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How to make a geometry puzzle(几何谜题) that most people can’t figure out?

You’ll need:

* Square piece of light cardboard or heavy paper

* Scissors

* Four brass paper fasteners

* Hole puncher

1 Cut the paper into four equal strips.(相同大小的)

Punch holes near the ends of each strip.

2 Make a square with fasteners.

3 Hold two opposite sides, gently pull them outward, and twist(扭转) your hands inward at the same time.

What happened?

You can reshape the square into a ring, and flip(翻转) that ring back into a square.

Give the square to 10 people and ask them,“can you make this into a ring?”   and see how many can.

There’s a mathematical science called topology(拓扑学).

It studies shapes that can be turned into other shapes like this.

【小题1】How many kinds of tools will you need in this experiment?
A.ThreeB.FourC.FiveD.Six
【小题2】What should you do after cutting the paper into four equal strips?
A.Make holes with puncher in each strip.B.Make a square with fasteners.
C.Pull the opposite sides inward.D.Twist your hands outward.
【小题3】Which of the following can probably happen?
A.You can’t turn the square into a ring.
B.You can turn the ring into a square.
C.You can’t turn the square into any other shape.
D.You can turn the ring into any other shape except a square.
【小题4】The passage is from a book about ____________
A.historyB.biologyC.scienceD.sports
【小题5】What is the main purpose of the passage?
A.To tell us a funny story.B.To teach us an important lesson.
C.To explain how to do an interesting game.D.To show an example of topology.
2018·河北石家庄·一模
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Our grandparents seem to have magic powers sometimes. Give them a Chinese lunar calendar (农历), and they will know what the weather will be like a few days or even months later. What’s the secret? They are following the 24 Solar Terms (节气), which is an important part of Chinese culture. And on Nov. 30, 2016, the United Nations added it to the list of the Intangible Cultural Heritage of Humanity (人类非物质文化遗产).

In ancient times, most Chinese people made their livings on farms. So, weather changes were important to them. Without satellites (人造卫星), the Internet or the weather report’s help, Chinese ancient people studied the sun’s movement with a sundial (日晷). They also paid attention to other natural changes such as air temperature, water and plant growth. As early as the Shang Dynasty, the Chinese people had already established (确立) four solar terms. During the Zhou Dynasty, eight solar terms marking the four seasons were established. Until the Han Dynasty, the present 24 Solar Terms was established completely. The terms became their guide to farming work. For example, the solar term jingzhe is when insects wake up from a long sleep. Farmers take it as a sign of warm weather and get busy working.

The 24 Solar Terms is regarded as China’s fifth great invention, after paper-making, printing, the compass and gunpowder. Now, people still say, “Do not show your feet after hanlu.” Why? It’s because the solar term hanlu marks the coming of cold days.


根据材料内容选择最佳答案。
【小题1】How did the Chinese people establish the 24 Solar Terms?
A.With the help of the Internet.
B.With the help of the weather report.
C.By learning from people working on farms.
D.By studying the sun’s movement and other natural changes.
【小题2】What is the 24 Solar Terms used for?
A.Waking up insects.B.Changing weather.
C.Learning Chinese history.D.Guiding people in farming work.
【小题3】Which of the following is TRUE?
A.Our grandparents have magic powers.
B.Jingzhe is regarded as the start of cold weather.
C.The 24 Solar Terms was established step by step.
D.Weather changed more often in ancient times than it does now.
【小题4】The saying in the last paragraph shows ________.
A.why hanlu marks the coming of cold days
B.what the five great inventions of China are
C.how the 24 Solar Terms guides people in their lives
D.why the 24 Solar Terms was regarded as China’s fifth great invention
【小题5】What’s the best title for the passage?
A.The insects on farmsB.China’s great inventions
C.The history of the 24 Solar TermsD.The influence of weather changes

