So if you have experience with calculus you know that you can use limits to sort of cheat physical reality and add an infinite number of infinitessimally small things to get a solid thing. However, I started thinking about compounding it. You can make a cube by adding an infinite number of infinitesimal squares, but what about making square?

I postulate that there is a mathematical way to add up an infinite number of points to create lines, then have the spacing between those lines go to 0 to create a plane or square, and then have thickness and spacing of those squares go to 0 to create a solid cube all in one equation. Anyone have ideas? Or is it impossible?

That sounds very like the integral from x=0 to x=1 of the line y=1 The integral is the sum of area calculations of the value of f(x) multiplied by the very small distance dx. you are basically taking lots of vertical lines and adding them together

Congratulations you have just conceived of Peano's space filling curve.

 

 

http://en.wikipedia.org/wiki/Space-filling_curve

 

PS you can also use it to fill 3 or more dimensions.

Congratulations you have just conceived of Peano's space filling curve.

 

 

http://en.wikipedia.org/wiki/Space-filling_curve

 

PS you can also use it to fill 3 or more dimensions.

It's sort of like that, but it's one step bigger than that. You need to create a summation of 1 dimensional points to create space filling lines which then creates a plane.

Edited May 23, 201312 yr by SamBridge