Pythagorean Triplets

by Andy Jiang | Mar 28, 2017 | Math

Cool Thing About Pythagorean Triplets

There is a cool property of all odd numbers except one, they can all form Pythagorean triplets. A Pythagorean triplet is any set of positive integers a, b, and c that satisfy the equation a² + b² = c². For example, a= 3, b= 4, and c= 5 is a Pythagorean triplet because 3² + 4² = 5². If a is any odd number except 1, it can make a Pythagorean Triplet of the form a= a, b= (a² – 1)/2, and c= (a² – 1)/2 + 1, or b + 1. You can prove this by substituting b and c with b= (a² – 1)/2 and c= (a² – 1)/2 + 1 in the equation a² + b² = c². “a” cannot be even for this case because if a were even, (a² -1)/2 would not be a whole number, and a cannot be one, because then, b would be zero. For all other odd numbers, this would work, and Pythagorean Triplets of this form include…

a= 5, b= 12, c= 13

a= 7, b= 24, c= 25

a= 9, b= 40, c= 41

Setting Goals

by Kira Pyronneau | Mar 28, 2017 | Math

Setting Goals for the Semester

As you progress through a semester, it is important to continuously assess your progress and set new goals for yourself. This is an important thing to do because it makes you more aware of how you are performing and helps you to create a focused path for the remainder of the term. Furthermore, setting goals helps you to better organize your limited time and resources available as well as improve your motivation

Assess Your Progress:

The first step to goal-setting is to assess your current progress. This includes knowing the grades you have received as well as the study habits you used to get them. Make a note of whether you have been doing things like reading the textbook, taking notes in class, completing your homework or thoroughly reviewing before tests. It is also important to assess how well you understand the course material as well as if your grades match your perceived understanding.

Decide What You Want from the Class:

Before setting defined goals, it is important to think about what you want to get out of the class. Do you want a good grade to raise your GPA? Do you want a strong foundation on a topic that will be important later in your curriculum? Do you want to be more knowledgeable about a subject that interests you? Knowing what you specifically want from a course will give you the motivation to keep focused and continue to work hard.

Setting Goals:

Now that you know how you are doing in your courses and what you want to gain from them, it is time to set goals for yourself.

Set goals for things you would like to see occur. For example, maintaining or improving your grades, study habits or your understanding of certain topics. It is important that your goals are both reasonable and specific to keep you motivated and focused.

In addition to setting goals, you need to create a plan to help you reach them. To get the grades that you want, you must understand what study habits you will need to have. Also, you must assess if you need extra help and find out what resources are available to you. The internet may have additional explanations and examples of topics. Additionally, your teacher may be able to give you additional help outside of class. Don’t forget that MaThCliX is also a great resource!

Once you’ve set goals and created a plan for yourself, you will be on track for a focused and productive term. Following the ideas discussed above will help you stay motivated while providing with the skills and resources to get the most out the courses you are taking.

by Chuck Summers | Jan 2, 2017 | Math

Study Habits 

“I don’t write it down to remember it later, I write it down to remember it now.” Umberto Eco

Here are a few of my ideas to help you study, take notes, and learn.

1. Take copious and detailed notes, especially in math and science. The more detailed and clear, with diagrams, the better. The process of making the drawing/diagrams and taking the notes will cement the concepts in your brain. It is almost like you are writing on a whiteboard in your brain that you can refer back to when you need it. The reason this works is because you are using multiple senses to learn and you are focusing to do it correctly.
2. If you have questions that arise, write them down in your notes and make sure you ask the questions as soon as possible. Interaction with the teacher will help you learn the material and how important the subject is to the teacher. If you can ask the questions during the class lecture time, do so: you will not be the only person with the question, and it will encourage others to ask helpful questions. It is my opinion that the only bad question is the one that is not asked.
3. Dedicate a specific time and place for studying. A special quiet place without distractions is best. MaThCliX provides such a place and many of our best students take advantage of the environment to do their work. For many, even if they intend on doing their math work at home, there are a host of distractions awaiting in that familiar environment. In college, we called the distraction of our bed the ‘rack monster’, so we were more productive in the library away from our familiar spaces.
4. This is controversial, but I believe, and many studies show, that music causes enough distraction to defocus and make you less productive in studying. It can be used when you take a break to recharge your brain, but during intense study, absolute quiet is best.
5. You may not know this, but your attitude have a huge effect on your success in learning a subject/topic. If you go into a topic with eagerness, wanting to learn and master it, you will be a lot more successful than if you do it begrudgingly, not wanting to learn it, or hating the subject. You will do a lot better if you trick yourself into finding something to enjoy in the subject. Finding some other subject that is related can help you find a mental link to hang the new facts on.

There are a lot more suggestions, but practicing these will help you as you study.