Excerpt for Today's Value for Pi Is Incorrect by , available in its entirety at Smashwords

Today's Value for Pi is Incorrect


Written by Dr. John G. Rose

Published at Smashwords.com

Copyright © May 15, 2018



Throughout the history of mathematics, it has been found that infinity can be tricky, in fact, very, very tricky. And, considering this essay, when working with infinity you must be aware that in three-dimensional reality, a.k.a. the real, material world, or the world we live in, infinity cannot exist between two points.

It is always important to distinguish what can exist only in the imagination from what exists simultaneously in the imagination and in the real world. Since pi is used to represent real, material objects, it cannot be infinite.

To prove that infinity cannot exist between two points in the real world—the imagination, three-dimensional reality, mathematics, and logic will be used:

Consider two objects in space. They start traveling away from each other faster and faster, but no matter how fast they go nor how long they travel there will never be an infinite distance between them. Picture this in your imagination.

This is logical proof that infinity cannot exist between two objects in the real world, but this is an expanding distance proof. What about as two objects come closer together? Can there be an infinite, diminishing distance between them? This is an important question for determining pi, because pi is an infinite number which is getting closer and closer as it closes in on an infinitely distant end point.

One must understand that numbers do not exist in Nature—they are a manmade tool. In Nature a distance isn’t determined by numbers. When you cross a certain distance, numbers will not keep you from getting to the end of the distance. In the real-world infinity does not exist in a distance. When two objects are closing in on each other, the distance will always be finite until the objects touch, and then there will be no distance between them.

When you see two objects, such as a pen and a pencil laying on a desk about a hand's width apart, you don't view the distance with numbers. Only numbers can make a distance infinite. In the real world it's just a distance that can become greater if you move the pen and pencil away from each other, or shorter if you move them toward each other. When mathematicians create infinity between two points they are working in the imagination, not the real world. And the work they're doing will never transpose to the world we live in.

Zeno's paradox is an example of how numbers can be manipulated to create untruths in three-dimensional reality.

For the second proof I will use Zeno's paradox, but I will use a different example than what he used.

When taking a stride to move across the living room, first my foot has to move to one half of my stride, and then it has to move to the next half of the distance and then the next half and the next half and so on into infinity. It's a ½ of a ½ of a ½ forever. This means my foot is getting closer and closer to the floor, but it will never complete the stride because it has to go an infinite distance. But Zeno takes it a step further, he states before my foot can reach half my stride it first has to reach half of the distance of half my stride, but it has to reach half of that distance, and half of that distance and half that distance, ad infinitum. And this means my foot will never leave the starting point.

And therefore, he concludes this will be a limit for every physical action. From this he believes motion does not exist. "Motion is a figment of our imagination," he says.

But we know motion is a reality, and I can walk across the floor. Therefore, there cannot be an infinite distance within a distance in the real world.

Because infinity is a difficult concept to grasp, the solution to this paradox was not found for nearly 2,500 years.

In conclusion, infinity cannot exist between two points in three-dimensional reality. No matter what mathematical form it comes in, including Cantor's Continuum Hypothesis, infinity can only exist in the imagination. If you believe infinity can exist between two points in the real world, then you will never walk across the floor.

Remember: distance in the real world is distance without numbers.

Here's an interesting idea: draw a straight line with a beginning and an end point. Now put an infinite number of points on the line or divide the line into an infinite number of segments. By the time you get to one quintillion, or perhaps sooner, you will realize no matter how many points or segments you put on or into the line you will never reach infinity. Why? Because infinity cannot exist between two points in three-dimensional reality. It can only exist in the imagination.

With this in mind let's examine the value of pi.

First, what is pi? It is a ratio of how many times the diameter will go around the circumference of its circle from the beginning of the circle around to the beginning of the circle. Today’s mathematicians believe the ratio of the diameter to the circumference, which is pi, is 3.14159 … ad infinitum.

