[aetzbar (OP)]

The big bang in geometry

[Bored chemist]

Why have you posted the same thing lots of times?
Is it because you don't like the answer you get?
https://www.thenakedscientists.com/forum/index.php?topic=71309.msg521957#msg521957

[jeffreyH]

Pi is an irrational number where the digits don't repeat. There are quit a few ways to calculate it. All of them give the same answer.
http://www.mathscareers.org.uk/article/calculating-pi/

[alancalverd]

Problem is that the simplest definition of π is the ratio of circumference /diameter of a circle, and the definition of a circle is the locus of points at a fixed radius from the centre. Now if we allow π  to be variable, either all circles will be differently shaped, in which case the definition of a circle is meaningless, or the ratio diameter/radius  is variable. But we know that d/r = 2 by symmetry, so if π is variable, so is 2. But 2 is defined as a constant.

And since e^iπ= -1, a variable π implies that e, i or 1 is variable. Which would be OK if numbers were psychic so that, for instance, 1 somehow "knew" what value to take when  π wobbled a bit.

[aetzbar (OP)]

Setting the circle as a collection of dots does not create a closed compass line.
The line is the fundamental concept of geometry.
The line has a real length (a quantity of mm) and a shape.
The expression of the shape is a unique pi.

[GoC]

  We live in a 3d point universe. Points can get closer together but never become a true circle. A pure circle is impossible and irrational to the make up of the universe. That is why centrifugal force can be created. Dilation will give you a curved aspect to space but it is still point to point. Dilation is just localized expansion to point to point in the presence of mass.

[aetzbar (OP)]

Everything you say is interesting, but the subject I raised is purely geometric.

[jeffreyH]

Problem is that the simplest definition of π is the ratio of circumference /diameter of a circle, and the definition of a circle is the locus of points at a fixed radius from the centre. Now if we allow π  to be variable, either all circles will be differently shaped, in which case the definition of a circle is meaningless, or the ratio diameter/radius  is variable. But we know that d/r = 2 by symmetry, so if π is variable, so is 2. But 2 is defined as a constant.

And since e^iπ= -1, a variable π implies that e, i or 1 is variable. Which would be OK if numbers were psychic so that, for instance, 1 somehow "knew" what value to take when  π wobbled a bit.

I think that Alan's answer sums it up nicely. It is absurd to think otherwise.

[evan_au]

Most people think of a circle as being a plane figure, as Euclid did around 300 BC.

But we have known for a similar period that the Earth is not a flat surface, so if you draw a circle on the Earth, the value of pi will not be the same as Euclid's Pi (although it will be pretty close, for small circles).
- If you measure distance around the surface of the Earth, you will find that a circle with "diameter"=20,000km will have a "circumference" of only 40,000km, so in this case, "pi"=2.
- If you draw a circle with a "radius" almost 40,000km, you will find that the "circumference" is much smaller than the "radius", and "pi" is around 0.

The opposite effect happens if you draw a circle on a shape like a horse saddle. "pi" is greater than the familiar 3.14159... (although it will be very close for small circles.

And that brings us back to cosmology. We can't tell from today's measurements if the universe is Euclidean (flat) or is more like a sphere or a saddle. But it's pretty close to flat, and pi is pretty close to 3.14159....

See: https://en.wikipedia.org/wiki/Non-Euclidean_geometry

Setting the circle as a collection of dots does not create a closed compass line.

Before the 1900s, mathematicians were allergic to infinities.
Now they are a bit more comfortable with the concept, and will happily accept that an infinite number of points, all equidistant from a given point, will form a shape that is indistinguishable from the line generated by an ideal compass.

This is called a locus of points. See: https://en.wikipedia.org/wiki/Locus_(mathematics)

The line is the fundamental concept of geometry.

I would say that the 2D line is one of the fundamental concepts of Euclid's geometry. It came in 2 flavors:
- A straight line, from a ruler
- A circular line, from a compass
- However, there are many other kinds of lines (like ellipses, parabolas and hyperbolas) which Euclid recognised as being real conic sections, but could not be generated by a straightedge and compass
- Ellipses can be generated with a piece of string and a couple of pins, but Euclid would call that "cheating" - it comes back to the allergy to infinities.

Euclid also recognised points, planes and some 3D shapes.

