Modern theories, as well as those which follow the Hellenistic tradition, are characterized by their narrow focus of logic and mathematics -- they explain how something works (Kuhn 104). However, the scientific predecessor of Hellenistic thought, Hellenic science, provided explanations for not only how something works, but also why it was there. Hellenic theories, by their nature, were loosely constructed in order to explain both observed anomalies and questions of existence. Since Hellenic theories tackle both of these questions, they often cannot be tested (how does a person test the nature of reality?). So Popper's claim of falsifiability can't apply to Hellenic science, as the majority of its theories fail Popper's criteria.
The problem of the interaction between the psychical and the thinking worlds as reverberations of the material one has been treated much earlier by ancient philosophy. Plato excludes any dependence of mathematics, it being the most brilliant representative of the mental world, of the sensations. Russell  (I. pp. 237-238) is concordant with the above. He considers that the mathematical truth is "applicable solely to the symbols," the symbols being "words," that "do not signify anything in the real world."
The symbol for zero was two slashes with a blank space between them. Unlike the decimal value system where we have ten distinct symbols to 2 represent zero through nine, the Babylonian’s only had two symbols: a vertical wedge for one and a crescent for ten. Zero in the sexagesimal base system only signified the absence of units of a certain order. The Babylonians did not use zero as “the number zero” as we do today. The concept of twenty minus twenty was still unknown to them.
Integer Constant An integer constant is made up of digits without decimal point. Rules The integer constant is formed with digits 0 to 9 Commas and blank spaces are not allowed. The constant can be preceded by + or – sign No special characters are allowed. The value of constant cannot exceed the specified minimum and maximum bounds. There are three types of Integer constants.
This means that it will continue infinitely without any repetition or pattern. It also cannot be expressed accurately as a fraction and the decimal never ends (Shell, 2013). The history of pi is a very confusing one. No one knows exactly who discovered it; they just know assumptions and possible coincidences. Many believe that the Babylonians were the first to find pi (Shell, 2013).
For them, zero was just a placeholder between numerals in a number such as 502 and never had an actual numerical value. Similarly, the Mayans in 350 CE independently began using zero, but just like Mesopotamia it was strictly for place holding (www.mediatinker.com). In 500 CE, Ancient India created the first known actual concept of zero. In 628 CE, the Indian mathematician Brahmagupta wrote the rules of zero in his book Bramhasputha Siddhanta. In this book the rules he alludes to are one, zero doesn't change the value to number when added or subtracted, and two, when zero is multiplied with a number the value becomes nothing (www.xslv.org).
Zero is a number lower than one. It is considered an item that is empty. There are two common uses of zero: 1. an empty place indicator in a number system, 2. the number itself, zero. Zero exist everywhere; although it took many civilizations to establish it. In the Roman civilization there was no symbol for zero.
The Reliability of Heidegger’s Reading of Plato’s Gigantomachia ABSTRACT: At issue is the reliability of Heidegger’s contention that Greek thinking, especially Plato’s, was constricted by an unthought "pre-ontology." "The meaning of being" supposedly guiding and controlling Greek ontology is "Being = presence." This made "the question of the meaning of ousia itself" inaccessible to the Greeks. Heidegger’s Plato’s Sophist is his most extensive treatment of a single dialogue. To test his own reliability, he proposes "to demonstrate, by the success of an actual interpretation of [the Gigantomachia], that this sense of Being [as presence] in fact guided [Plato’s] ontological questioning .
Imaginary numbers were known by the early mathematicians in such forms as the simple equation used today x = +/- ^-1. However, they were seen as useless. By 1572 Rafael Bombeli showed in his dissertation “Algebra,” that roots of negative numbers can be utilized. To solve for certain types of equations such as, the square root of a negative number ( ^-5), a new number needed to be invented. They called this number “i.” The square of “i” is -1.
Early surveyors found that the maximum error in fixing the length of the sides was only 0.63 of an inch, or less than 1/14000 of the total length. They also found that the error of the angles at the corners to be only 12", or about 1/27000 of a right angle (Smith 43). Three theories from mathematics were found to have been used in building the Great Pyramid. The first theory states that four equilateral triangles were placed together to build the pyramidal surface. The second theory states that the ratio of one of the sides to half of the height is the approximate value of P, or that the ratio of the perimeter to the height is 2P.