How dare you call it's 12.56 ;D ;D ;D

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Danang

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How dare you call it's 12.56 ;D ;D ;D
« on: December 19, 2024, 10:05:54 PM »


while the cylinder has full r=1, the sphere mostly UNDER r=1, even ZERO

logic failure detected  :o ;D 8)
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #1 on: December 21, 2024, 12:09:34 AM »
The most logical for sphere area is cube surface area times (arc ratio)³ × r² AKA 24 × 0.7928932³ × r² = 11.96342 × r²

It's a simple algebra.
As simple as calculating sphere volume.

Sphere Volume = cube volume times (arc ratio)³ × r³ AKA 8 × 0.7928932³ × r³ = 3.987806 × r³

For any circle related calculations, every side lengths, i.e. 2, becomes 1.5857864.

length, width, hight



 
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #2 on: December 25, 2024, 10:23:52 AM »
You're speechless?
It means Phew is verified  ;D🙏
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #3 on: December 25, 2024, 10:32:51 AM »
Cube has 6 times 2×2 unit of area.
Each area has length & wide, which are corrected by arc ratio each
Because it becomes round, the height automatically gets corrected by arc ratio.

Total correction = 0.7928932³
Area after total correction = 0.7928932³ × (2×2) = 1.9939033

The whole cube after total correction = 1.9939033 × 6 = 11.96342
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #4 on: December 31, 2024, 05:22:51 PM »
What does 3.17157 mean?
It means there are 4 parts: 1 and 1 and 1 and 0.17157

6 round surface areas cover 3 AKA 1 and 1 and 1,
The rest equals 0.17157.

Example:
a) 1 of 6 sides has area 1.886039 and the whole ⅙ sphere equals 1.9939033.
The ratio = 3 : 3.17157

b) ⅛ sphere:
It consists of 3 identical segments + 0.17157 part.
The whole area equals 1.4954275.
The 3 identical area equals 1.4145305, or 0.47151 each.
Ratio (0.47151×3) : 1.4954275 = 3 : 3.17157 AKA 0.9459 : 1
The rest equals 1.4954275 - 1.4145305 = 0.080896 which is 0.17157 part of 1.4954275 or 0.17157 : 3.17157 AKA 0.054096 : 1.
« Last Edit: December 31, 2024, 05:24:51 PM by Danang »
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #5 on: December 31, 2024, 05:32:40 PM »
Interestingly, ⅛ sphere : round circle part = 1.4954275 : 1.886039 makes circle ratio i.e. Phew/4  AKA 0.7928932 : 1.
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #6 on: December 31, 2024, 05:34:24 PM »
Phew day is March, 17th okay?  ;D ;D ;D
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markjo

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #7 on: December 31, 2024, 07:50:35 PM »
Phew day is March, 17th okay?  ;D ;D ;D
No.  March 17 is drunken Irish day.  Try again.
Science is what happens when preconception meets verification.
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #8 on: January 01, 2025, 04:55:17 PM »
The original idea of March, 17th is 👉 Saint Patrick.

What's the issue then?  ;D 8)
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #9 on: January 06, 2025, 05:07:48 AM »
Sphere volume in reality equals approximately a half of cube volume. (r=1).

What about sphere area? It's practically the same ratio, although it's harder to demonstrate visually.
BUT, you can start from the height zero to 1-cos45. The area limit is Phew × 0.7928932² = 1.9939. The 45° dome area should be under 1.9939.
Phew standard determines it's 1.88604. Pi standard might be close to that number.

The Pi's contradiction begins when calculating the hemisphere area from the height 1-cos45 to 1-cos90.
You have excessive area from the height 1-cos45 to 1-cos90. Guess what?

Phew has a nice calculation at that area.
Area 45° to 90° of hemisphere = hemisphere area - the 45° dome area = 5.98171- 1.88604 = 4.09567.
While the cylinder area from 45° to 90° equals [ (1-cos90) - (1-cos45) ] × 2 phew = 4.48527
So sphere segment : cylinder segment (45° to 90°) = 4.09567 : 4.48527 is a nice ratio.

4pi × r² is too large, for cylinder's radius is always full from zero height to the top height, while sphere's radius varies between 0 to 1 depending the height.

You shouldn't resemble cylinders area as large as sphere's area. Such magnitude gives a logic failure.
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #10 on: January 06, 2025, 06:08:31 AM »
Feel free to correct it if any.
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #11 on: January 06, 2025, 05:04:34 PM »
As long as Jackblack don't touch this thread for a long time, the content of this thread is already verified.

Thank you, Jack 🙏
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #12 on: February 13, 2025, 02:32:31 PM »
Correction:

Area of 'umbrella' at sin45 is not 3/3.17157 × 1.9939033 = 1.886039.

It's sin45/0.7928932 radian ×  1.9939033 = 1.77817.
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #13 on: February 13, 2025, 02:40:14 PM »
So far this thread is free from objection due to its clear logic, especially the entire cylinder area surrounding the sphere is definitely larger than the sphere area. 4 Pi AKA cylinder area is incorrect for determining sphere area whose area must be smaller than cylinder area, coz it lies inside the cylinder. 
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Danang

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Re: How dare you call it's 12.56 ;D ;D ;D
« Reply #14 on: February 13, 2025, 02:52:08 PM »
From half cube to hemisphere, there are 3 rounding by 0.7928932 AKA Phew/4.

1. Circumference = 4 sides × 0.7928932 = 6.34314
2. Height = 1 × 0.7928932 = 0.7928932
3. Diameter of top circle = 2 × 0.7928932 = 1.5857864

Hemisphere area = 12 × 0.7928932³ = 5.98171.
Total sphere area = 2 × 5.98171 = 11.96342 × r²
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