The Procedure to Calculate a Cone's Volume

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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #30 on: December 30, 2018, 03:37:56 AM »
Yes, points with the same distance to the center point will form a perfect circle line.

Who are hoaxers here.... hands up please ~

;D ;D       ;D ;D ;D ;D
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #31 on: December 30, 2018, 10:22:21 PM »
Now I'm at office. Autocad is one click far to me. Whose want me to split a circle to 1.000.000 triangle?   :)
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #32 on: December 30, 2018, 11:14:26 PM »
Damn danang is right about autocad draws it wrong!

Autocad could not overlapped the circle and a line has value of R.

First I draw a circle has radius of 1 000 000 000



Then splitted one of its quarter to two equal part by using a line has same radius as 1 000 000 000



Until now, everything is okay. In this point, we have to check the intersection point about, is danang right or not. So we are zooimg the intersection:



Shit. Our line has 1 000 000 000 units is longer than radius has theorically 1 000 000 000. But as far as we see, circle is actually less than 1 000 000 000. There is some missing areas here. My job is harder now. Because this circle never will be perfect. Even so I'll done the working by considering the missing area.

This proves pi is actually bigger than calculated. But how much? We can make an estimation about it as comparing the lenghts by shrinking our line:



This is the ratio:

999871538 / 1000000000 % mistake. But we will calculate pi depends on square of R. So we have to multipy it by itself. Then it turns to:

0,999871538^2= 0, 99974309.

If same mistake continues during all circle, pi turns to:

3.14159265359/0,99974309= 3,1424

This is an estimation value related whether if same mistake continues. We'll do better estimation even at the end of this working by correcting all values right this way.
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #33 on: December 30, 2018, 11:58:17 PM »
For continue the drawing, I have took line as R as same and enlarged the circle till R value. Then splitted it to two.

Inother say, this is real arc has real R value and corrected.



And one more time; R value wants to be bigger!



Arc value is R= 1 000 000 000

And line we used it for split the arc;



You see one arc and one line has same Radius or Line lenght, but could not intersected.

For continue to project; I'll get line as true, because it is a line and change the arc value through line again.

In this point, we can calculate a corrected second pi value.

Pi was equal to 3,1424

Now it turns to:



3,1424/0,999972659^2 = 3,1426

If you wondr it; no, I'm not shrinking the line. Oppositely I'm enlarging the arc to make them equal. I'm just shrinking the line temporary for see the temporary pi values. Then I'm going to enlarge it then draw an arc overlaps to it.
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #34 on: December 31, 2018, 12:23:41 AM »
Third correction:

We had a pi value as 3,1426

Now we have another splitted circle and another missing point. I have dvided the arc two parts with a line has R value again.



Then we have missed the intersection one more time:



One more time again, line is longer.

Average mistake here:



So corrected temporary pi value:

Pi was as a last:3,1426

Now Pi= 3,1426 / 0,999939272^2= 3,1430.

Did it speed up to increase?
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #35 on: December 31, 2018, 02:36:43 AM »
I've gave up to examine the differences and started to directly continue the drawing by correct-verify-correct-continue. Otherwise it takes a lot of time. By this way I can finish it within a hour.
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #36 on: December 31, 2018, 03:43:13 AM »
It has still not finished. I came through 1/8192. After that Autocad has started to lost its sensitivity, interestingly.





If we can not trust to autocad so who do we trust to?



There will always a missing area. Even so, it is almost line so that I'll finish the working by geting the R value as line again and correct values as soon as possible. Even so I'll try to correct those mistakes as far as possible. So much so that, we may make a mistake atmost 1/8192. It makes pi atmost 3,141592* (1+1/8192)= 3,1419. But we have calculated earlier we'll calculate a pi value perhaps bigger than it. We'll see, soon...
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #37 on: December 31, 2018, 04:05:00 AM »
After arrived the 65536 sensitivity, I have gave up to continue. Because it has turned to line and more process decreases sensitivity.

Ok.

result.

Pi= 3,14159997

As we see that they are deceiving us. This is not the 3,141592 but 3,141599.

