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GeoGebraGeoGebra Classroom

Graphical Theory 2

The Concept of the First and Second Derivative : It's like this: The Rate of Change of Both the Velocity and Acceleration is obtained in this Fashion; " t " - has it's own " Path " and by Multiplying time by distance " a " : Times serves as the" Vehicle " for the rates of change needed without actually taking the derivatives of the equation. And Naturally the Multiplication rules provide the rate of change of the time: It squares the term and multiplies terms by the fourth power making acceleration Note: The Main thing to Understand is This: i and i^2 are only symbols which I treat the same as x and y which are the dimensions: Subsequently It's the Rules of Multiplication that takes x time y = i and the same for x^2 = 1 y^2 = i^2 and that is where you obtain you Velocity and Acceleration from. After all, It's a " distance " moved to a new location which takes time to do: Therefore the only two factors involved here is distance and the time to move that distance - t x = Time Vector and that is why I can equate i and i^2 to Distance and " a " which the whole plane is " a ". Moreover the Velocity Term is a Linear relationship with parallel vectors which can be Multiplied together as I have done and the acceleration term naturally through the rules of Multiplication by squaring the Velocity term serves as the Acceleration eg. i = Velocity i^2 = acceleration and so I actually defined what i and i^2 are. Because if you remember I said i and i^2 are entities that are equal in distance so that was simply a special relationship between the two entities : if did not say were the two entities reside hence the i^2 A =0 reference number which is were all dimensions are referenced too. Additionally I would like to point out that A = pi r^2 in the real plane has only one item in the set : and that is Area(a) which on transfer to the complex plane now is equated to the new area D(a) which are subjected to different dimensions and so that is Time Space - the Circle becomes Distorted due to the fact that the same circle is located at a different Center but still covers the old dimensions in the Real Plane so it has to be Stretched for that to happen and that takes time to do and that is Time Space in a Nutshell. Why the Numbers Work 1) The Axis actually starts below the X - Axis 2) You Can now see that b and k make up a 45 degree Triangle and is why b = K 3) You can now see how d = square root of 5 4) You can all so see that the Distance Between i and i^2 are equal distances 5) The Entire plane is Dimension(a) which is a x a and is why I can say " a " equals all Dimensions is because it does 6) The plane is " a " -- a x a