An Introduction To Counter Space
Counter space (also known as negative space, and co-space) provides an alternative perspective on geometry. and relate to many natural processes. For ease of introduction we begin with 2D counter space. This is obtained by taking the duels of preexisting objects. A pair of points linked by a line, in normal space, would be transformed to a pair of lines that join at a point. The similar logical standing of points and lines in projective geometry means that the counter space contains all the information which the original picture does. People often tend to think in in point-like ways, for example,imagining a curve to be a set of points and so on. Looking at the same scenario in counter space, we see how 2D pictures can be represented and understood, in terms of their co-spaces of lines. The polarity notions of Apollonius are one of the simplest ways to experience co-space, We shall take a visual, fun approach, by using GeoGebra to explore the counter space of the Ampersand Curve with colorful pictures. We also describe how to create the dual of an object in practice.
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