Timeline for answer to The incenter of a quadrilateral is a rational function of the vertex coordinates by Blue
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| Jan 5 at 14:32 | comment | added | Blue | @hbghlyj: "For a kite, the formula's result is path-dependent." Indeed. This kind of thing seems a bit problematic for an "incenter map", but it's also fascinating. :) ... Now I'm curious about cases of non-kites that have one diagonal bisecting the other. (The ones that send $H_1$ to infinity.) ... Anyway, neat problem! I'm delighted to have come across the "complex harmonic" representation. I wonder if the right-hand side of $(2')$ evaluating to $-Q$ might amount to a (novel?) characterization of tangential quads. That's in puzzle for another day. :) ... Cheers! | |
| Jan 5 at 12:09 | comment | added | hbghlyj | For a kite, the formula's result is path-dependent. A limit of tangential quadrilaterals (AB+CD=AD+BC) converges to the incenter. A limit of ex-tangential quadrilaterals (AB+BC=AD+DC) converges to the excenter. A limit of orthodiagonal quadrilaterals converges to diagonal intersection. For a generic sequence, the limit is unstable and can lie anywhere. | |
| Jan 5 at 0:16 | history | edited | hbghlyj | CC BY-SA 4.0 |
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| Jan 5 at 0:05 | vote | accept | hbghlyj | ||
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| Jan 4 at 23:33 | history | edited | Blue | CC BY-SA 4.0 |
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| Jan 3 at 7:17 | history | edited | Blue | CC BY-SA 4.0 |
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| Jan 3 at 4:23 | history | answered | Blue | CC BY-SA 4.0 |