贔 (hi-i） Season ▲ Appendix １ : Birds and the Pyramid (Part 1) What is a Right Triangle with a 1/Φ Angle?

60 Stars Astrology Season ▲

English　Version

By　TOKYOｰTANUKI

贔(hi-i）Season ▲　Appendix １　: 

Birds and the Pyramid (Part 1) 

What is a Right Triangle with a 1/Φ Angle?

1. The Bird’s Eye View

When you think of pyramids, you think of the God Horus—strong, powerful, with those massive wings spread wide.

Flap, flap!

But at the end of the day, a bird is a bird.

So, let’s try looking at the pyramids through a bird’s eyes.

2. That Triangle in NYC

Remember that triangle in NYC I mentioned before? 

It has a base angle of 1/Φ, which is a steep incline of about 84.99°.

As you can see in my sketch, this triangle is hidden all over the pyramids! 

You find it in the Grand Gallery, the Queen’s Chamber, and the antechamber of the Red Pyramid........maybe...

Why this specific triangle? I’ve touched on this on Twitter before, but let’s dive deeper.

3. The Math of the "Golden Angle"

If we split that NYC building’s triangle into two right triangles and look at it through the lens of the Golden Angle (Φ ≈ 137.5°), we get a right triangle with these angles:

Base Angle: 1/Φ
Top Angle: 1 / 2(Φ^4)

If we ideally represent the full circle of 360° as "1 + Φ = Φ^2", then 90° is naturally approximated as (Φ^2 ）/ 4.

It’s a bit hard to see the meaning yet, right?



4. Splitting the Circle: 20 and 12

Since the sum of a triangle's angles is 180°, we have:

1/Φ + 1/4(Φ^4) = Φ^2 / 4 = 90°

By multiplying both sides by 4(Φ^4), we get:
4(Φ^3) + 1 = Φ^6

This means the ratio of the angles (with the narrowest angle as "1") is:
4(Φ^3) : 1 : Φ^6

Using the rule Φ + 1 = Φ^2$, we can rewrite this as:
8Φ + 4 : 1 : 8Φ + 5

If the 90° angle is 8Φ + 5, then the full 360° is four times that: 32Φ + 20.

............Wait... 360° = 32Φ + 20.

This can be broken down into 20（Φ^2） + 12Φ.

Does that ring a bell? 

It looks just like the way we divide a circle into 20 progression periods and 12 zodiac signs!




5. Soccer Balls and Crows

20, 12, 32... does this remind you of anything?

Exactly! 

....A soccer ball, a golf ball, and the icosidodecahedron family. 

It’s a 32-faced polyhedron that’s almost a perfect sphere.

No wonder crows love golf balls so much!



6. Confusion between Φ and π?

So, the numbers 12-20-32 connect the narrow tip of that NYC triangle to the geometry of a sphere.

I’m personally fascinated by the fact that the icosidodecahedron was a composite shape first created by Leonardo da Vinci.

............Next time you see a bird, try asking them about it!

But, I think maybe birds get confused between Φ and π. 

...Why? 

Because:　360°÷　Φ^10 ÷(√５/２)＝2.618008≒Φ^2

It’s enough to make anyone’s head spin! 🌟

That’s all for today.

.....Believe it or not, there’s still one more part to this!




Tanu-chan  💓  TOKYO-TANUTANU 💛