Reciprocating Shapes

So basically I was thinking a while back about how I could extend units of measure from the natural set of numbers to the real set in which we can now express the following units: ft^3, ft^(-2), ft^(3/2), ft^(pi=π=3.1415926535897932384626433...), and so from that concept, I began thinking about how to draw those types of shapes. Now, if I were to define a shape as lines connected by vertices, then maybe to invert them, I should swap every line with an inverted vertex and every vertex with a line; that way, we can start creating new shapes in not just the 2nd dimension, but any dimension for that matter. Okay, so that's cool and all, but what about a circle? It technically has no edges and no vertices, so...does this idea fail? No, no it does not because technically a circle is just made up of infinite edges and vertices; therefore, let's replace all of them, or at least do our best to approximate that. The bottom part of the paper shows my label for an inverted/reciprocated circle. 
 
This math does not exist. I came up with this idea myself. I'm guessing it needs some tweaking and there are more papers associated with this idea but for right now I am simply uploading this one. Hope you enjoyed the read.

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Posted in Automotive Services on January 22 2021 at 01:29 PM
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