Guadou principle: If the distance ratio between two moving points and the base point is constant and the arrival angle is fixed, the moving paths of the two moving points are the same. Guadou principle is a master-slave linkage trajectory problem. The driving point is called melon and the driven point is called bean. Melons move in a straight line, and so do beans. The movement of the melon is round, so is the trajectory of the bean. The key is to make the trajectory of the driven point, and make the special point of the driven point according to the special position of the driving point, so as to connect the trajectories.
Type: Point moving in a straight line
1, line segment+line. Conditions: A on the AB line is the moving point on the I line .. C is the midpoint of the AB line, B is the fixed point, and A is the moving point. Conclusion: 1 The trajectory of point c is half that of point a.
2. the trajectory of c is parallel to that of a.
3. Angle+straight line. Conditions: A is the fixed point, B is the active point, C is the driven point, the included angle between A and B and C is unchanged, and AB is not equal to AC.
Conclusion:
1 and the trajectory of c are the same as that of b, and they are all straight lines.
2. The included angle between the straight line of B motion and the straight line of C motion is equal to ZA.
3.AB/AC is a constant value k.
4. the ratio of movement length c to movement length b is equal to K.
5. If AB is not equal to AC, there is 4ABM~AMC, and the similarity ratio is k6. If AB=AC, there is ABMeAMC.
The general problem of drinking horses is a mathematical problem. This question studies when the path is the shortest. Li Qi, a poet in the Tang Dynasty, wrote two words at the beginning of "Warsong": "mountains cover the white sun, look up at the sky, and drink the horse at dusk". There is an interesting math problem in this poem. In the poem, after watching the bonfire, the general starts from point A at the foot of the mountain, drinks horses by the river, and then camps at point B ... How to walk to make the total distance shortest?
This problem existed as early as ancient Rome. It is said that there is a scholar in Alexandria who is proficient in mathematics and physics, and his name is Helen. One day, a Roman general paid a special visit to him and asked him a puzzling question. Every day, the general starts from the military camp A, goes to the river to drink horses, and then goes to the place B on the same side of the river for a meeting to find out how to take the shortest route.
Since then, this problem known as "the general drinks horses" has been widely circulated. It is not difficult to solve this problem. It is said that Helen solved it after a little thinking.