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Most of us have an unclear memory of learning about the Pythagorean Theorem (勾股定理) many years ago in math class. 

If you're anything like us writer-types, that 2, 000-year-old theorem went in one ear, and immediately out the other! But for two students at St. Mary's Academy in New Orleans, Louisiana, the theorem presented a challenge they simply couldn't resist taking on. As a reminder for those of us who aren't potential mathematicians, the Pythagorean Theorem is the basis of trigonometry (三角学). For over 2, 000 years, math scholars have stated it's impossible to use trigonometry to prove the Pythagorean Theorem because doing so would be circular logic. In other words, an idea cannot prove itself.

Calcea Johnson and Ne'Kiya Jackson have challenged that concept in their new abstract. The two high school seniors recently presented their abstract in front of the American Mathematical Society (AMS) at their annual southeastern conference. Unsurprisingly, they were the only teenagers there in a sea of math scholars! Their abstract states, "We present a new proof of the Pythagorean Theorem which is based on a fundamental result in trigonometry. " In plain English, that means Calcea and Ne'Kiya proved the theorem using trigonometry after all, and without using circular reasoning.

How did a pair of teenagers solve a riddle that has stumped so many mathematicians before them? Countless math scholars can do nothing facing this theorem. According to Calcea and Ne'Kiya, they have their teachers to thank!

The St. Mary's school slogan is "No Excellence Without Hard Labor", and they mean it! Both girls say their teachers push them to think outside the box and encourage them to discover new concepts. "We have really great teachers, " Ne'Kiya said with a smile. Calcea is proud of herself and her friend for doing something no other high school students have ever done.

Let's review some of the year's best books so far.

The Astronaut's Guide to Leaving the Planet

In this book, retired astronaut and pilot Terry Virts paints a lively picture of life aboard the International Space Station. And he describes what it takes to conduct a successful mission. Young space enthusiasts will enjoy this guide. Ambitious astronauts will treasure it. 

Lasagna Means I Love You

In this touching realistic novel by Kate O'Shaughnessy, Mo and her grandma, Nan, live together. But after Nan dies, Mo's uncle can no longer take care of her. To deal with these changes, she starts cooking, using family recipes that she collects from friends and through her food blog. There's only one problem: She doesn't have family recipes of her own. Hoping to define what really makes a family, Mo learns there's no perfect recipe.

The Enchanted Life of Valentina Mejia

In this fast-paced adventure by Alexandra Alessandri, 12-year-old Valentina and her brother Julian are searching for mysterious creatures. Falling into another world during an earthquake, they discover a different, magical Colombia. Valentina learns that all of the legends about her country are true. But will they be able to leave this place and return home?

Just Jerry

It's written by Jerry Pinkney, who writes about his growing up in Philadelphia, Pennsylvania, during the 1940s and 1950s. He struggled with dyslexia (阅读障碍), but he always pursued his artistic calling. When he got a job at a newsstand, his boss gave him a chance to draw and sell his work. He was able to go to college to study art, and eventually built a career in publishing.

We all make mistakes. Sometimes, it is hard to admit them. However, there is a magic power in this world that can give us the courage to do so. 

I grew up in a small town in Ohio. There was a man in town that everyone seemed to know. We all called him Bob. Bob was uneducated. It seemed that because he was good-natured and not very smart, every one teased(戏弄) him. 

One day when I was sitting on the porch, he came walking by. I was about 12 years old and thought it would make me feel grown up to tease him like some adults did in the town. 

He asked how I was doing. I told him that my father had lost his job, and that we were short of money. I could see my friends laughing in the background so I went on with the lie. I had him fooled so completely that every time he asked me a question, I would make the situation seem worse and worse. I knew he made a meager (贫困的) living doing odd jobs, so it seemed funny when he asked me if we needed anything. I told him that we didn't know if we would have enough to eat. He replied, "You poor thing. I will pray for you. "

That night I heard the door rattle (沙沙响) softly. I thought it was the wind beating against the door. So I didn't pay much attention to it. Later when I opened the door to go outside, I realized it wasn't wind.

