Danang says pi=3

Quote from: th3rm0m3t3r0 on October 17, 2017, 03:20:43 PM

If a circle doesn't exist in euclidean space and satisfy pi = 3.1416, it's, by definition, not a circle.

Show me a circle where C/d != pi, and I will show you a non-circle.

Pretty much any smooth line of constant curvature in Euclidean space.
Even great circles arguably.
Consider a spherical space, with a "radius" of 12/(2*pi).
This means a great circle in this space has a length of 12.
Draw a circle with radius 3 (or diameter 6).
This goes around the "equator" of this space. Thus the length of the circumference of the circle is 12.
Thus you have a circle (in non-Euclidean space), with C/d=2.
Now consider a circle with radius 1 (diameter 2). This would correspond to a line at 60 degrees north on Earth. This means it has a circumference of 6.
This means it has C/d=3.

Are we talking about different circles?

A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.

All circles are similar.
A circle's circumference and radius are proportional.
The area enclosed and the square of its radius are proportional.
The constants of proportionality are 2π and π, respectively.

...the number pi remains constant: its value never changes. This is because the relationship between the circumference and diameter is always the same.[1]

Are we talking about different circles?

Quote

A circle is a simple closed shape in Euclidean geometry. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant.

Considering I am discussing ones which include those in NON-EUCLIDEAN geometry, I would say yes, we are talking about different circles. You are talking about a subset of the ones I am talking about.

I am using this definition:

a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the centre).

So going to focus on the non-Euclidean circles, or just limit it to Euclidean ones?

Note: Similar things can be said for parallel lines, which only hold in Euclidean geometry.
Just because there are statements like that doesn't mean they hold universally.

Also note that most 2D geometries are defined using Euclid's postulates or their equivalents, with the 5th postulate being removed for the non-Euclidean geometries.
These 4 remaining postulates which are also used for spherical and hyperbolic geometry are:

1. To draw a straight line from any point to any point.
2. To produce [extend] a finite straight line continuously in a straight line.
3. To describe a circle with any centre and distance [radius].
4. That all right angles are equal to one another.

Notice a key one? 3. Circles need to exist.

Are we talking about different circles?

No, different geometries.

Quote from: JackBlack on October 17, 2017, 12:33:30 AM

Quote from: th3rm0m3t3r0 on October 16, 2017, 05:54:33 PM

This doesn't make any mathematical sense. What would circles look like if pi = 3?

It would mean space isn't Euclidean.
For example, in spherical geometry (what the FEers kind of need), it is 2 (at least in some instances).

The problem is that only holds for one circle or one point. Anywhere else and it breaks.

If a circle doesn't exist in euclidean space and satisfy pi = 3.1416, it's, by definition, not a circle.

Yes, "in Euclidean space" for a circle, the circumference = 2 × π × radius,
But that is not true if all points are confined to a non-Euclidean space, such as Spherical Geometry.

Show me a circle where C/d != pi, and I will show you a non-circle.

For many examples of circles in Spherical Geometry, where the circumference ≠ 2 × π × radius see: Google,  Circle in Spherical Geometry.

In these the radius and circumference must be measured along the surface of the sphere.
One particular example is a Great Circle where the the circumference = 4 × radius.
On this diagram, the equator is a Great Circle and the radius is the distance along any Meridian of Longitude from the North (or South) Pole to the Equator.
To a very close approximation, the circumference of the equator is 40,000 km and the radius (in Spherical Geometry) is 10,000 km.

But, as far as I am concerned, Spherical Geometry and Spherical Trigonometry are just artifices that are useful in calculating distances and bearing on the surface of the Globe.

The real earth is not a perfect sphere, but much closer to (within a couple of hundred metres) an ellipsoid.
Though even those "couple of hundred metres" are significant when applying GPS coordinates and altitudes.

Quote from: Danang on October 17, 2017, 10:30:11 PM

C=4(1+¾²)r

Why?
I don't think anyone understood your post where you explained that. Can you clarify what you wrote there?

Analysis of a quarter of the frame square:
In 1 m radius scale, total distance of the ¼ square frame equals 2m. It has two chambers: 2m=1m+1m each.
So, the two chambers give full distance.
The ¼ circle within has two chambers as well: 1m+0.5625m each. The average=(1m+0.5625m):2=0.78125.
This is the proportion between the circle & the frame.

So the curve within ¼square will be (0.78125:1)×2 m = 1.5625m.

Total circle=¼circle×4=1.5625m×4=6.25 m.
Phi=½circle AKA C:d=6.25m:2m=3.125.