To move forward in this essay, the idea of a ‘ratio’ must be understood.

A ratio is a comparison between two Natural numbers; for example, one cup of water to two cups of flour is a ratio, or 1:2, or the amount of water is ½ the amount of flour is a ratio. If you are cooking for a large group of people and you want to use twenty cups of flour, then the water will be ten cups. But with the changing of the amount of flour and water the ratio stays the same, 1:2. Whatever the amounts, they can always be reduced to the ratio. But an infinite number cannot be reduced.

Pi is a different type of ratio than what is typically used, e.g., a ratio of two cups of milk to five cups of flour, 2:5. Or the ratio of carbon atoms to the number of oxygen atoms, and so on. In a normal ratio there are no equal signs. But with the ratio of pi to the diameter, pi is = to the number of times the diameter will go around the circumference of a circle. This means that no matter how small nor how large the circumference, πd will always be = to it. The fractions of the first part are always = to the whole of the second part. Or the diameters are = to the circumference. Or pi, which is the diameters, is = to C. Or π = C.

For further clarification, consider this:

On Earth there are only two systems of measurement—the metric system, including the millimeter, the meter, and the kilometer, etc.; and the U.S. standards, including the inch, the foot, the yard, the mile, etc. Thus far they haven’t come up with a better system of measurement. Someday they might. Nevertheless, both systems of measurement include numbers, which can be used for comparing distances.

But before a measurement is assigned to a circle and its diameter, the following will be brought to light.

No matter how big nor how small the circumference, the diameter will always be one distance with a ratio of π to C. The obvious has been stated, but it’s necessary to show a measurement has not been assigned to either the diameter or the circumference. And the related equation follows.

C = πd; wherein π is the number of times d will go around the circumference. But d will always = 1; until a measurement is assigned to it;  C = π.

Now you can add the measurements. If d is 1 meter, then C = 3.14159 … ad infinitum meters. If d is one inch, then C = 3.14159 … ad infinitum inches. This means the circumference of a pipe has an ongoing infinite distance. But this cannot be true.

Let’s view the measurements from the other side of the equations. If C = 10 meters, then d can no longer = 1; and πd, which represents the diameters going around the circumference, will also = 10 meters.

This equation: C =πd, which is used by mathematicians worldwide, proves pi cannot be infinite.

This is actually easy to understand without the equation. Just by using the imagination it can be visualized since pi is the number of times the diameter will go around the circumference, then pi will always = C. The number of diameters it takes to go around the circumference will always = the circumference. This logic makes sense.

Without solving for the ratio of the diameter to the circumference, and just solving for the distance, it is found that whatever measurable distance C has, π will have the same distance. So, if the circumference of a pipe is 10 meters, π will also be 10 meters. The length of the diameters going around the circumference is = to ten meters. This means there is no irrational number, because π and the circumference are = to each other. And it is simply a distance compared to another distance in the real world.

Now we will solve for the ratio. Take a pipe with an outer diameter of one meter. Wrap a thin piece of paper around the pipe and put a mark where the paper meets the paper. Lay the paper out on a flat surface and measure three meters from the beginning of the paper and put a mark at the end of the third meter. The distance from the end of the third meter to the mark on the paper (representing the circumference) is a fraction of a meter with no irrational number involved. And now you have the ratio.

This is a very crude way to determine the ratio, and therefore it will not be the true value. It will be close, but as they say, ‘no cigar.’ The exact ratio will not be found until tools for measuring are more exact.

The next question is why do today’s mathematicians believe pi is infinite?

The problem starts with the mathematicians who use infinity to find the ratio. The truth is the value of pi has been determined by mathematicians who treat a circle as if it has an infinite number of points. But in three-dimensional reality this is not true. If a perfect circle, made of wire, is reshaped into a perfect straight line, then it can be demonstrated to have a definite length. And the diameter of the circle can be laid next to it three times with a little bit left over. But the little bit left over cannot be infinite. So, this is where the mistake is made. It must be understood that in the real world all circular objects have a finite or measurable circumference.