注意：  1 . 续写词数应为 150 词左右；2. 请按如下格式作答。

On the doorstep, I found a box of food with a note beside it. 

The next evening, with a big apple pie made by myself, I stood at the doorstep of Bob's house.

注意：1. 词数80左右；2. 可以适当增加细节，以使行文连贯。

A recent report shows an amazing 400 percent year-on-year increase in global durian(榴莲) demand because of the (prefer) of Chinese consumers. China now plays a key role in the market, consuming as much as 91 percent of global durian. Over the past two years, imports of durian (reach) an amazing $6 billion. 

In 2022, ASEAN durian exports covered 90 percent of the global total, with Thailand leading as the main exporter, contributing to an (impress) 99 percent of ASEAN's total exports.

Durian, (know) as the "King of Fruits", is tropical fruit rich in vitamin C for immune(免疫) support, dietary fiber for digestion (消化), antioxidants (抗氧化物), and plenty of essential minerals, makes it a healthy choice .

, durian is among the high-sugar and high-calorie fruits. Typically, every 100 grams of fresh durian flesh contains about 140 to 160 calories and approximately 16 to 30 grams of natural sugars. It is (strong) recommended that adults consume no more than 200 grams of durian per day. 

Durian serves  a key ingredient in making a delightful series of treats, including delicious durian pastries, cakes, and ice cream. No wonder so many Chinese (addict) to the special taste of this remarkable fruit, regardless of its price . 

Jen is a 39-year old community dancer with Down's Syndrome(唐氏综合征). She is the founder of Dance Syndrome, a non profit organization that brings together1  dancers and make them feel equal to everyone. 

Dancing has always been in her veins. As a young girl, Jen seized every opportunity to dance with full2  both in the morning and during her 10 minutes of3  before bedtime. The dynamic workout would keep her4  all day long. 

Life hasn't been straightforward for Jen. She was5  by a number of dance clubs in primary school and encountered numerous6  while pursuing her passion for dance. Despite these challenges, her ambition to share her love for dance and7  disabled individuals in the art grew stronger. 

After leaving school at 18, Jen spent over 10 years searching8  for opportunities to be trained as a dance leader. Eventually, she had to give up and decided to try her own way, not knowing where it might lead!

Despite the9 , Dance Syndrome was established in 2009. Jen and her fellow disabled dance leaders took 10  of the charitable organization, working alongside non-disabled dance artists who helped them work more professionally. 

Over the decade, Dance Syndrome has 11  thousands of disabled dancers, cultivating an environment where every person is recognized as equal, 12  and accepted for who they are. The year 2019 witnessed Jen 13  for the third time as a member of Shaw T rust's Disability Power 100. She is a living proof that 14  can come from unexpected places and that disabled individuals can 15  society in extraordinary ways. 

When people first come across the Law of Attraction(吸引力法则), their hearts and minds often immediately think of one specific thing that they'd love to achieve in their lives. However, the next thought is often "But I can't do that". You may come up with all kinds of excuses. Here are the reasons why you should believe you can use the Law of Attraction to obtain whatever you want.

Small steps create big changes. One of the most common reasons for abandoning dreams is that they simply seem too huge to realize. Usually it's manageable to think of following your dream as taking a series of significant but small steps. Then look at each of them. Not so unrealistic now, is it?

When people are interviewed on their deathbeds or write about their lives in autobiographies (自传), it is often observed that major regrets tend to relate to things that were not done. In older age, it's likely that you will be uncomfortable with the idea that you didn't even try to do the thing that you loved or attempt to obtain what you truly wanted. But you don't ever need to feel this way! Make today the first day of your new journey towards avoiding regret.

Steps towards your dream are never backwards steps. Another common worry is that if you follow your dreams, you'll be "taking steps back". However, what looks like backward steps in your old life can more productively and accurately be seen as forwarding steps in the brand new life you're creating.