0.78125 comes from quadratic value of ¾ s>> ¾²=9/16 AKA 0.5625. It is gaining of one chamber for one ¼ circle.
It is added with another chamber which get full gaining.
Total : 1+0.5625=1.5625 (either by meters or by second).
Comparion:
1.5625m:2m=0.78125.
This value is correcting the previous 1½:2 AKA ¾.
It's 1.5625, not 1.5, coz we play in 2 dimention calculation (slope). Not 1 dimention (straight distance AKA d=½.a.t²) which gets 1 part of velocity+ ½ part of acceleration, whose distance is compared to 2 max, resulting pure ¾)


Equation:
C=(¾²+1²):2×8m=0.78125×8m=6.25 m.

Conclussion:
frame:curve=1:0.78125
Radius:curve=0.5:0.78125=1:1.5625

Assuming the observable universe is a perfect sphere and you know its diameter, if you wanted to calculate its circumference and be accurate to within a Planck length, you would only need something like 63 digits. Just saying 

Pi works. Just leave it be

I appreciate this method, but I tried to search the calculation by a formula to get the exact measurement.
Till this moment.

Analysis of a quarter of the frame square:
In 1 m radius scale, total distance of the ¼ square frame equals 2m. It has two chambers: 2m=1m+1m each.
So, the two chambers give full distance.
The ¼ circle within has two chambers as well: 1m+0.5625m each. The average=(1m+0.5625m):2=0.78125.
This is the proportion between the circle & the frame.

Still not sure what you are trying to say.
Can you draw a picture?

Or try and explain a bit better.
For example:
You have 2 squares, each with side length 1. The corners of 1 square are (0,0), (0,1), (1,1), (1,0).
The corners of the other square are (0,0), (-1,0), (-1,1), (0,1).

Now, where is the circle centred, and what is its radius?

I appreciate this method, but I tried to search the calculation by a formula to get the exact measurement.
Till this moment.

Pi is irrational and transcendental. You cannot get an exact measurement.

If you define it as three, I have found out it is interesting, but not relevant

If you define it as three, I have found out it is interesting, but not relevant

Like your relativity model.

Actually, Pi would have to be a variable on the flat earth model when you back-engineer it based on the actual distance per the circumference of the earth at each latitude compared to the same circumference on the flat earth azimuthal map. It would range from 3.142 close to the North Pole, to around 2 at the equator and up to infinity at the South Pole. Here is a table of values:

           Globe Earth radius (kms)    6369       (from center of sphere)   
      Flat Earth radius (kms)   10001.75       (from North pole to Equator, unless any FE'er thinks otherwise)   
                                                                                                                                                              Required
   Latitude in        Circumference of Flat       Approx. latitude               % Ratio Flat Earth              change of Flat Earth Pi
       Degrees            Earth latitude            circumference on Globe             value to actual                to get actual results
         90.0                         0                                 0.00                                 100.000                               3.141593
         89.9                       69.83                          69.84                                   99.974                               3.142424
         89.5                     349.13                        349.22                                   99.975                               3.142386
         89.0                     698.25                        698.40                                   99.979                               3.142266
North 80.0                   6982.54                      6948.98                                 100.483                               3.126496
         70.0                 13965.08                    13686.83                                 102.033                               3.078997
         60.0                 20947.62                    20008.80                                 104.692                               3.000795             
         50.0                 27930.15                    25722.82                                 108.581                               2.893311
         40.0                 34912.69                    30655.27                                 113.888                               2.758491
         30.0                 41895.23                    34656.26                                 120.888                               2.598765
         20.0                 48877.77                    37604.25                                 129.979                               2.416993
         10.0                 55860.31                    39409.65                                 141.743                               2.216405
Equator                     62842.85                    40017.61                                 157.038                               2.000530
         10.0                 69825.39                    39409.65                                 177.178                               1.773124
         20.0                 76807.93                    37604.25                                 204.253                               1.538087
         30.0                 83790.46                    34656.26                                 241.776                               1.299383
         40.0                 90773.00                    30655.27                                 296.109                               1.060958
South 50.0                97755.54                    25722.82                                 380.034                               0.826660
         60.0               104738.08                    20008.80                                 523.460                               0.600159
         70.0               111720.62                    13686.83                                 816.264                               0.384875
         80.0               118703.16                      6948.98                               1708.209                               0.183912
         89.5               125336.57                        349.22                             35890.940                               0.008753
         89.9               125615.87                          69.84                           179852.406                               0.001747
         90.0               125685.70                            0.00                                   infinite                               0.000000