Today, geometry has been generalised in a number of ways, such as:
- non-Euclidean geometry (see above)
- Multidimensional geometry, which is the basis for string theory, a hot topic in theoretical physics
See: https://en.wikipedia.org/wiki/M-theory#Number_of_dimensions

[aetzbar (OP)]

Maybe I did not explain myself correctly.
I'm talking about circles on plane.
A circle is a closed line drawn in the plane, using a device (calipers)
For any actual length of such a closed line, there is a unique ratio number.
The actual length of such a closed line, expresses a quantity of mm
The ratio of closed lines varies from 3.1416 to 3.164
3.164 belongs to a very small closed line, that approaches zero mm
3.1416 belongs to a huge closed line, which approaches infinity mm

thanks

[Bored chemist]

Maybe I did not explain myself correctly.
I'm talking about circles on plane.
A circle is a closed line drawn in the plane, using a device (calipers)
For any actual length of such a closed line, there is a unique ratio number.
The actual length of such a closed line, expresses a quantity of mm
The ratio of closed lines varies from 3.1416 to 3.164
3.164 belongs to a very small closed line, that approaches zero mm
3.1416 belongs to a huge closed line, which approaches infinity mm

thanks

It's not a problem of explanation.
We understand what you mean.
It's just that you are wrong.

[aetzbar (OP)]

I do not expect those who respond to me to approve the changing pi idea.
The certificate can only provide a real experiment.
I hope that a scientific institution will conduct the experiment I described.
At this point I just wanted to present an idea.
The idea is innovative, and no wonder it is opposed.
Why did Pi change? Pi has been considered fixed for 2000 years.
Thank you for your active participation.

[Bored chemist]

The certificate can only provide a real experiment.
I hope that a scientific institution will conduct the experiment I described.

Why do you keep saying that?
I posted a report of people actually doing the experiment (and showing that pi is constant).
Did you not understand it?

[aetzbar (OP)]

Your answer supports the changing pie idea.
Measurement can not determine perfect equality.
Therefore, measurement can not determine that pi is equal in two selected circles.
Measurement can only determine inequality.
The measurement I am proposing should reveal inequality.
The ratio of diameters of two circuits> of the circumference ratio of the circles

Science has not yet made such a measurement.
This is the challenge of the 21st century
I hope that a scientific institution will accept the challenge.

[Bored chemist]

Measurement can only determine inequality.

That's correct.
And, in the case of the experiment I told you about they were able to show that the variability of pi was less than 20 parts per billion.

Do you understand what that means?

Among other things, it means that you are simply wrong to say "Science has not yet made such a measurement."
Yes it has.
The measurement shows you are wrong.

[aetzbar (OP)]

where is the measurement  ?

https://en.wikipedia.org/wiki/Experimental_uncertainty_analysis

[aetzbar (OP)]

Where is the measurement on circles?
The link you presented does not have this measurement.
If there was such a measurement, it had a primary purpose.
Determine whether the diameter ratio of two circuits is (equal or not equal) to the circumference ratio of the circuits.
But such a measurement has never been made, since it is very difficult to perform.
And what did the mathematicians do? They simply decided that the relationship was exactly the same.
The result: a fixed pi for all circles, and this error takes thousands of years.
The measurement I propose will correct the mistake

[Bored chemist]

Where is the measurement on circles?
The link you presented does not have this measurement.
If there was such a measurement, it had a primary purpose.
Determine whether the diameter ratio of two circuits is (equal or not equal) to the circumference ratio of the circuits.
But such a measurement has never been made, since it is very difficult to perform.
And what did the mathematicians do? They simply decided that the relationship was exactly the same.
The result: a fixed pi for all circles, and this error takes thousands of years.
The measurement I propose will correct the mistake

OK, the purpose of the experiment is to define the kilogram.
It's remarkably easy to get an accurate mass of a single atom ("easy" in this case means the equipment costs less than a million pounds).
So, all they have to do is get a lot of atoms together, and count them.
So, in essence they did just that.
They made a sphere of silicon (they chose silicon because the semiconductor industry has learned to make big, near perfect, crystals of it.)
And they counted the atoms in it- They did that by measuring the individual atoms - which are very small spheres- and scaling it up to the sphere they made- which is about 10 cm in diameter.
If the value of pi varied with the radius of a circle, then it would also vary with the radius of a sphere.
And, if that happened, they would get the "wrong" value for the mass of the sphere.
But the measurement agreed with other methods.
So they know that pi is constant. (It's not what they set out t look for but if pi varied they would have got the wrong answer.)

So, that experiment shows that you are, in fact, wrong.
So does my "thought experiment" of the shadow of a ring.

Why can't you accept that you are just plain wrong?
There's a mistake somewhere in your so-called proof.

[aetzbar (OP)]

I know that thousands of years teach us .... "Pi is a fixed number".
So I'm not surprised you object to the idea ... "Pi is a variable number in a narrow field."
I can not convince you with words, but only with the results of actual measurement.
Science does not know this measurement.
When a scientific institution agrees to do the measurement, everyone will agree that pie is not constant.
Pi of a tiny circle - it is bigger - the pi of a huge circle.
What a beautiful geometric reality - each circle has a unique pie.

[aetzbar (OP)]

if this interests you, this is an experiment that a scientific institution should do.

Thanks