Pi belongs to a group of transcendental numbers. A few more key terms we need to understand: “shape”, “boundary”, and “points.” If we want to understand pi, we must understand what circles are, and if we want to understand what circles are, we must first understand what “points” are. Because, a rational number is an algebraic number of degree one. If this is true, then it’s no criticism of base-unit geometry, because all the round objects that we encounter would be polygons. You see, mathematicians do not believe these objects qualify as “lines” or “points.” In their minds, lines and points cannot be seen, and in fact, they’d say the above “lines and points” are mere imperfect approximations of lines and points. If you don’t believe in the existence of “perfect circles” – made up of an infinite number of zero-dimensional points – then you do not believe pi is irrational, and you’ve joined an extremely small group of intellectual lepers. Its boundary is composed of an infinite number of zero-dimensional points. Simple: it’s one integer over another – however many base-units make up the circumference, divided by however many units make up the diameter. If an object actually has shape, if it takes up space, then it’s got to be made up of spatially-extended objects akin to computer pixels, not mathematical points. Mathematics is not exempt from criticism or skeptical inquiry. It’s got no walls, floors, or a ceiling!” You’d think he was crazy – especially if he added, “And all other houses are a mere approximation of it!”. You don’t concrete from abstract. (If you want to understand why pi changes slightly, think of it this way: as the size of the base-unit increases, the area enclosed by the circumference shrinks; as the size of the base-unit decreases, the area enclosed by the circumference increases, yet at a diminishing rate. Among other things, this also means there’s no such thing as a “unit circle” – a supposed circle with a radius of 1. The term rational is derived from the word ‘ratio’ because the rational numbers are figures which can be written in the ratio form. Because even if you disagree it will at the very least provide you with food for thought. Inter state form of sales tax income tax? They are constructed from a finite number of points which themselves have dimensions. This object has both length and width – it is extended in two dimensions. Turns out, there are many different definitions. They are “zero-dimensional” objects. More formally we say: Within that framework, there is no smaller unit of distance, by definition. I, for one, do not think that mathematicians know what lines are. Perfect precision is actually possible, since there are no approximations or infinite decimal expansions to deal with. Not so with base-unit geometry. But note that π π is NOT a rational number because the exact value of π π is NOT 22 7 22 7 Its value is a decimal 3.141592653589793238... 3.141592653589793238... which has no repeating patterns of decimals. Base-unit geometry loses no explanatory power, eliminates an infinite number of unnecessary objects, and gives a logical foundation on which to build a stronger theory. First of all, this framework fully explains all of the phenomena we experience, and it loses exactly zero explanatory power when compared to standard Geometry. Therefore, I’ve no need to posit an extra entity – especially one with such remarkable properties. However, that doesn’t mean we’re prevented from talking about smaller-dimensional base units. Meaning, it is not a root of any integer, i.e., it is not an algebraic number of any degree, which also makes it irrational. Has anybody encountered even one true “line” or “circle”? Therefore, the objects of geometry must themselves take up space. The outermost points take up exactly zero space. No. Thus, if a number is … Higher levels of heresy might be about religion or science – disagree with orthodox assumptions here, and you’ll be seen as quite-possibly-crazy. A few of the nice implications of this theory: (Note: this GIF was taken from Wikipedia to show the supposed irrationality of pi. As pi is the subject of this article, let’s lay out the definition that we’ve all learned in school: Pi is the ratio of a circle’s circumference to its diameter. For example, this is a “circle”: If you believe these objects are indeed circles, lines, and points, then you too believe that pi is finite. “Points”, in orthodox geometry, aren’t really “defined” per se. A number is rational if we can write it as a fraction where the top number of the fraction and bottom number are both whole numbers. That’s all that’s required to conclude that pi is a rational number for any given circle. If God doesn’t exist, the entire theoretical structure built on top of this assumption gets destroyed. So, let me present an alternative geometric framework. People have calculated Pi to over a quadrillion decimal places and still there is no pattern. a rational number is one that can be expressed as a ratio of two integers (ex: 414 / 391) pi cannot be expressed this way (although there are rational approximations, the exact value is irrational) 1 0 At no point are you looking into infinity; you’re always looking at a finite number of pixels. Post was not sent – check your email addresses! Rational numbers are the ratio of two different unified integers. Those objects simply won’t correlate to our universe. It is not itself a circle. Every “line”, to a mathematician, is actually composed of an infinite number of points – yet, each point is itself without any dimension. In this case, the universally-accepted claim that “Pi is an irrational, transcendental number whose magnitude cannot be expressed by finite decimal expansion” is false because of a metaphysical error. Imaginary numbers are all numbers that are divisible by i, or the square root of negative one. The venn diagram below shows examples of all the different types of rational, irrational numbers including integers, whole numbers, repeating decimals and more. Many people are surprised to know that a repeating decimal is a rational number. Here’s another one: A “point” is a precise location or place on a plane. Instead, it lives in another realm that our minds can faintly access. Why don't libraries smell like bookstores? This proof uses the characterization of π as the smallest positive zero of the sine function. The words “a red fruit” are a description of the object, not the object itself. There is much more to say in the future. They themselves do not occupy physical space. The objects we experience are composed of pixels. There are concrete, actual circles, each of which is a composite object constructed by a finite number of points. However, Pi/Pi is equivalent to 1, which is certainly rational. Below is an excerpt from some of his thoughts and observations and opinions on mathematics, as of 9 November 1995. Has anybody, ever, seen or experienced these mathematical shapes in any way?