The issue of this issue was very famous before 2000...
Avanti harvested 1,000 pounds of turnips, and he couldn't finish eating them, and if he wanted to sell them, he had to go to the big market. But because Avanti is isolated, the place where he lives is very remote. To get to the city you need to cross 100 miles of desert hanhai.
It is known that the maximum weight of Avanti's donkey is 100 pounds, and for every 1 mile walked in the desert, it is necessary to eat 1 pound of turnips. Avanti needs to bring his own food and drink, so he can't help the donkey share the burden. Obviously, Avanti can't bring turnips to the market all at once, but he can adopt the following strategy.
Avanti took a donkey and buried some of the turnips in secret locations along his way as supplies. Of course, going back and forth like this will also consume a lot of turnips. But because Avanti's own plantation of radishes can increase intellectual attributes, the price of each stick is equivalent to 800 years old ginseng - as long as it is sent to the market, even if it is a big profit.
Now ask, how many pounds of turnips can Avanti sell in total in the market? (Note that you have to go back and forth)
Middle school geometry topics circulating online
First of all, it is wrong to think that a straight line passing through the center of mass can divide the area equally.
Interpreted with ID ≠0
If you have passed the centroid equal part, try the equilateral triangle centroid parallel to one side of the straight line? The centroid is the balance of moments, which is equivalent to each point being weighted by its distance from the straight line, while the weight of all points is 1 when calculating the area.
For example, an equilateral triangle, which crosses the geometric center and is parallel to one side, divides the original triangle into small triangles above and trapezoids below. The small triangle is similar to the original triangle, and the similarity ratio is 2:3. The ratio of area is 4:9. Obviously, this line does not divide the area of the original image equally.
Positive solution
In the quadrilateral ABCD, take the midpoint O of the diagonal BD and connect the OA, OC. Obviously, the polyline segment AO-OC can divide the area of the quadrilateral ABCD equally, and then point O is OE∥ AC crosses the CD to E, then the straight line AE is sought.
prove:
Because OE ∥ AC,
So S△AOE=S△COE,
So S△AOF=S△CEF,
And because the polyline AOC can divide the area of the quadrilateral ABCD equally,
So the straight line AE divides the area of the quadrilateral ABCD equally
Another chicken:
Quad ABCD. Parallel lines that cross the AC midpoint O to BD, cross AB or BC to P. Straight PD bisected quadrilateral ABCD. Proof: Since O is the AC midpoint, it is not difficult to find that the triangular AOB and triangular AOD areas account for half of the quadrilateral ABCD. And since the OP is parallel to BD, the area of the triangle OPD is equal to the area of the triangle OPB. The quadrilateral ABPD (or triangular APD) area is equal to the triangular AOB + triangular AOD - triangular OPB + triangular OPD, i.e. half of the quadrilateral ABCD.
Wing marks
Set the clockwise four vertices for ABCD, connect one of the diagonal AC, through the B point to do the parallel line of AC, then arbitrarily moving the B point on this parallel line will not change the area of the triangle ABC, the parallel line intersects with the DC extension line with E, then it becomes the problem of bisecting the triangle AED, find out the center point of DE F, need F to fall between CDs, connect AF that is, divide the area equally.
In addition, nerv classmates mentioned
This question reminds me of a question that came to mind when I was in college before: for any egg, is there a way to divide the egg white and yolk equally at the same time. Every time I go to buy meat sandwich steamed buns to eat, I think about it for a while, which has bothered me for several years.
Search for "sandwich theorem" for answers.