MATHUP Animations

They asked a mathematician how much 2 + 2 would be, and the mathematician thought and said: “If 1 + 1 = 2, 2 + 2 is 4” The first time I heard Russell's word came to mind, the Euclid's 5th postulate. Before we move on to this postulate, let's look at the answer to the question: what is postulate? Every science for proof starts with the assumptions that constitute the principles of its subject. Some of these assumptions are common to all fields of science (Aristotle calls them axioms); others are principles specific to each subject's own subject (Aristotle calls them postulates). Postulates are propositions that determine the objects of study, their properties and relationships. For example, geometry assumes objects such as ‘point’, ‘line,, and other defined objects such as‘ triangle ’and‘ circle, are built on the basis of default objects. For example, the postulate “All right angles are equal getirmek expresses a particular property of a set object. Summaries Axiom is valid for all fields and its accuracy is obvious. For example, eşit Things equal to the same thing are equal to each other. ” Postulate is a specific proposition that is specific to a particular subject or area of ​​study. For example, "There is only one parallel line from any point other than a line to that line." Axiom accuracy is a mandatory proposition; whereas there is no obligation for postulate. (I) In spite of all these distinctions, we have to accept the existence of an understanding that considers axiom and postulate as roughly a “proposition considered unproven” (ii). Now let's go back to the beginning and listen to Euclid. In Euclid's 5th postulate, he says: Orsa If the two straight lines on the same plane both intersect with a third straight line, and if the sum of the inner angles on one side is less than two right angles, then if the sum of the angles is less than two right angles, the two intersect correctly. ” Or as we are more familiar with: ilebilir Only one parallel line can be drawn from a point outside a line. ” Who can object to it so clearly and clearly. Of course, if we expand our perspective, when we look at the events in the wider framework, we see that there are environments in which this postulate is invalid. p: yalnız Only one parallel line can be drawn from a point other than a line. p So when we accept our proposition p, we suddenly find ourselves in Euclidean geometry. But if we change our proposition p, we open the door to brand new geometries. So perhaps we have looked at what Russell means in the broadest window.

Why is Mathematics a Language?

Mathematics is called the language of science. Italian astronomer and physicist Galileo was one of the first modern thinkers to say that the laws of nature are mathematical. In Il Saggiatore, “Philosophy is written in this great book; the universe is in the language of mathematics and its characters are triangles, circles and other geometric figures. ” But is mathematics really a language like Turkish or English? In order to answer this question, it is necessary to know which words and grammar are used to form sentences in mathematical language. “Language birden has multiple definitions. A language can be a word or code system used in a discipline. The language can also refer to a communication system using symbols or sounds. Linguist Noam Chomsky defines language as a set of sentences constructed using a finite set of elements. Some linguists also believe that language must represent events and abstract concepts. Whichever language is used, a language contains the following components: Words or symbols should be words that can be used. Meaning should be added to words or symbols. A language uses grammar, a set of rules that illustrate how grammar is used. The syntax arranges symbols with linear structures or propositions. A narrative or discourse consists of strings of syntactic propositions. There must be a group of people who use and understand symbols. Mathematics meets all these requirements. Symbols, meanings, syntax and grammar are the same worldwide. The words of mathematics benefit from very different alphabets and symbols specific to mathematics. A mathematical equation can be expressed in words such as a sentence in the spoken language by creating a word and a sentence with a verb...

Calculus: Understanding the Mathematics of Change

Life is not constant, every minute is different from the previous; The world is in a state of flow and change. Our effort to make sense of this change brings us to the mathematics of change. Calculus was developed as a result of human desire to look up into the sky and understand the solar system and beyond. Newton and Leibniz’s hands were used to calculate the motion of the planets. Nowadays, we come across everywhere we want to define, measure and understand change. The basic idea of calculus is that a quantity that we measure changes is based on the value of variables.

1 and 0 is Life

Programs are an important part of our lives. Our clocks, phones, TVs, computers work according to the orders of the people. We command according to our needs and expect to fulfill our wishes. We actually have a lot of help. As technology evolves, so do our assistants. How do programs make our lives easier? Every machine has a language that every device understands. In fact, they don't know anything, we people are teaching them and we want to go back. We try to solve problems by compiling the code we have written and translating it into machine language. If we want to make a robot, we can use many sensors, one or more processors and development boards. We can control different types of engines. Processors and development cards can be programmed. We give the sensors commands according to the processor, development card or programming language we choose (C, C #, Java, Verilog, VHDL, Processing, Python, etc.) and they direct the system elements according to our requests.

Chaos and Mathematics

There are natural phenomena that make human beings very hard throughout history. Movement and time are the main ones. Unfortunately, there is no one (single) mechanical theory that can explain all the movements in the universe, and there is no time concept that everyone can accept. The phenomena known as chaos today are directly related to the concept of movement. Modern science developed after the 17th century has gone a long way towards explaining the movement. As Aristotle did in many areas in 300 BC, he set rules for movement based on his observations.