㐂 (yo-ro-ko-bi) 60stars Astrology season 6 mini-appendix 1 "Third power + Fourth power = Seventh power" triangle

60stars astrology

English version

By Tokyo-Tanuki

60stars Astrology Season 6

㐂　(yo-ro-ko-bi)    60stars Astrology season 6 mini-appendix 1　

"Third power + Fourth power = Seventh power" triangle

1. Well, since we are running out of Greek letters to use in the mini-appendix, from Season 6 onward, I will occasionally use Kanji (Chinese characters)!

I'll make it so that it has the same three parts, like "森" [forest] or "州"[state] etc. !




2. By the way, I don't know if this is true or not, but according to what Mr. Herodotus heard from a priest in Egypt,

“The Great Pyramid was built so that the area of one side is equal to the height.”

In other words, if one side of the square at the base of the pyramid is 2 and the height of the pyramid is √Φ, the slope of the pyramid is,

√(√Φ squared + 1 squared) = √(Φ + 1) = Φ


Then the area of one of the triangle faces of the pyramid is,

2×Φ×1/2=Φ!




3. Now I wonder if I can make something cool like a pyramid by specifying about the volume, width, and height of the solid.
I've been thinking a lot about it.

....But, we'll talk about that some other time, today's story is a little different,



It came out in the example above,
√Φ:1:Φ right triangle,  i. e,
√Φ:√Φ√Φ:√Φ√Φ√Φ right triangle, whose line length ratio is √Φ:√Φsquared:√Φcubed  is very well-known,

However, right triangles ratios of line lengths are as follows don't seem so common.

(1) √("a" squared):√("a" cubed):√("a" to the 5th power) 
(2) √("b" cubed):√("b" to the 4th power):√("b" to the 7th power)


Why are they not famous?　

...So, let's examine it for a moment!




4.  First, about (1) triangle, squares each number (removing the root) from the Pythagorean Theorem, then we get,

("a" squared) + ("a" cubed) = ("a" squared to the 5th power)

If we simplify, let "a" be the number that becomes
1 +"a" = "a" cubed.

Calculating this, the solution that is positive is, 

"a" = 1.3247179572448....　

Yes, the solution is 1.3247179572448.


Then,
"a"3rd power = 2.3247179572448, 
"a"4th power = 3.079595556123,
"a"5th power = 4.07959555556123,
"a"(-4th power) = 1/("a"4th power) = 0.3247179572448
　
∴　 "a"5th power - "a"4th power = "a"3rd power - "a" = "a"-1/"a"(-4th power) = 1

....well, that sounds mysterious and somewhat useful, maybe！

I'll study it next time I'm on the train.





5.  Next, about (2)triangle, squares each number (removing the root) from the Pythagorean Theorem,

("b" cubed) + ("b" 4rth power) = ("b" 7th power)

Then, simplifying, let b be the number that becomes
1 + "b" = "b" to the fourth power.

Calculating this equation, the solution "b" that is positive is,
1.220743468955935....

Yes, the positive solution "b" is 1.220743468955935.


If we square this to the 3rd power, we get,
1.81916976104....
If we square it to the 4th power, we get
2.220743468955935....
If you multiply it to the 7th power, you get
4.039902336051....

and 

adding the 3rd and 4th powers yields the 7th power.


In this case,
1/b is "b" cubed -1, so 0.81916976104....


Looks like it may or may not work....??
It looks cool in the picture, though.

Tanu-chan likes cool formulas!

I think the coolest one is, as well, the,

" 1:√Φ:Φ triangle " of King Khufu's pyramid!

...I'll research these triangles on the train.




That's all for today!




Tanu-chan💓 TOKYO-TANUKI💛