Tolstoy's "What Does Man Live With?" In his famous story, there is a sad and exemplary story of Pahom, a farmer who dreams of becoming richer while living an ordinary life. Let's tell the story briefly first...
– Pahom: How much is this place?
– Chief of the Heads: We have only one price. 1000 rubles per day.
Pahom did not understand anything from this answer.
-What kind of payment method is this daily? How many acres? How is it measured?
-We don't talk about it as a measure. We sell the land for a day like this; the more land you turn in a day, that land will be yours for 1000 rubles.
Pahom is surprised.
However, don't I turn too much dirt in a day?
The chief laughs dirty and says it's all yours. There is only one contract. If you can't go back to where you started by the end of the day, you will lose your money.
– How will I determine where to go? By Pahom.
– We will stand where you catch your eye. You walk and circle while we are standing. Take something to scrape with you, mark where it is suitable, make a hole and put ploughs on them. You can get the apartment you want, but go back to where you came from before sunset. No matter how much you translate, it's all yours.
The bastres disperse. They decide to gather at dawn tomorrow and set off before sunrise.
The dawn began to break in the steppe. The chief came to Pahom and pointed to the area with his hand.
– Chief: Everywhere you can see is ours. You can choose the place you catch your eye
The chief removes the cap from the fox fur and puts it on the ground.
– Wherever you go, every place you mark will be yours.
When the sun appeared on the horizon, Pahom only took the tool to scrape the ground and set off.)
(Pahom stopped, dug a hole and went a little further. He dug another hole.)
Pahom: I travelled about 5 km. The sun has become visible, now it's time for breakfast. It's too early, there are four chapters in a day and I think one chapter is over. I go another 5 km and curve to the left. It continues straight from the left side. I've turned enough soil from this side, he thinks I should curl up a little more. He digs another hole and turns to the left.
He continues to run from this side and digs the second hole. He looks at the hill. The weather has started to cloud from the heat, he can barely see people behind the hill.
He thinks that the soil on this side will be enough and runs to the left, that is, to the third side. The sun slowly begins to set. He runs 2 km from this side. It is almost 15 km from the starting place.
No need to think too much, he thinks it can be a curly summer house, the important thing is to reach the flat.
He quickly digs a hole and starts running towards the hill. The hill was right in front of Pahom now.
But he was very tired. He wanted to rest, he shouldn't rest, he had to catch up the hill. The sun was now very close to the skyline.
It became very difficult for Pahom to walk. Everything started to burden him, even his steps... He walked, but it was far further away. He started running. His shirt and pants were glued to his skin from sweat, he was thirsty. His chest was rising and falling like a blacksmith's bellows, his heart was beating like a mallet.
Now the sun was on the horizon and Pahom started to run with his last strength. The sun would set...
He could see the chief and his hat from the fox fur standing on the ground. He started running towards the hill with his last strength. His knees were cut off from fatigue, his foot tripped and fell on the hat.
-(The chief was shouting.) You captured too much land. Congratulations.
They tried to lift Pahom from the ground. Blood was coming from Pahom's mouth and he was dead...
***
In fact, it is possible to find out how many hectares of land were promised to Pahom? How?
Read this story carefully and remove all the geometric instructions. It is not very difficult to get all the data to get the answer to the question.
Thanks to Mathematics and Geometry, it is even possible to draw a plan for Pahom's land.
First of all, in the story, we clearly know that Pahom begins to run from one side of the quadrilateral.
We read about the edge like this: "I travelled about 5 km. I go another 5 km and curve to the left." So the 1st side length of the quadrilateral is about 10 km.
Since it turns immediately to the left from the first edge, we understand that the 1st and 2nd edges are perpendicular. However, the length is not given in the story.
Since it turns immediately to the left from the second edge, we understand that the 2nd and 3rd sides are perpendicular here. “He runs 2 kilometres from this side.”
The 4th side length is given directly: “There are almost 15 kilometres instead of the beginning.”
By drawing the plan according to the guidelines here, we obtain the ABCD quadriangre:
If we go perpendicularly from point D to the edge of IABI, we will find IDEI.
If we apply the Pythagorean Relation in the AED triangle, the x can be approximately 13. From here, we can find the total area approximately thanks to a simple domain calculation.
Area of triangle: 52 km2 ; Area of rectangle: 26 km2 therefore total area: 78 km2 i.e. 78000 acres...
Maybe Lev N. Tolstoy wrote his story with a drawing similar to the drawing above in front of his eyes...
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