A. You can avoid regret. 

B. It makes sense to move forward confidently. 

C. Luckily, the truth is that it's never too late to follow your dream.

D. It often comes up when people are at the top of careers they hate. 

E. It is painful to feel like you haven't ever found your true purpose.

F. For example, challenge yourself to write down the path to success in ten stages. 

G. You have enough life experience and knowledge to make changes to pursue your dream. 

Since the 1950s, some 

9. 2 billion tonnes of plastic have been produced globally, of which only about 10% has ever been recycled. Yet environmentally conscious companies and consumers continue to look to recycling as a way to ease the plastic problem. Manufacturing giants claim to be committed to making more of their products and packaging from recycled materials. However, this confidence masks(掩饰) a complex web of issues around plastic recycling. Recycling rates remain extremely low and critics argue that we should look at alternative ways to tackle plastic pollution. 

While many plastics have the potential to be recycled, most are not because the process is costly, complicated and the resulting product of a lower quality than the original. Despite rising demand for recycled plastic, few waste companies turn a profit. Part of this is because virgin plastic-linked to oil prices -- is often cheaper than recycled plastic, meaning there is little economic incentive to use it. Worse yet, much of our plastic waste is difficult to recycle. Lightweight food packaging, like a mozzarella packet, contains different plastics, dyes and toxic additives(添加剂). This dirty mix means plastic recycled through mechanical methods- the most common form- can only be melted down and moulded(浇铸, 塑造) again a couple of times before it becomes too fragile to be reused. And the nature of the process means plastic recycling has a carbon footprint of its own. 

Given all of these difficulties, environmental critics say recycling is not the solution-and argue that creating more products from recycled material to attract environmental consciousness merely worsens the problem. "The solution is to use less plastic and to stop misleading the public about the recyclability, " says Enck, president of Beyond Plastics, a US campaign group with a mission to end single-use plastic. "They should stop making false claims about the recyclability of plastics since they know most will either be littered(乱扔) or; burned or landfilled (填埋). Using less plastics means shifting to reusable products and relying more on paper, cardboard, glass and metal一all of which should be made from recycled content. "

Michael and his wife, new residents in a San Francisco apartment, learned about their neighbor Jeff Dunan's volunteer work for Bangladesh Relief, an organization that provides food, clothing and essential supplies for disadvantaged people in northern Bangladesh, Inspired, Michael donated $ 150 to Dunan's GoFundMe campaign. However, a credit card notification alerted him to an unintended $ 15, 041 charge. 

When he saw the five-figure number, he was confused, Soon, it all made sense, Michael's credit card number started with four and one. Clearly, he accidentally began typing his credit card information while his cursor(光标) was still in the donation box. 

Michael planned to call Dunan to explain, but before he had the chance to do that, he started receiving Facebook messages from Shohag Chandra, the charity's Bangladesh-based program manager, thanking him for his generous donation. After he looked through the photos of people holding thank you signs that read his name, Michael's heart sank. He felt terrible that he had to withdraw his handsome donation. Once his original contribution was refunded, he decided to donate $ 1 , 500. 

Although Michael had told his family and friends about the tale, he decided to share it publicly on social media, after Dunan told him the organization was desperately in need of funds. "The least I could do was take the time to post this story online and see if I could inspire other people to donate to the cause, " Michael said.

Little did he know, though, that the story would be seen far and wide, ending up raising more than $ 120 , 000 for Bangladesh Relief in the span of only a few weeks- about eight. times Michael's mistaken donation. According to Dunan, more than 3, 700 people have contributed because of Michael's post. Michael has been stunned(震惊) by the ongoing outpouring of support. "Never in my wildest dreams did I imagine this reaction, " he said. "People can be amazing when they come together for something like this. "

Angus, Doris, Gabriel and Kamil are some of the 21 names that have been chosen to be given to storms in the UK in the 2016/17 season. 

The Met Office, the UK's national weather service, decided to give storms boys' and girls 'names in 2015 in the same way as they did in America. 

The Met Office hopes that naming big storms will make people more aware of them and how dangerous they can be. Derrick Ryall, from the Met Office, said, "We have seen how naming storms elsewhere in the world raises people's awareness of storms before they break. "

In the past, the same UK storm could be given different names by different organizations. "We noticed that many organizations during the last couple of winters started giving names to them. Think back to the St Jude's Day storm in 2013, and the so-called(所谓的) Hurricane Bawbag in Scotland in 2011. But it led to confusion(混淆), "a Met Office spokeswoman said.