Scientists are saying the circumference of a circle is infinite and the diameter is finite. By today's definition this value of pi cannot form a ratio, because an infinite number cannot be compared to a finite number. But, in this essay, it will be proven pi IS the ratio of the diameter to the circumference, because the circumference of a circle is finite.


Further considerations:


Keep in mind that pi times d (diameter) is equal to the circumference. In three-dimensional reality the circumference of any circular material or circular object has an exact measurement, and consequently pi has to have an exact measurement.


Circumference = πd, or C = πd.


If the diameter = 1, then the circumference = π, or C = π.


C = the circumference

d = the diameter

x = the distance from the end of the third diameter to the end of the circle which is now in a perfect straight line.


The equation is:


C = 3d + x


To make the diameter one unit, the number 'one' will be substituted for the d. And now we have:


C = 3 + x


To complete the circumference the infinite decimal will be substituted for the x. And now we have:


C = 3 + 0.14159 … ∞


After a moment of studying this equation you will realize this number cannot represent the true circumference of a material, circular object. In this scenario there will be a gap in the material making up the circle. By adding more and more numbers, the gap will get smaller, but it will never be closed.

This equation clearly shows that today's value of pi is not equal to the circumference. It's like my shoe, in Zeno's paradox, never reaching the floor. Infinity won't let it.

From this equation it can be concluded that x has to be a finite number—one which will close the gap.

Remember: when a material circle is reshaped into a straight line, that line has a measurable distance. And so does pi, because pi is equal to the circumference. Infinity cannot be part of the measurement.


Another Example:


If a manufacturer plans to produce a pipe with a one inch inside diameter, then the equation becomes:


C = πd, and d = 1 inch,  C = π inches


Today's value of π equals 3.14159 … ad infinitum.


So, C = 3.14159 ad infinitum inches. This means the circumference is 3 inches plus an infinite decimal of inches.

In this situation, today's value of pi for the inside circumference cannot be correct. The distance of the circumference will be a never-ending fraction. Circles in the real world are not infinite, which means their circumferences are not infinite. If the inside circumference is taken from inside the pipe and reshaped into a straight line, it will have a beginning point and an end point. This straight line is a measurable distance with no infinity involved. In the real-world infinity cannot exist between two points. Therefore, π cannot equal 3 plus an infinite decimal. It must be a finite number. This means the circumference inside the pipe will be three inches plus a finite fraction of an inch.

Mathematics is a strict discipline, and therefore this essay is pointing out that today's value for pi is not accurate.

I'm assuming the correct number for pi is 3.1416 because the numbers after 3.14159 are converging on 3.1416, but this is just an assumption with no proof. It is for the mathematicians to prove the correct number. And the correct number cannot be infinite. The gap has to be closed in a real situation.

As a Note: I have recently read an internet article, which is a summary of a book, written by Mohammad-Reza Mehdinia (correctpi.com) in which he claims pi is = to 3.125. The difference between 3.14159 and 3.125 is only 0.01659. And once again, this means more exacting instruments are going to be needed to calculate the exact value of pi. On the other hand, he’s claiming to have proven this using mathematics with no measuring involved. And by the way, he’s offering a large amount of money to anyone who can prove him wrong.

At this point in time I can only imagine one method for determining the value of x: use a material to create a diameter of one unit, create a circle around the diameter, reshape the circle into a perfect straight line, lay three diameters next to the perfect straight line, and accurately measure the distance between the end of the third diameter and the end of the straight line.

Or, more simply, if the diameter is one inch, mark off three inches on the straight line and measure what's remaining. Then you will have 3 + x as the ratio; except x will be a finite decimal.

Another question: why is it scientists and mathematicians can use today’s value of an infinite pi, when, indeed, pi is finite?

