第二节课从最简单的模型开始入手：七桥问题。
首先，先去wikipedia上了解一些有关七桥问题的背景知识。http://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg
而这节课要做的事情，其实在wiki上已经有所介绍，建模分两步：
1. 将地图分隔开的部分染成四种颜色，并且标记桥：
2. 再将其抽象成node和edge...
然后是证明：
一笔画的证明很容易，难点在于用英语。在说明清楚的同时，如果能配一些示意图则会更佳。
比较好的说明有：
1. 一种说明的思路(from gx)：
假设，在至少具有2个节点，且具有n(n∈N*)个奇数度节点的连通图中，存在一条路径，经过且仅经过每一条边一次.
根据条件可得：
A.每一个节点出度必定对应另一个节点的入度，因此所有节点的出度与入度之和为边数的两倍，必定为偶数。
B.当节点不为起始或终点时，节点的入度应当等于出度，因此奇数度的节点只能是起始点或者终止点。
若假设成立，则
① n=0 图中仅具有两个偶数度节点，结论显然成立。
② n=1 仅有一个奇数节点，度的总和为奇数，与A矛盾，不成立。
③ n=2 a)一个或两个奇数节点不是起点或终点，与B矛盾，不成立
b)两个奇数节点为起点与终点
↑待证明
④ n>2 至少有一个奇数度节点不为起点或者终点， 与B矛盾，不成立。
2. 比较好的Problem Restatement:
The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges.
The problem was to find a walk through the city that would cross each bridge once and only once. The islands could not be reached by any route other than the bridges, and every bridge must have been crossed completely every time; one could not walk halfway onto the bridge and then turn around and later cross the other half from the other side. The walk need not start and end at the same spot. It is proved that the problem has no solution. There could be no non-retracing the bridges. The difficulty was the development of a technique of analysis and of subsequent tests that established this assertion with mathematical rigor.
3. 有人找到了柯尼斯堡现在的卫星云图：
可惜桥已经不在了，被换成了高速公路了，另人唏嘘不已。
P.S. 有人用flash高仿了一个wiki上的插图：
非常高端有木有？！