Reciprocal star (no ontology)
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| - | <div style="display:block; float:right; padding: 8px 8px 0px 8px; margin: 0px 0px 8px 8px; border: 1px solid #888; background-color: #EEE;">http:// | + | <div style="display:block; float:right; padding: 8px 8px 0px 8px; margin: 0px 0px 8px 8px; border: 1px solid #888; background-color: #EEE;">http://teamikaria.com/dl/wBtwSfebpkBgk8DAxq07NDy1VUXg_L8oFR7bDwhKIL60L7II.png<p>A '''3M''' reciprocal star with ''k'' = 1.</p></div> |
'''Reciprocal stars''' are a set of objects in three dimensions defined by implicit equations. They are so named because their appearance is similar to that of the 2D reciprocal graph, ''y'' = ''kx''<sup>-1</sup>. The implicit equations of reciprocal stars take the form: | '''Reciprocal stars''' are a set of objects in three dimensions defined by implicit equations. They are so named because their appearance is similar to that of the 2D reciprocal graph, ''y'' = ''kx''<sup>-1</sup>. The implicit equations of reciprocal stars take the form: | ||
Latest revision as of 13:34, 24 October 2008
A 3M reciprocal star with k = 1.
Reciprocal stars are a set of objects in three dimensions defined by implicit equations. They are so named because their appearance is similar to that of the 2D reciprocal graph, y = kx-1. The implicit equations of reciprocal stars take the form:
f(x,y)g(y,z)h(x,z) = k
The ten basic reciprocal stars
The basic reciprocal stars are a set of ten specific stars. These are created by using the three bracketopic products: sum (S), max (M) and root-sum-square (R). Each possible combination of these to replace the functions f, g and h becomes a basic reciprocal star, which are given the following names: 3S, 3M, 3R, S2M, S2R, M2S, M2R, R2S, R2M and SMR, where 3X means that all functions are replaced by X, X2Y means that one function is replaced by X and the other two by Y, and SMR means that all three of the functions S, M and R are used.
