h*l
发帖数: 19 | 1 It's more like a "advanced geometry" problem. It
may be cumbersome (though maybe clever) to solve it
by pure Euclid method. Two brochures can be used to
look up. One is
Chen Long's "Techniques in Analytical Geometry"
(MO traning series, arround 1989-1990),
another is
Feng KeQing's "Introduction to Projection Geometry"
, (High school students library series, late 80's)
They both lead to beautiful advanced geometry
theorems like Desargue (?), Pascal , duel, finite
group... which maybe on | d*z
发帖数: 150 | 2 No!!!
Because each points only satisfy two equations, not five
equations.
How could u construct the result equation? Not so easy. And
I think
it is not convenient to use Projection Geometry, because it
will
transform circles to ellipses.
【在 h*l 的大作中提到】
: It's more like a "advanced geometry" problem. It
: may be cumbersome (though maybe clever) to solve it
: by pure Euclid method. Two brochures can be used to
: look up. One is
: Chen Long's "Techniques in Analytical Geometry"
: (MO traning series, arround 1989-1990),
: another is
: Feng KeQing's "Introduction to Projection Geometry"
: , (High school students library series, late 80's)
: They both lead to beautiful advanced geometry
| h*l
发帖数: 19 | 3 1. The 5 equations below are for 5 circles, pairs
of them can be used for those 10 points, but not my
intension.(at most use like (1)-(2) to be as the
equation for "gen1 zhou2") As I said, I failed to
construct the final circle equation although I believe.
2. There are techniques in Projection Geometry other
than like "warping transform" (Fang3 She4 Bian4 Huan4)
ect. I think it should be in Feng's book or other
books. I regret I did not learn that far long time ago.
3. By the way, someone
【在 d*z 的大作中提到】
: No!!!
: Because each points only satisfy two equations, not five
: equations.
: How could u construct the result equation? Not so easy. And
: I think
: it is not convenient to use Projection Geometry, because it
: will
: transform circles to ellipses.
| d*z
发帖数: 150 | 4 Not so.
Because the common point of (1) and (2) not only include
one of the five points, but also include another point that
should not in the result circle.
//Yes, 反射变换？But It doesn't transform anything at all.
Me too.
【在 h*l 的大作中提到】
: 1. The 5 equations below are for 5 circles, pairs
: of them can be used for those 10 points, but not my
: intension.(at most use like (1)-(2) to be as the
: equation for "gen1 zhou2") As I said, I failed to
: construct the final circle equation although I believe.
: 2. There are techniques in Projection Geometry other
: than like "warping transform" (Fang3 She4 Bian4 Huan4)
: ect. I think it should be in Feng's book or other
: books. I regret I did not learn that far long time ago.
: 3. By the way, someone
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