It is said that it was put forward and calculated by isaac newton (1642- 1727), a famous British physicist, astronomer and mathematician.
Generally speaking, it takes 30 trees to cut trees into 10 rows, with 3 trees in each row. There are only nine trees left now. In order to meet Newton's requirements, some trees need to be cut to the intersection of several rows. Mathematically, the point where two or more straight lines intersect at the same point is called the key point. To this end, the wise man skillfully cut these nine trees to the point and solved the problem beautifully. As shown in the figure (drawing is not supported here, so it is omitted. )
Wonderful and exquisite design, exquisite composition!
How did you get up here?
Pascal (1623- 1662) is a famous French mathematician, philosopher and essayist. When he was young, he wrote a pamphlet about conic curves. It's a pity that there were so few copies in those days that even his unique copy could not be found long ago. He put forward the famous Pascal theorem:
If a hexagon is inscribed on a conic curve, the intersection of three pairs of opposite sides of the hexagon is on a straight line.
In fact, as early as the third century BC, the ancient Greek mathematician Pappus gave a similar weak condition proposition:
Let {A 1, A2, A3} and {B 1, B2, B3} be three-point groups on L and M, respectively. Let A 1B2 and A2B 1 intersect at point p, A 1B3 and A3B 1 intersect at point q, and A2B3 and A3B2 intersect at point r, then {P, q, R} three-point * * line.
So, we can arrange nine points like this:
Step 1, randomly select three points A 1, A3 and A5 on a straight line L;
Step 2, randomly select two points A2 and A4 on the straight line M;
Step 3, connecting straight lines A 1 A2, A2A3, A3 A4, A4 A5 and A1A4; ;
Step 4, remember that the intersection of A 1 A2 and A4 A5 is A7, and the intersection of A2 A3 and A 1 A4 is A8;
Step 5, connecting straight lines A5 and A8 and intersecting straight line M at point A6;
Step 6, connect the straight line A6 A 1 and cross A3 A4 at point A9.
The above nine points A 1, A2, A3, A4, A5, A6, A7, A8 and A9 are located on nine line segments respectively, thus solving the problem of "nine trees and nine rows". So how do you draw the 10 line segment in the problem of "9 trees have 10 lines"?
According to Pappus theorem, three points A7, A8 and A9 are on a straight line. Connecting A7A8A9 is the 10 line segment of the "9 trees 10 line" problem.
How is Pappus theorem proved?
This requires another famous Menelaus theorem in ancient mathematics.
Menelaus (A.D. 1 th century famous mathematician and astronomer in ancient Greece): If a straight line intersects with the sides BC, CA and AB of triangle ABC at L, M and N respectively, there are: (an/NB) * (BL/LC) * (cm/MA) =1(Consider the direction of the line segment.
The problems of "ten trees and five elements" and "nine trees and ten lines" seem simple, and there seems to be no profound mathematical truth. However, when we break through the fog, we are presented with the beautiful scenery of one mountain and one mountain!