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A case study of fifth-grade mathematics in the form of stories
1. The spider's "gossip" net is a complex and beautiful octagonal geometric pattern, and it is difficult for people to draw a symmetrical pattern like a spider's web even with the compass of a ruler.

In winter, when a cat sleeps, it always hugs its body into a ball. There is also mathematics in it, because the shape of the ball minimizes the surface area of the body, so it emits the least heat.

The real "genius" of mathematics is coral. Coral writes a "calendar" on its body, and "draws" 365 stripes on its wall every year, apparently one a day. Strangely, paleontologists found that corals 350 million years ago "painted" 400 watercolors every year. Astronomers tell us that at that time, the earth only had 2 1.9 hours a day, not 365 days a year, but 400 days.

2. Tang Priest and his disciples pick peaches

One day, the Tang Priest told his disciples Wukong, Bajie and Friar Sand to go to Huaguoshan to pick peaches. Before long, the three disciples returned happily after picking peaches. Tang Priest and his disciples asked: How many peaches did each of you pick? Bajie said with a silly smile, Master, let me test you. Each of us took the same amount of money. There are less than 65,438+000 peaches in my basket. If we count three peaches, there are 1 peach left in the end. Do the math. How many did each of us choose?

Friar Sand said mysteriously, Master, I will test you, too. If there are four peaches in my basket, there is 1 left in the end. Do the math. How many did each of us choose?

Wukong smiled and said, Master, I'll test you, too. If there are five peaches in my basket, there is 1 left in the end. Do the math. How many shall we each choose?

3. the skill of ">"

A long time ago, the kingdom of mathematics was in chaos and disorder. The ten brothers from 0 to 9 not only dominate the kingdom, but also boast about their best skills. Digital angel was very angry when he saw this situation, so he sent three little angels, ">", "

The angel smiled and said, "We are the judges sent by the angel to help you manage your country well. I am an equal sign. The numbers on both sides of me are always equal. These two are' greater than number' and' less than number'. Who they open their mouths to is big, and who they point at is small. On hearing that the judges were sent by digital angels, and with the introduction of "=", 0~9 brothers obediently obeyed the order of ">".

4. The story of "0"

Roman numerals are symbols representing numbers, which are combined to represent different numbers according to certain rules. When using this number, the number "0" is not needed. At that time, a scholar of the Roman Empire discovered the symbol "0" from Indian notation. He found it very convenient to use "0" for mathematical operations, and he also introduced the Indian method of using "0" to everyone. The Pope knew then. The Pope was very angry. He rebuked that the sacred number was created by God, and there was no "0" monster in the number created by God. So he ordered the scholar to be arrested, and his ten fingers were tightly clamped with a clamp, so that his hand was disabled and he could no longer write with a pen. In this way, "0" was banned by the ignorant and cruel Pope. However, although the use of "0" is forbidden, Roman mathematicians still use "0" secretly in mathematical research regardless of the ban, and still make a lot of mathematical contributions with "0". Later, "0" was finally widely used in Europe, but Roman numerals were gradually eliminated.

5. The oldest and most interesting math problem

In seven houses, each house has seven cats; No matter which of the seven cats can catch seven mice; Each of these seven mice eats Three wheat; If each ear of wheat can peel off seven grains of wheat, how many houses, cats, mice, ears of wheat and grains of wheat add up?

A: The total number is 19607.

There are 7 rooms in the house, with 7x7 = 49 cats, 7X7X7=343 mice, 7x7x7 = 240 1 ear wheat and 7x7 = 16807 grains of wheat. All add up to 7+72+73+74+75 = 19607.

6. Honeycomb conjecture

Honeycomb is a very sophisticated construction project. When bees build nests, young and middle-aged worker bees are responsible for secreting flaky fresh beeswax, each of which is only the size of a needle, while other worker bees are responsible for carefully placing these beeswax in a certain position to form a vertical hexagonal column. The thickness and error of each beeswax partition wall are very small. The width of the six partition walls is exactly the same, and the included angle between walls is exactly 120 degrees, forming a perfect geometric figure. People have always wondered why bees don't make their nests into triangles, squares or other shapes. Why is the partition flat, not curved? Although the beehive is a three-dimensional building, each beehive is a hexagonal cylinder, and the total area of beeswax wall is only related to the cross section of the beehive. This leads to a mathematical problem, that is, to find the plane figure with the largest area and the smallest perimeter.

7. Snails climb wells

German mathematician Reese once wrote a math problem: the well is 20 feet deep and the snail is at the bottom of the well. It climbs 7 feet during the day and drops 2 feet at night. How many days will it take to reach the wellhead?

Analysis: If you think the answer is 20/(7-2)=4, it's all wet! The key to solve this problem is to consider that the crawling situation on the last day is different from that of the previous days.

Solution: The height of snail crawling day and night in the first 3 days:

(7-2)×3= 15 (feet) Last crawling time: * * Time spent:

8. Measure the height of the pyramid

One day, Thales saw people reading the notice, so he went up to read it. The initial notice said that Pharaoh wanted the smartest person in the world to measure the height of the pyramid. Thales is going to Pharaoh. Pharaoh asked Thales what tools he used to measure the pyramids. Thales said that it is strange that everyone only uses a stick and a ruler. He put the stick next to the pyramid, and when the shadow of the stick was as long as the stick, he measured the pyramid. He measured the length of the shadow of the pyramid and half the length of the bottom of the pyramid. Add these two lengths to get the height of the pyramid. Thales is really the smartest man in the world. He can easily measure the height of the pyramid without climbing to the top.