According to the Met Office, there is a name for each letter of the whole alphabet (字母表), except for Q, U, X, Y and Z. That is the same as the naming tradition used in America. And not all storms will be big enough to get names-only those expected to cause great damage. 

If there are more than 21 storms in a year, the Met Office will start again with another name beginning with "A". However, according to Met Office spokeswoman Lindsay Mears, "It's less possible we would get through the whole alphabet in one season. We had 14 storms in the very bad winter of 2013/14, and if the naming system had been in operation then we wouldn't have used the whole alphabet. "

There are a variety of free magazines that kids can receive in the mail. Kids love getting mail, so these magazines will bring double joy!

Animal Wellness Magazine

If your child loves animals, a free copy may provide him or her with hours of educational entertainment. This magazine is especially wonderful if you have a dog or a cat at home and want your child to learn about pet care. 

Kids Discover Online

This is an excellent online resource (资源) where elementary school children can learn about different aspects of science and social studies topics. It gives you access (使用权) to 30 units with 200 topics. 

National Geographic Kids

The content there is various. You can gain even more access by creating a free account. There are educational articles on dozens of countries around the world, as well as articles on animals, planets, and more. Aimed at children aged 8 to 14, this magazine is a great choice for learning and fun. 

Sports Illustrated Kids

If you have children that are sports fans, look no further than the Sports Illustrated Kids. They can get analysis of recent games, forecasts about next season, and fun games. It's all free, and your son or daughter will love getting to know the latest sports news.

The neighborhood kids nicknamed the strange old couple Crazy Jack and Ruby Rednose. Rumor was that they sat inside and drank tea all day. The only words we ever heard from them were "Keep out of our rosebushes!"

The rosebushes served as a fence between our house and theirs. I was eleven at the time and the oldest of six active girls. We should have played our softball games elsewhere to avoid hurting the roses, but we secretly enjoyed annoying Crazy Jack and Ruby Rednose. One day, we had a neighborhood softball game in our yard. Mary was trying to catch a fly ball. She stumbled (绊倒) over one of Ruby Rednose's rosebushes and fell on top of several more. Just at that moment, Ruby Rednose sprang out and ran toward Mary. She screamed angrily, "Look at what you've done to our family's roses! You've always been a trouble. You have no idea what this rosebush means to me! "

Hearing this, my sisters and I ran into our house. Breathlessly, we told Mom what had happened. "Girls, I have told you not to play softball near those bushes. Come outside right now and help me fix them. " "Mom, we thought you didn't like the couple, " we protested. "They're mean to us. " Mom just glared at us. We followed her outside to help repair the rose fence. While Mom was examining the damaged roses, Ruby slowly walked out. She looked sad. And it wasn't her nose that was red — it was her eyes.

注意：1. 续写词数应为150左右；2. 请按如下格式在相应位置作答。

Ruby walked over to my mother, we girls holding our breath. 

A few weeks later, the plants all came back to life. 

注意：1. 词数100左右；2. 可以适当增加细节，以使行文连贯。

Dear Tony, 

Yours, 

Li Hua

Recent videos claiming that a school in Ganzhou, Jiangxi, serves pre-made meals to its students  (spark) heated discussions across the country. People doubt if pre-made meals, despite being convenient, are healthy and nutritious enough for growing teenagers. 

Pre-made meals refer to half-finished or finished dishes that are already cooked or prepared, according to the China Cuisine  (associate). There are several types of pre-made foods, including ready-to-eat food, such as a canned food or cooked food in package and ready-to-heat or ready-to-cook food,  requires heating or cooking before being served. 

Many people tend  (think) that ready-to-heat and ready-to-cook foods are less nutritious because they usually need to be kept in  (freeze). 

"Actually freezing does not cause a loss of nutrients, " Liu Junya, -year-old dietitian in Beijing, told Teens. "Nutrient loss (typical) occurs during the heating or frying process. Pre-made foods can be less nutritious than freshly prepared and cooked foods, " Liu said.

