1. Geometry: inversion is defined for cicles. Lines and circles are mapped into lines and circles. Why use circles? It should be possible to define inversion with arbitrary conics.
2. Posets: Dilworths theorem states that, to cover a poset with chains, you need as many chains as you have elements in the largest antichain. There's another theorem that says that to cover a poset with antichains, you need as many antichains as elements in the largest chain. There's some sort of dual action going on there, something that needs to be explored.
I haven't found anything on Mathworld to suggest an answer yet. I'll keep scratching my head about them.
Comments (3)
AAAUGH!
My brain blew up, briefly, when I read this. Then I revived it with gin and Margaret Atwood. Math is like the ultimate super-virus: it destroys all in its wake. Leaves us slobbering, foaming, insanely determined to write short stories.
Posted by Joy | February 25, 2005 10:42 PM
Posted on February 25, 2005 22:42
Funny, I just want to know what he's talking about.
University can be seperated into two groups. People who went into Arts because they hate math and those who went into Science because they hated essays. :)
Posted by Majeric | February 26, 2005 4:01 AM
Posted on February 26, 2005 04:01
or more groups: I went into FINE arts so I could avoid math AND essays. Not that it worked completely, but I mostly write stories, poems, and make films...
Posted by ben | February 26, 2005 2:05 PM
Posted on February 26, 2005 14:05