Ok, danang. You're right. It is not 3,141592 but 3,141599. They are deceiving us.
If you're not on the side of wise, so you're probably on the wrong side.


Why is it Bill Gates?




Re: The Procedure to Calculate a Cone's Volume
« Reply #38 on: December 31, 2018, 05:44:40 AM »
Damn danang is right about autocad draws it wrong!

Autocad could not overlapped the circle and a line has value of R.

First I draw a circle has radius of 1 000 000 000



Then splitted one of its quarter to two equal part by using a line has same radius as 1 000 000 000



Until now, everything is okay. In this point, we have to check the intersection point about, is danang right or not. So we are zooimg the intersection:



Shit. Our line has 1 000 000 000 units is longer than radius has theorically 1 000 000 000. But as far as we see, circle is actually less than 1 000 000 000. There is some missing areas here. My job is harder now. Because this circle never will be perfect. Even so I'll done the working by considering the missing area.

This proves pi is actually bigger than calculated. But how much? We can make an estimation about it as comparing the lenghts by shrinking our line:



This is the ratio:

999871538 / 1000000000 % mistake. But we will calculate pi depends on square of R. So we have to multipy it by itself. Then it turns to:

0,999871538^2= 0, 99974309.

If same mistake continues during all circle, pi turns to:

3.14159265359/0,99974309= 3,1424

This is an estimation value related whether if same mistake continues. We'll do better estimation even at the end of this working by correcting all values right this way.
I used a spreadsheet to so this.  I assumed a circle with a radius of 1 and broke it up into 251327 triangles.  When I added up the area of all the triangles I got 3.1415875.

If I break it up into ≈1,000,000 triangles and the sum of area of the triangles is 3.141592.

Since it costs 1.82 to produce a penny, putting in your 2 if really worth 3.64.

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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #39 on: December 31, 2018, 09:06:59 AM »
The program which I used did not let me divide more the circle. Perhaps your method was better. I agree this.
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Re: The Procedure to Calculate a Cone's Volume
« Reply #40 on: December 31, 2018, 09:55:19 AM »

I used a spreadsheet to so this.  I assumed a circle with a radius of 1 and broke it up into 251327 triangles.  When I added up the area of all the triangles I got 3.1415875.

If I break it up into ≈1,000,000 triangles and the sum of area of the triangles is 3.141592.



Your example (in which we don't see the formulas) is using calculations where Excel is manipulating lots of small numbers (b ~ 6E-6) and in one case *squaring* that value. But you should be aware that Excel results cannot be treated as infallible.

For example, type the following into a cell in Excel:

=((1-(1/900000000)-1)*900000000)+1

The result *should* be zero, right? And none of these numbers is anywhere near the 15 digit limit where roundoff error might occur.

What does Excel return?

0.000000017179701217173700000000

It can be even more deceptive in cases that look trivial:

=((1-(1/9^9)-1)*9^9)+1

Should be zero, Excel returns

-0.000000014612343779418800000000


So don't take for granted that Excel is always providing you with the correct value when manipulating a million triangles.

Re: The Procedure to Calculate a Cone's Volume
« Reply #41 on: December 31, 2018, 01:33:31 PM »

I used a spreadsheet to so this.  I assumed a circle with a radius of 1 and broke it up into 251327 triangles.  When I added up the area of all the triangles I got 3.1415875.

If I break it up into ≈1,000,000 triangles and the sum of area of the triangles is 3.141592.


Your example (in which we don't see the formulas) is using calculations where Excel is manipulating lots of small numbers (b ~ 6E-6) and in one case *squaring* that value. But you should be aware that Excel results cannot be treated as infallible.

For example, type the following into a cell in Excel:

=((1-(1/900000000)-1)*900000000)+1

The result *should* be zero, right? And none of these numbers is anywhere near the 15 digit limit where roundoff error might occur.

What does Excel return?

0.000000017179701217173700000000

It can be even more deceptive in cases that look trivial:

=((1-(1/9^9)-1)*9^9)+1

Should be zero, Excel returns

-0.000000014612343779418800000000


So don't take for granted that Excel is always providing you with the correct value when manipulating a million triangles.
I understand you're point but the calculations I'm doing are well with in the internal mantissa and are straight forward equations. 