Meanwhile, "many pre-made food companies prioritize taste over nutrition, " said Liu. This leads to (high) levels of salt and sugar in the food, which may lead to health problems, such as high blood pressure or diabetes (糖尿病) the long term.

It is hoped that regulations on pre-made meals can  (strengthen) to better ensure nutrition and hygiene (卫生). 

One summer night, my friends and I stole into the Jordans' backyard and started harvesting their sweet, juicy raspberries (树莓). We were enjoying every bite of the tasty berries 1 Mr Jordan came charging outside all of a sudden.

"What are you boys doing out here?" he yelled as my friends ran off 2 all directions. He attempted to catch one or two as they rushed past him, but they were too 3 for the older gentleman to catch. Within seconds, the boys 4 into the dark of the summer night. All except me. Speed was never my 5 . I took the tongue-lashing (痛骂) that Mr. Jordan gave me as he marched me down the block to my house, where my mother took over and scolded me 6 . My friends said they could hear every colorful word she spoke from the darkness of our backyard, where they had gathered to 7 their escape and to observe my capture.

They 8 me about it for days afterwards, while all I could do was complain about how 9 it was that I was the only one who had to pay the price. After about a week of this, I complained to my father about the inequality of the situation. Dad said, "You took raspberries without 10 , and you get exactly the punishment you deserved. "

"But what about the other guys?" I asked. "They didn't get punished at all!"

"That's not my concern nor should it be yours, " Dad said. "You can't 11 what happens to others. You can only 12 what happens to you. You made a bad choice that night, and you were punished for it. "

For the duration of the following years, I come to realize there is no 13 that life will treat us fairly. That's why we can't 14 comparing our lives with the lives of others. Like Dad said, that isn't our 15 .

My students frequently ask me how I planned out my career to become president of Fidelity Investments. I always tell them, "There was no grand plan; I backed into my career one step at a time. " In this tough economy and ever-changing world, it is more important than ever to smartly evaluate each step in your career. To prepare for whatever surprises lie ahead, try to make choices today that will maximize your options in the future.

Gaining transferable knowledge begins with the choices you make at school. You want your education to provide you with the necessary skills and expertise to succeed in a wide variety of jobs.  I favor those that involve extensive writing, rigorous analysis, or quantitative skills. 

Once you have finished your formal education, search for jobs that will allow you to further expand your transferable knowledge — to help you find your next job. Let's say you take a job putting together airplane leases. Within a few years, you could become the world's expert on the subject. By contrast, if you take a job that will expand your computer programming skills, you can greatly boost your options for later steps in your career.

Remember gaining transferable knowledge is only one piece of the puzzle. As a saying goes, "Organizations don't hire people. People hire people. " The more people you know, the more people will think of you when a job pops open — even when it is not publicly advertised.

Of course, you can build your network to some degree without changing jobs.  But this sort of event-driven networking pales in comparison with the deep bonds you can develop with your colleagues by working, communicating, and traveling with them. 

A. You can make yourself more attractive. 

B. Gain transferable expertise and form close bonds with your colleagues. 

C. Your next step should help you expand your web of personal relationships. 

D. This later helped me evaluate and start business units throughout the world. 

E. You can attend conferences or participate in committees at trade associations. 

F. This means that you need to make smart choices about the courses you will follow. 

G. However, this narrow expertise probably won't help you in any other line of work.

Search "toxic parents", and you'll find more than 38, 000 posts, largely urging young adults to cut ties with their families. The idea is to safeguard one's mental health from abusive parents. However, as a psychoanalyst (精神分析学家), I've seen that trend in recent years becomes a way to manage conflicts in the family, and I have seen the severe impacts estrangement (疏远) has on both sides of the divide. This is a self-help trend that creates much harm.

"Canceling" your parent can be seen as an extension of a cultural trend aimed at correcting imbalances in power and systemic inequality. Today's social justice values respond to this reality, calling on us to criticize oppressive and harmful figures and to gain power for those who have been powerless. But when adult children use the most effective tool they have — themselves — to gain a sense of security and ban their parents from their lives, the roles are simply switched, and the pain only deepens.

