of the same size (P and P", Q and Q" are in the same position),
Square of arc PQ = arc PQ + arc QP (= curve P"Q")
So, then, Curves ” P" Q" ” are, in the end, as follows,
If the length of the entire circumference = Φ squared, and the point Q is the point that divides the circumference of the original circle in the ratio of Φ:1, then the curve ”P" Q"” will have the same length as the arc QP.
(Fig.)
(Fig.)
Well, in short, the formula " b squared = a + c ", in the case of a circle, becomes similar to the so-called golden angle problem,
Let's turn it upside down a little bit and say,
"a" squared = a + c = a + b = circumference
Conversely, there is no point Q on the circumference such that b-squared = a + c.
4. In this way, there is an essential difference between a circle and a polygon.
If we create an ∞-angle that is similar in shape to a circle, it will never be a circle.
But for polygons and circles, such as the Kepler triangle and the regular pentagon, there is a common feature, i.e., "Φ".
Then, even if it is impossible to make a circle by the method of increasing the angles of a polygon (∞ - gon),
Can't we transform a polygon into a circle or a circle into a polygon through Φ?
......It's just Tanu-chan's delusion!
Let's turn it upside down a little bit and say,
"a" squared = a + c = a + b = circumference
Conversely, there is no point Q on the circumference such that b-squared = a + c.
4. In this way, there is an essential difference between a circle and a polygon.
If we create an ∞-angle that is similar in shape to a circle, it will never be a circle.
But for polygons and circles, such as the Kepler triangle and the regular pentagon, there is a common feature, i.e., "Φ".
Then, even if it is impossible to make a circle by the method of increasing the angles of a polygon (∞ - gon),
Can't we transform a polygon into a circle or a circle into a polygon through Φ?
......It's just Tanu-chan's delusion!
Don't worry about it!
That's all for today.
Tanu-chan💓 TOKYO-TANUKI💛
Comments
Post a Comment