RS-106 - Math and Euclidean Geometry

Transcript

foreign on the reciprocal system of theory by Dewey B Larson a universe of motion the concept to be discussed now is maths and euclidean geometry in the reciprocal system I am Gopi Krishna and I will be guiding you through this presentation so let's start off firstly in the postulates it is mentioned that we use ordinary commutative mathematics and also that the geometry of the universe is euclidean so what does the euclidean geometry mean and what does ordinary commutative mathematics mean more importantly what does it imply as a property of motion this is the thing which we will be trying to understand first of all euclidean geometry the rules for a euclidean geometry in a coordinate reference system are as follows firstly the parallel lines meet only at Infinity Pythagoras Theorem holds wherein the sum of the squares of the sides of a rectangle triangle is equal to the square of the side of the hypotenuse the difference in coordinates is what we call the magnitude it has three mutually orthogonal axis lastly this kind of geometry is called a flat geometry let us try to understand this euclidean geometry is known as a flat geometry because the rules work well on a perfectly planar or flat surface these rules can be further extended to a three-dimensional body what does it mean to say a planar or a flat surface to understand that let's look at something which is not flat a curve geometry like the surface of the Earth when we use the reference frame like the surface of the Earth and take the points on it as the points on a reference system we notice that in this reference system the parallel lines intersect the two points which originally gave rise to lines which were parallel to each other now join up at the North Pole this is a common point for both the lines whereas in a flat geometry parallel lines never intersect it is always planar another important property is in case of a flat geometry the distance between two points is also the shortest distance between the two also called the difference in coordinates whereas the distance in a non-flat or curved geometry is much larger then the shortest distance hence the shortest path between two points is only there on the flat geometry and the metric meaning is hence retained this is the summary of the metric meaning in pleasure euclidean geometry having a metrical meaning is very important because in the theories of conventional science for example in special and general relativity space and time are seen not to have metrical meanings and requires suitable modifications whereas in the reciprocal system we maintain that the metric meaning of coordinates is always true and this also implies that in the reciprocal system both the spatial and the temporal coordinate reference frames work in euclidean geometry consequently all the theory of planar trigonometry and coordinate geometry and even solid geometry a hence valid coming next to the phrase ordinary commutative mathematics this includes algebra arithmetic calculus coordinate geometry logic and probability Theory all of these are very well known branches of mathematics and form a part of ordinary commutative mathematics and throughout the development of this reciprocal system we maintain some basic principles of mathematics and logic for example smaller numbers are held to be more probable than larger numbers and another very well known fact is symmetrical systems are more probable than asymmetrical systems this brings us to the end of this presentation thank you the next you can check out the glossary of terms which have been used in the presentations