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Pi(π), the circumference of the circle divided by the diameter, is calculated using a new mathematical discipline, called phenometry, in which points do  have dimensions. Lines are developed and studied as expressions of points, areas as expressions of points, areas as expressions of lines and volumes as expressions of areas. Common sense: "every circle ends at the point it begins and therefore pi(π) cannot be perceived as having an infinite number of digits".Mankind used to believe that the earth was flat, and people were scared of falling off the edge of the earth. They also thought, that if people were meant to fly, they would have wings! Galileo was persecuted for his scientific beliefs. The
Catholic Church did not reverse his 17th Century conviction until
1992, which was almost 300 years after his death. But only thinking outside the ordinary, achieved scientific and mathematical leaps. This website , will feature a book, that will allow for thinking outside the "established". The book, written by Hisham Z.A El-Amin, is entitled: "The Scientific Base of the World Remade. Pi(π) Discovered. 21st Century and Beyond". Most western geometries are built on three fundamental concepts: point, line and plane. Euclid's fifth postulate has differentiated Euclidean and non-Euclidean geometries. (Pi in History) . A A ________________________ A' (Euclid's fifth postulate: Given a line AA' and a point O outside line AA', there is one and only one line -on the same plane- that goes through point O, and is parallel to AA'). It is generally accepted that points have no dimensions, lines have one dimension, and planes have two dimensions. In phenometry, patterns -being forms of order-, set a basis from which one can begin the process of reasoning. To understand this premise, one has to ponder the following two points. First, that the universe is finite and calculable and secondly, that the universe is continuous.(Pi - Philosophy)Then it will stand to reason, that patterns are the base that ensures the maintenance of continuity, and therefore can be used for the discovery of continuity. The most fundamental pattern of this universe, is its paired nature. (Paired nature, not dual nature, since pairing indicates two expressions of the same “intent”, and duality implies two different “intents”).The number two, with the elemental property 2+2=2x2, is an indicator of that paired nature, but using this elementary property to reason with, becomes infinitely more complicated, when one has to reason on more advanced concepts like the square root of two. The definition of the square root of two, finds its base on the Pythagorean theorem (Pi in History) ( Other Books). The author presents a new definition of the square root of two, based on a new definition of constants. Constants, as they appear in laws of physics (chemistry of other physical science), are in most cases a result of mysterious philosophical thinking and experimental endeavor. (Examples: Plank's constant ( E=h×ν ), or Newton's gravitational constant k: ( F=Mm / r2). The author presents a new definition of constants and consequently redefines the square root of two. An even more in depth discussion by the author on the square root of two, will be presented in subsequent publications. The concept of the point is also redefined by the author. Now the point is not dimensionless, but possesses potentially infinite dimensions. By observing then the point's expression through space, we observe the construction of lines and figures, only now lines and figures have origins, and they are not randomly placed on a sheet of paper. What is revolutionary in this book, is the construction and analysis of the “arc” or the quarter measure of a circle. Based again on a dimensional point and its dual expression, the value of Pi (π) is now finite and calculable. What is interesting in this approach, is that lines are not simply calculated using geometrical laws: lines are an outcome of strict construction , in the mind and on paper, construction without which, the lines would not have come into existence. With the arc reconstructed and redefined, the author proceeds to also calculate the area of a circle, the area of a sphere and the volume of a sphere, calculations which are currently based on successive integrations of the formula for the length of the circumference of the circle. As it should be obvious to the reader, who can appreciate the definition of concepts based upon pure reasoning, without allowing the mind to settle for approximations, the discipline of calculus is rendered mute, in lieu of phenometric considerations. For those, bold enough to endeavor to seek understanding instead of merely accepting the established, we present the challenge and the opportunity, to read the book, which will broaden horizons, increase perception and lead to a path of discovery, in areas of science and mathematics presently being explored, or simply for one's own advancement that they are currently working with, or are presently interested in working in. Comments and questions from our readers are welcomed at our e-mail address: elaminpublishingcompany@yahoo.com.
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As it can be seen by the figures above, it does not matter which direction is chosen or if another direction is chosen adjacent to that direction; you can with a finer tool find a direction between them that was not chosen. It is in this respect that we say that the potential for directional expression is limitless.
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