The Geometry Nutshell at JManimas dot com

Real, physical pi is rational and variable.

Here, thousands of viewers have seen a fairly massive amount of geometrical constructions and essays on geometry and the statement, either implied or explicit, that one can square the circle.  There is a reason for this, and herein is the simple explanation:  All of the geometry on my website, shared with the world, and all of the material and arguments related to squaring the circle and the ancient riddle about squaring the circle are not work in the field of mathematics.  All of this material is my work and it is a work in history.  In essence, my position is that the assertion made by mathematicians that one cannot square the circle is trivial and is in fact based upon an error that mathematicians, due to their authoritarian nature, cannot publicly admit and correct.  The error is that the original ancient riddle was not a question but instead was a declarative statement, and the purpose of the declarative statement was to affirm that the real physical universe exists because there is a smallest possible particle.  This assertion also relates to modern theoretical physics, because physicists, erroneously, refer to events that occur within the atom as particles.  They are not particles; they are events.  A particle is a piece of matter, and that means one person can pick up a particle of calcium or iron or carbon and do something with it.  It has a definable stability that is the basis for deeming it to be matter, and to be a particle, and to be a form of matter that is distinct and separable from other forms of matter or other molecules.  But the extended story of what a particle is goes beyond the ancient riddle about the circle and the square.

Here is the ancient (Pythagorean) riddle:  “Can we construct a circle with exactly the same area as a given square using only the compass and straightedge?”

Here is the declarative statement that is the origin of the ancient Pythagorean riddle – in my opinion as a historian:  “Because there is a smallest possible particle, one can construct a circle with exactly the same area as a given square, because there is no such physical reality as the Euclidean circle, which defines the circle as being comprised of points with no dimensions, and the only circles that exist in the real physical universe are regular polygons.  Pi, therefore, if it is the circumference of a real, physical circle, being a real, physical regular polygon, is a rational number and is in fact variable, although the variations deviate only at a level of very high precision.”  Precision is the essence of truth.

To round out this history, the ancient Pythagoreans were not only scientists and geometers, but there are historians who also describe them as being members of a religious order.  The ancient Greeks of Alexandria and Athens produced theories and scientific treatises on the real, physical universe, and one of the theories from ancient times was that there is a smallest possible particle of matter.  The ancients were all philosophers to some extent, in addition to exercising some respectable level of rigor as scientists, or geometers.  In the ancient world, geometry was mathematics.  This is so because geometry is natural mathematics.  Geometry is a description of the real world.  Mathematics is the process of calculation, measuring and counting, in the human brain.  Geometry is the universal language.  Mathematics is a human language and many mathematical languages are possible.  But only one geometric language is possible, because anywhere in the universe a square is a square.  If there were no smallest possible particle, that would mean that real, physical matter diminishes infinitely down to zero, and the entire universe is comprised of nothing.  Therefore, the reason we have this misunderstanding of the ancient riddle about whether or not we can square a circle is because the ancient Pythagoreans believed and taught that there is a smallest possible particle and the universe is made of something rather than being made of nothing.  This can be defined, some might argue, as a philosophical issue.  However, I argue that it is the point of human knowledge where philosophy and physics cross paths.  For both philosophy and physics, a universe made of nothing is very different from a universe that is made of something.  And, if the universe is made of something, then there is a smallest possible particle – particle of matter – not a blip forced into existence in an experimental artifice or inorganic machine.  And, if there is a smallest possible particle, then any circle or cylinder or cone or sphere, any real, circular object, must be comprised of particles.  The circumference of a real circle is comprised of particles, and we could call them points or anything else, but whatever we call them they DO POSSESS A FINITE DIMENSION.    That real circumference is therefore comprised of real matter that cannot be reduced to points with no dimensions.  That real circumference of that real circle is in reality the exact same shape as the sides of a many-sided regular polygon.  And, any regular polygon, no matter how numerous its sides, possesses exactly the same area as a constructible square. 

This is why you see all the geometry on this website, to show you that I did the work, both the geometry and the history.  And I am trying to tell you that the mathematicians are wrong because they are stubborn authoritarians and afraid to challenge a mathematical religious doctrine.  Mathematicians are religious, and they worship pi.  The pi of mathematicians is a religious object.  It is more likely that there is a God than that infinite pi is real.  To believe in the infinite pi, the pi that has thousands or millions of non-repeating decimal places, is believing in something that does not exist.  Thus, we have at least one occurrence where mathematicians are caught believing an irrational doctrine because the institution requires that belief.  If you do not get the nutshell, no amount of evidence or argument will change your mind.  The belief is neither mathematics nor physics; it is a religious belief.  We can “square the circle” because real pi is the perimeter of a regular polygon, rational, and variable at a high level of precision.