Physicists, chemists, biologists, mathematicians, etc., can use the infinite pi value and get practical results, but only because the number is close enough to the real number. And also, when pi is used it is shortened to a finite number, whether it be 3.14159 or 3.14. This procedure changes pi to a real and rational number—no longer irrationally infinite. However, these shortened numbers, although close, are not the true value of pi.

Finally, when considering any real circular object there are three diameters to be considered: the inside diameter, the outside diameter, and the middle diameter, which is the same as laying a perfect circle on top of the perfect circle and using one for the circumference and the other for the diameters. It’s probable most engineers will use the inside diameter when working with pipes for determining the pressure being applied to the liquids forced through the pipe. Anyway, it won’t matter which diameter is being considered since all three diameters will be finite.


In Conclusion:


The following is irrefutable proof that pi is finite. It will be demonstrated without using measurements. Remember: C = π. And pi is the number of times the diameter will go around the circumference.

Lay out a piece of wire in a perfect circle. Cut a straight piece of wire for the diameter. Lay the circle out in a perfect straight line. Mark the diameter three times on the straight piece of wire. Now cut a piece of wire that matches the end of the third diameter to the end of the laid-out circle. This small piece of wire is the fraction of the diameter that completes the circle. Pick up the wire and study it closely. You will note there is nothing infinite about it, which proves pi is finite.

Or further: C =πd. If the diameter is 1 inch, then C = 3.14159 … ad infinitum inches. In the real world the circumference of a pipe will never be an unending infinite distance. It will have a finite measurable distance.

Even though we can prove this with our imagination, there is a problem with the actual procedure. Every step has to be completed with precision, and even if this can be done, then the small piece of wire has to be measured to at least ten thousandth of an inch, .0001, and possibly one hundred thousandth of an inch, .00001, in order to get the true value of pi.

It’s possible a new system of measurement is needed before we can get the true value of pi.


Synopsis:


  1. All distances in the real world are finite.

  2. Two objects in the real world traveling away from each other will never reach an infinite distance.

  3. Two objects in the real world traveling toward each other travel a finite distance.

  4. Zeno’s paradox proves infinity cannot exist between two points in the real world.

  5. Today’s value of Pi is infinite, therefore it cannot exist in the real world.

  6. Pi is always equal to the circumference.

  7. The circumferences of circles in the real world have a measurable distance, therefore pi has a measurable distance.

  8. Circles with infinite points can only exist in the imagination.

  9. Mathematicians use a circle with infinite points to determine the value of pi.

  10. When googling ‘ratio,’ the definition is: “the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.” Or, it’s the comparison of two Natural numbers.

  11. Today’s value of pi is supposed to be a ratio of how many times the diameter of a circle can go around the circle.

  12. A Natural number cannot be compared to an infinite number. Therefore, today’s value of pi is not a ratio.

  13. Scientists can use today’s value of pi, because they reduce pi to a finite decimal.

  14. Pi is always equal to the circumference, because pi is the number of times the diameter will go around the circumference.

  15. If the circumference has a measurable, finite distance in the real world, then pi will also have a measurable, finite distance.

  16. The ratio, when using an infinite pi, cannot be reduced.

  17. Since materials have a thickness, use the side touching the pipe to obtain the circumference. For example, if a sheet of rubber is one inch thick and it is wrapped around the pipe, use the side touching the pipe to determine the circumference.

  18. Take a thin piece of paper and wrap it around a pipe with a one inch outside diameter. Use a razor blade and make a cut where the paper first touches the paper. Now you have the circumference. Lay the paper flat and measure three inches from the beginning of the paper. Mark off the diameters. Measure from the end of the third diameter. And now you have the ratio.

  19. Considering the thicknesses of materials and considering finding the exact measurement of the circumference and finding the exact measurement of the diameter, the true ratio of pi cannot be determined until technology can produce instruments to measure smaller than 1/10,000 of an inch, i.e., 0.0001 of an inch.


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