几何题求解. 若给出正确答案，俺请吃饭，俺请吃饭！
- 主题发起人 heureux
- 开始时间
- 注册
- 2004-07-18
- 消息
- 46,146
- 荣誉分数
- 20,140
- 声望点数
- 1,393
目前为止最好的答案是 55 楼的。 23 块板。
1 可以证明这个正方形是稳定的。 要两页纸
2 但要证明这是最少的，难，很难！
3 要找出更少木板稳定正方形的，也很难
可以在 Google 上搜一搜！
- 注册
- 2010-07-14
- 消息
- 3,260
- 荣誉分数
- 200
- 声望点数
- 73
- 注册
- 2004-07-18
- 消息
- 46,146
- 荣誉分数
- 20,140
- 声望点数
- 1,393
没奖品的！
- 注册
- 2010-07-14
- 消息
- 3,260
- 荣誉分数
- 200
- 声望点数
- 73
没奖品的！
不是请吃饭的吗？
- 注册
- 2004-07-18
- 消息
- 46,146
- 荣誉分数
- 20,140
- 声望点数
- 1,393
吃饭小意思啦！ 就按小傻的标准请，两人吃一顿 $500
- 注册
- 2004-07-18
- 消息
- 46,146
- 荣誉分数
- 20,140
- 声望点数
- 1,393
这饭不是那么好吃的啊，这题目放这都四年了
- 注册
- 2010-07-14
- 消息
- 3,260
- 荣誉分数
- 200
- 声望点数
- 73
Just to quickly type down some notes for myself and to establish a semi-serious starting point of effort on this problem. 
===
0.0. The object we consider belongs to a special kind of graphs which we shall define later. Here, whenever speaking of graphs, we refer to simple, undirected, connected graphs.
0.1. A graph is said to triangulated if any cycle of size no less than 4 has a chord.
0.2. A graph may be embedded in an Euclidean space, namely, having each of its vertices associated with a coordinate in a Euclidean space. In particular, the Euclidean space we consider is going to be R^2, the two dimensional vector space over the reals. In this case, a graph becomes a geometric graph.
0.3. We are interested in a particular kinds of geometric graphs, called planar straight-line graphs, in which each edge in the graph is a straight line segment in R^2. From here on, whenever speaking of graphs, we exclusively refer to planar straight-line graphs in which each edge has length precisely 1.
0.4. Further without loss of generality, we will assume that in a graph, there always exists a vertex whose coordinate is (0,0), the origin.
0.5. Two graphs are said to be equivalent, if it is possible to rotate/translate/reflect one graph to obtain the other.
Now I am trying to define a notion of "stability", which I call "rigid".
Definition 1. [Rigid] A graph G is said to be rigid if any other graph H that is graph-theoretically isomorphic to G is equivalent to G.
(to be continued ...)
===
0.0. The object we consider belongs to a special kind of graphs which we shall define later. Here, whenever speaking of graphs, we refer to simple, undirected, connected graphs.
0.1. A graph is said to triangulated if any cycle of size no less than 4 has a chord.
0.2. A graph may be embedded in an Euclidean space, namely, having each of its vertices associated with a coordinate in a Euclidean space. In particular, the Euclidean space we consider is going to be R^2, the two dimensional vector space over the reals. In this case, a graph becomes a geometric graph.
0.3. We are interested in a particular kinds of geometric graphs, called planar straight-line graphs, in which each edge in the graph is a straight line segment in R^2. From here on, whenever speaking of graphs, we exclusively refer to planar straight-line graphs in which each edge has length precisely 1.
0.4. Further without loss of generality, we will assume that in a graph, there always exists a vertex whose coordinate is (0,0), the origin.
0.5. Two graphs are said to be equivalent, if it is possible to rotate/translate/reflect one graph to obtain the other.
Now I am trying to define a notion of "stability", which I call "rigid".
Definition 1. [Rigid] A graph G is said to be rigid if any other graph H that is graph-theoretically isomorphic to G is equivalent to G.
(to be continued ...)
