An interesting Function on the space of quadrilaterals
Drag the large BLACK dots {A, B, C, D} to form a quadrilateral you are interested in.
This environment constructs a function, [call it Q], from the space of quadrilaterals
to the space of quadrilaterals as follows -
--circumscribes a circle around points A,B,C with center at E
--circumscribes a circle around points B,C,D with center at F
--circumscribes a circle around points C,D,A with center at G
--circumscribes a circle around points D,A,B with center at H
and then constructs the quadrilateral EFGH (in GREEN)
Explore this function - what is the domain of Q ? the range of Q ?
Conjectures ?
Proofs ?
Extensions ?
Challenge - How cyclic is my quadrilateral ?
Given a collection of n-sided polygons - some cyclic, others not - can you devise a measure of "cyclicity" - that is, a way of ordering them from "least cyclic" to cyclic ?
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