Post by yardstick on Aug 2, 2017 21:29:09 GMT -6
So in response to an inquiry in another thread about 10th+ dimensional beings and our 'perfected bodies' after the Harpazo, I offered to make a Math Class thread, for purposes of demonstrating as many dimensions as I know how. I'll try to keep it in as plain english as I can. I expect this to be a very long thread so I appreciate your patience wading through a lot of math. I'll try to keep it as non-technical as possible...
I apologize in advance if the thread is pedantic, I have no way of knowing the reader's mathematical skill level; and therefore, have assumed the lowest level as possible. I hope that to offset this, my unusual perspective on math may give some insights that are not otherwise obvious.
First, I'd like to share a little background related to the topic. I am no expert, but I have done the math in my coursework, and done some tutoring. I have completed 5 courses in calculus, a couple in statistics and the tutoring of everything from basic grade school math all the way up to the 4th course in calculus.
let's begin:
In one-dimensional math, we have with a single horizontal number line, which has 0 in the middle and goes to infinity, incrementally, to the right and to the left. This is commonly referred to as the X axis:
This kind of number line is good for learning how to count, and add and subtract.
The next time we see number lines in math, we are using two-dimensions. The same X-axis, but over the top of it, vertically is another number line, the Y-axis. Where the X and Y axes cross is called the Origin. The values for both axes where they cross is 0. This is commonly referred to as Cartesian coordinate system, where we have combinations of X and Y values to locate points that are not on the lines themselves, but in one of the four sections, called quadrants. Think: Battleship (the game), but with numbers and numbers, instead of letters and numbers. The values for X and Y are organized like this: (X,Y) as shown below.
With two-dimensions, we can go from single lines (called rays) to making two dimensional shapes and basic geometry: Triangles, Squares, Circles, et c.
Three-dimensional objects such as cubes and spheres and pyramids all require a third axis, called the Z axis, where we can plot things 'in space'. Like the two dimensional cartesian graph, we need coordinates to plot points to connect together with lines; but now we add a Z-dimension: (X, Y, Z) for each point we want to plot. As shown in the sketch below, each corner of the box would have a different combination of values for X, Y and Z, with one corner of the box have all three values (0,0,0). This point is the one that is located at the origin (O).
(continued)
I apologize in advance if the thread is pedantic, I have no way of knowing the reader's mathematical skill level; and therefore, have assumed the lowest level as possible. I hope that to offset this, my unusual perspective on math may give some insights that are not otherwise obvious.
First, I'd like to share a little background related to the topic. I am no expert, but I have done the math in my coursework, and done some tutoring. I have completed 5 courses in calculus, a couple in statistics and the tutoring of everything from basic grade school math all the way up to the 4th course in calculus.
let's begin:
In one-dimensional math, we have with a single horizontal number line, which has 0 in the middle and goes to infinity, incrementally, to the right and to the left. This is commonly referred to as the X axis:
This kind of number line is good for learning how to count, and add and subtract.
The next time we see number lines in math, we are using two-dimensions. The same X-axis, but over the top of it, vertically is another number line, the Y-axis. Where the X and Y axes cross is called the Origin. The values for both axes where they cross is 0. This is commonly referred to as Cartesian coordinate system, where we have combinations of X and Y values to locate points that are not on the lines themselves, but in one of the four sections, called quadrants. Think: Battleship (the game), but with numbers and numbers, instead of letters and numbers. The values for X and Y are organized like this: (X,Y) as shown below.
With two-dimensions, we can go from single lines (called rays) to making two dimensional shapes and basic geometry: Triangles, Squares, Circles, et c.
Three-dimensional objects such as cubes and spheres and pyramids all require a third axis, called the Z axis, where we can plot things 'in space'. Like the two dimensional cartesian graph, we need coordinates to plot points to connect together with lines; but now we add a Z-dimension: (X, Y, Z) for each point we want to plot. As shown in the sketch below, each corner of the box would have a different combination of values for X, Y and Z, with one corner of the box have all three values (0,0,0). This point is the one that is located at the origin (O).
(continued)
folded (3-D) 
unfolded (2-D)