If you simplified your initial equation to =(-1/900000000)*900000000+1 you do indeed get 0.00. 

Further, if you breakdown your example as follows you also get 0.00 as the answer.
=(-1/900000000)*900000000
=1+A1
=A2-1
=A3+1

This is why its important to understand how floating-point calculations work and ensure youre using properly formatted equations.

As you can see from the formulas, my equations are very straight forward and do not rely on pi.  I get the exact same results with my HP48-GX and a simple FORTRAN program I wrote. 

Ive provided the formulas so anyone can verify my results using any software they want.



Mike
Since it costs 1.82 to produce a penny, putting in your 2 if really worth 3.64.

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Danang

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Re: The Procedure to Calculate a Cone's Volume
« Reply #42 on: December 31, 2018, 02:03:35 PM »
To count a triangle:
Area = 1/2 Sin x.

The more fractions counted -say in 45- the lesser degree for a fraction, at the same time the more quantities of "umbrella" areas will be abandoned - although its area sizes become narrower, it cannot regarded as "zero". Even this tiny areas become bigger in quantity in line with the smaller angle per fraction counted. The abandoned tiny umbrella areas quantity can be 64 or 128 or 1024 or even can be 1.000.000 pieces and more. These fractions maybe small in area size but many in quantity and they cannot be abandoned.

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Danang

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Re: The Procedure to Calculate a Cone's Volume
« Reply #43 on: December 31, 2018, 02:15:59 PM »
The abandoned umbrella area = [ (X/45)0.3964 ] - 1/2 sin X

The umbrella quantity = 45/X
Angle = 45/umbrella quantity

The smaller angle the bigger quantity of umbrellas.
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Danang

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Re: The Procedure to Calculate a Cone's Volume
« Reply #44 on: December 31, 2018, 02:20:17 PM »
"In the rainy day, abandoning the umbrella makes you get wet" - Saturn Proverb  8)
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Re: The Procedure to Calculate a Cone's Volume
« Reply #45 on: December 31, 2018, 02:30:56 PM »

I understand you're point but the calculations I'm doing are well with in the internal mantissa and are straight forward equations.


Can you point out where my calculation is not within the internal mantissa? Excel holds 15 digits. What's wrong with mine?


If you simplified your initial equation to =(-1/900000000)*900000000+1 you do indeed get 0.00.


That's the point. The equation done by hand correctly reduces to zero. But I am only giving a concrete example. Suppose A, B, C, D, E, and F are variables

=(((A-(B/C))-D)*E)+F

Then, in the situation when
A = 1
B = 1
C = 900000000
D = 1
E = 900000000
F = 1

the error occurs. It means that you cannot implicitly trust Excel for the correct answer.


This is why its important to understand how floating-point calculations work and ensure youre using properly formatted equations.


I agree it's important to understand how floating point calculations work. Please show in my example where this is a floating point calculation error.


As you can see from the formulas, my equations are very straight forward and do not rely on pi.


Really? The number of triangles that you are summing (the rather bizarre value of 1000507) is dependent on Cell C21, which is the arcsin function.

Since Excel returns ASIN(1) = 1.570796327 (i.e., pi/2), Excel's value of pi is built into the very heart of your calculation.

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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #46 on: December 31, 2018, 07:16:03 PM »
To count a triangle:
Area = 1/2 Sin x.

The more fractions counted -say in 45- the lesser degree for a fraction, at the same time the more quantities of "umbrella" areas will be abandoned - although its area sizes become narrower, it cannot regarded as "zero". Even this tiny areas become bigger in quantity in line with the smaller angle per fraction counted. The abandoned tiny umbrella areas quantity can be 64 or 128 or 1024 or even can be 1.000.000 pieces and more. These fractions maybe small in area size but many in quantity and they cannot be abandoned.



But the missing area is going to small with increasing number of every fractions.



After a while we do not have to calculate them; even with your phew, it turns to the ordinary pi.
If you're not on the side of wise, so you're probably on the wrong side.