A day at the shops can help you live longer, and surprisingly, the benefits are actually greater for men, says a study group from Taiwan. The study even suggests that shopping regularly is better than going to the gym. Seeing friends and just people-watching can stave off loneliness and improve psychological health, suggests the study. It looked at almost 1850 people aged 65 and over living alone at home in Taiwan, who were asked how often they went shopping. They found those who shopped daily lived longer than those who shopped less, with thinking of people’s physical or other health problems. By comparing with those who didn’t often go out to the shops had the best life record, with a 28% cut in their chances of dying, while older women saw a bit fewer benefits with a 23% cut in dying.   The researchers said, “An elder who shops less for food would be at risk of poorer diet to keep healthy. This makes a bad cycle. Shopping less causes poor health and poor health causes less shopping. ” But the study added, “In shopping situations, communicating with, or watching others can provide social and mental benefits. ” “Compared with other types of spare-time physical activity, like exercise, which usually needs motivation and sometimes professional instruction, shopping is easier to keep on.”

【小题1】The study suggests that ________ is better than going to the gym.
A.watching peopleB.seeing friendsC.shopping regularlyD.living alone
【小题2】According to the survey, old people who live alone would live longer if they ________.
A.shopped dailyB.never shoppedC.shopped lessD.shopped with friends
【小题3】The underlined word “stave off” in the third paragraph probably means ________.
A.turn offB.cut offC.take offD.keep off
【小题4】An elder who shops less for food would ________ to keep healthy.
A.provide social benefitsB.be at a risk of poorer diet
C.have physical problemsD.feel even lonelier
【小题5】Which of the following is Not True according to the passage?
A.The benefits of shopping regularly are greater for men.
B.The study interviewed almost 1850 people aged 65 and over living with their families.
C.Older men who often went shopping would have 28% cut in their chances of dying.
D.Shopping less causes poor health and poor health causes less shopping.
【小题6】We can learn from the end of the passage that ________.
A.some physical activities are easier to keep onB.old people don’t have motivation to exercise
C.you need some professional instruction to shopD.it is not easy to exercise regularly

Li Mei feels worried about her looks — not her face, but her clothing. When she sees fashionable people on the street, she tries her best not to run into them. “I’m afraid that they think I’m out of style,” says a teenager from Chengdu, Sichuan.

What Li is experiencing is fashion anxiety (焦虑). It bothers many people today. And she is not the only. Last month, an internet user shared a video about her fashion anxiety on Sina Weibo, and it quickly caused a discussion.

A big reason for fashion anxiety is fashion bullying (霸凌) among people. As fashion magazines, advertisements (广告) keep showing the “latest and greatest” fashion, teenagers think they need to follow them, no matter how expensive it might be. “The need to be in a group is very important to young learners. They are sad and worried if they aren’t there,” said Andy Cranham, a teacher, at City of Bristol College in the UK.

Another reason some people might have fashion anxiety is that they are not confident (自信的) enough to know why we care so much about how fashionable people look at us. The fact is that those people usually don’t notice us at all.

Fashion comes, goes and changes all the time. The key is to find your own style. If you’re able to wear something with confidence, you may probably start a new fashion. What you need to focus on is not what fashion is but what kind of fashion you can create (创造).

【小题1】From paragraph 1, what we can know?
A.What is Li Mei good at?
B.What makes Li Mei worried?
C.What do fashionable people look like?
【小题2】What does the underlined word “bothers” in paragraph 2 mean?
A.(使)烦恼B.(使)改变C.(使)自信
【小题3】Which is NOT the things that make fashion anxiety?
A.Following the latest fashion. B.Being not confident. C.Starting a new fashion.
【小题4】According to the passage, which of the following is TRUE?
A.Teenagers should follow the latest fashion to get popular.
B.Young people will feel sad if they are in a fashion group.
C.Creating a new fashion is more important than following it.
【小题5】Why did the writer write the passage?
A.To remind people of the latest fashion.
B.To tell people to stay away from fashion.
C.To encourage people to be more confident.

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