Often, what I see in my practice are cases of family conflict mismanaged, power dynamics turned upside down rather than negotiated. I see the terrible effect of that trend: situations with no winners, only isolated humans who long to be known and feel safe in the presence of the other. 

The catch is that after estrangement, adult children are not suddenly less dependent. In fact, they feel abandoned and betrayed, because in the unconscious, it doesn't matter who is doing the leaving; the feeling that remains is "being left". They carry the ghosts of their childhood, tackling the emotional reality that those who raised us can never truly be left behind, no matter how hard we try.

What I have found is that most of these families need repair, not permanent break-up. How can one learn how to negotiate needs, to create boundaries and to trust? How can we love others, and ourselves, if not through accepting the limitations that come with being human? Good relationships are the result not of a perfect level of harmony but rather of successful adjustments. 

To pursue dialogue instead of estrangement will be hard and painful work. It can't be a single project of "self-help", because at the end of the day, real intimacy (亲密关系) is achieved by working through the injuries of the past together. In most cases of family conflict, repair is possible and preferable to estrangement — and it's worth the work.

I'm a talker. I'm into debating, gossiping and teasing. I solve problems by talking them through. This works perfectly well when I have people to talk to. Under lockdown, however, I've only had my partner, Peter. We not only lived, worked and traveled together, but mostly socialized together, too. Under the first UK lockdown, our constant closeness began to feel uncomfortable.

For the first time in our 10 years together, we needed to be alone. I tried to manufacture this by going on walks on my own, but a short walk in the local park wasn't doing the job. I considered my options and hit upon an idea: the semi-solo hike. Could we do a circular hike but walk in different directions? This would give us the space and peace of a solo hike. It felt like a promising compromise, so I told him about it. He thought it was thoroughly silly but agreed to give it a try.

We started with a four-mile loop (环形) from Reeth. At the start, we parted ways. At first, I was aware of how close we were, which lessened the appeal. Walking alone offers freedom and alone time, but here I was with my boyfriend nearby. As I gained ground, however, I found myself very much alone. I set my own pace, and I decided to take my time. 

I sat on a rock and breathed out. That moment — with the weak sun through the clouds and the breeze blowing across makeshift pools — felt extraordinary to me. I was born and raised in London and had never imagined leaving until I met an outdoorsman. Now, my former life as a city girl felt crazy. Realizing what I had gained, I felt the tension leave me. There, in the chilly air, I no longer needed to talk. The semi-solo hike gave us a shared experience with added room to breathe. I didn't see Peter on route but reunited back where we started, both of us sheepish (难为情的) but pleased. The semi-solo hike is admittedly silly in theory, but for me it has been a lifeline. It has given me the gift of time alone and, in a year of constant closeness, the joy of reuniting.

Dear Tommy, 

I am Ole Orvér, Finnair's chief commercial officer. It's my pleasure to warmly welcome you back to the skies with Finnair. I'd like to reflect on some of the developments that we hope you find exciting and helpful:

●This summer season you can fly with Finnair to over 70 European and five US destinations. In Asia, we serve eight cities, including Guangzhou and newly added Mumbai starting 6 August. We operate over 300 daily flights and I'm excited about the addition of Seattle and Dallas to our US network.

●Travel is recovering everywhere, and airports around the world are working hard to manage increased traffic volumes. It is a good idea to reserve some extra time at the airport before your flight. We are doing our very best together with our partners both at Helsinki and in our outstations to offer you a smooth travel experience during this popular travel season. 

●You are again able to offset flight carbon emissions (碳补偿), this time with a service that combines sustainable aviation (航空) fuel and certified climate projects. We at Finnair have ambitious emissions targets and our customers wish for a simple and transparent way to contribute. 

●Finnair Plus turned 30 in May. We are committed to developing the programme further to serve you in the best possible way. To make your flight bookings smoother, we recently upgraded the experience of booking award flights in the Finnair app. 

Finally, I'd like to thank you for your patience when we haven't got things quite right. Wherever you're travelling in the next few months, I hope it's memorable. Thank you for flying Finnair.

Kind Regards, 

Ole Orvér