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Danang

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Re: The Procedure to Calculate a Cone's Volume
« Reply #47 on: December 31, 2018, 08:08:48 PM »
After arrived the 65536 sensitivity, I have gave up to continue. Because it has turned to line and more process decreases sensitivity.

Ok.

result.

Pi= 3,14159997

As we see that they are deceiving us. This is not the 3,141592 but 3,141599.

Ok, danang. You're right. It is not 3,141592 but 3,141599. They are deceiving us.

They've got "superstitions", so they changed the actual number to be whatever they wish. based on that "superstition". They don't care about the truth.
(Curved Grided) South Pole Centered FE Map AKA Phew FE Map
Downwards Universal Deceleration.

Phew's Silicon Valley: https://gwebanget.home.blog/

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Danang

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Re: The Procedure to Calculate a Cone's Volume
« Reply #48 on: December 31, 2018, 08:13:53 PM »
To count a triangle:
Area = 1/2 Sin x.

The more fractions counted -say in 45- the lesser degree for a fraction, at the same time the more quantities of "umbrella" areas will be abandoned - although its area sizes become narrower, it cannot regarded as "zero". Even this tiny areas become bigger in quantity in line with the smaller angle per fraction counted. The abandoned tiny umbrella areas quantity can be 64 or 128 or 1024 or even can be 1.000.000 pieces and more. These fractions maybe small in area size but many in quantity and they cannot be abandoned.



I'm sorry I took the picture from Google. It's supposed to be clear without any number n degrees
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wise

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Re: The Procedure to Calculate a Cone's Volume
« Reply #49 on: January 01, 2019, 02:40:04 AM »
After arrived the 65536 sensitivity, I have gave up to continue. Because it has turned to line and more process decreases sensitivity.

Ok.

result.

Pi= 3,14159997

As we see that they are deceiving us. This is not the 3,141592 but 3,141599.

Ok, danang. You're right. It is not 3,141592 but 3,141599. They are deceiving us.

They've got "superstitions", so they changed the actual number to be whatever they wish. based on that "superstition". They don't care about the truth.

If we would talk about lenght or the circumference, then you would have a right point. But we are calculating the area depends on rectangles or triangles and the missing area is going to be zero after a while. Inother say, mistake limit of our calculations are going to zero.
If you're not on the side of wise, so you're probably on the wrong side.


Why is it Bill Gates?




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Danang

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Re: The Procedure to Calculate a Cone's Volume
« Reply #50 on: January 01, 2019, 05:38:27 AM »
After arrived the 65536 sensitivity, I have gave up to continue. Because it has turned to line and more process decreases sensitivity.

Ok.

result.

Pi= 3,14159997

As we see that they are deceiving us. This is not the 3,141592 but 3,141599.

Ok, danang. You're right. It is not 3,141592 but 3,141599. They are deceiving us.

They've got "superstitions", so they changed the actual number to be whatever they wish. based on that "superstition". They don't care about the truth.

If we would talk about lenght or the circumference, then you would have a right point. But we are calculating the area depends on rectangles or triangles and the missing area is going to be zero after a while. Inother say, mistake limit of our calculations are going to zero.

So far I probably haven't shared the following amazing facts about C & A in Phew calculations:

>>  C & A are indeed of different dimentions. But C magnitude is precisely Twice of A magnitude.
E.g.: for 45, C = 0.79289 (length unit) and A = 1/2 0.79289 = 0.396445 (area unit)

The same case applies to the sin magnitude within C segment equals Twice of triangle area within A fraction.
E.g.: for 45, the arc's Sin value equals 0.7071 (length unit), while its area equals 1/2 Sin 45 = 1/2 0.7071 = 0.35355 (area unit)

The umbrella gives the similar reality:

The arc length & sin difference equals Twice of umbrella area.
E.g.: for 45, arc length & sin difference equals 0.79289 - 0.7071 = 0.08578 (length unit) while the umbrella area equals 1/2 0.08578 = 0.04289 (area unit).
(Curved Grided) South Pole Centered FE Map AKA Phew FE Map
Downwards Universal Deceleration.

Phew's Silicon Valley: https://gwebanget.home.blog/