Tag: mathematics tricks

If you thought music was not mathematical language, then think again. In fact, music and mathematics are very much intertwined, so much so that I think you might say could not live without the other. Here we explore the relationship clearly shows the strength of this tie. Let the music begin.

For those with a rudimentary knowledge of music, diatonic scale is something quite familiar. To understand why certain pairs of notes sound good together and others do not, you need to look into the points pattern wave physics and frequencies. The sine wave is one of the basic pattern surge in mathematics and is displayed well alternately Crest-lowest extent. Many physical phenomena and real-world can be explained by this basic wave pattern, including many of the fundamental tonic properties of music. Certain musical notes sound good together (musically this is called reconciliation or consonance ) due dots pattern waves strengthen each other at select intervals.

If you play the piano, then how each of the different notes sound to you depends on how your instrument is configured. There are different ways to tune instruments and these methods depend on mathematical principles. These artefacts are based on the whole frequency applied to a particular mind, and as such, this product whether groups of notes sound well together, but we say such comments are in harmony, or incompatible, but we say such remarks are out of harmony or dissonant.

When this product coming from the launch of criteria instruments manufacturer and today there are certain criteria that these fabricators follow. Still criteria Despite a multiple nature of mathematics. For example, in more advanced mathematics, students learn some numbers. A series is simply the pattern numbers are determined by some rule. One famous series is harmonic series . This includes the reciprocals of integers, it is 1/1, 1/2, 1/3, 1/4 … The harmonic series serves as one set of criteria for certain tunings, one in particular called Pythagorean intonation .

In Pythagorean intonation, comments are set according to “ rule that perfect fifth .” A perfect fifth consists of “ musical distance ” between the two tones, such as C and G. Again without trying to turn this article into a thesis on musical theory, are notes between C and GC #, D, D #, E, F, F #, and G. The “ from ” between each of these notes is called a half-step. Thus, the perfect fifth 7 half-step, CC #, C #, D, DD #, D # -E, EF, FF # and F # -G. When we consider the notes in a musical harmonic series, a number considered a C note and attributed to G mind will always be in the ratio of 2: 3 So the frequency of these notes will be adjusted to their ratios in accordance with the 2: 3 There is C- note the frequency will be 2/3 G-note frequency, or vice versa, G note frequency will be 3/2 C note frequency, the frequency is measured in cycles per second or Hertz.

Now, continue to adjust according to the perfect fifth, fifth above G is D. Use perfect fifth rate , D note will be tuned to the frequency of 3: 2 G frequency or watched from below, G note is 2/3 frequency D note. We can continue the same way until we complete what is called Ring of the fifth , bringing us back to the C note by applying a series of ratios 3/2 in the previous note in the cycle. This includes the Twelve Steps and when complete, the frequency of the second C or higher octave C note should be exactly twice frequency lower C note. This is a requirement of all octaves. But this does not happen by applying this ratio to 3/2.

Musicians have corrected this problem by resorting to none other than the field irrational number . Recall that the numbers are such that they can not give up the offense, that is, a decimal representation of them, like the number pi or the square root of two, providing not and do not repeat. Thus failure of a Pythagorean tuning method for producing perfect octaves, tuning methods have been developed to prevent this situation. Is called “ equal temperament ” Tuning, and this is standard procedure for most practical applications. Believe it or not, this tuning method involves the rational powers of the number two. That’s right: folded chose number two . So if you thought you were studying rational exponents for nothing in algebra class, here is one example of where such a debate is used in real life

Route equal temperament tuning works as follows :. Each note through its octave has a frequency multiplier repeated twelfth root of two to get to the next higher note. That is, if we start with the traditional note, which vibrates at 440 Hertz, let’s say, getting to # 440 multiplied this by 2 ^ (1/12). Because the twelfth root of two is equal to 1.05946 to five decimal places, A # was tuned to 440 * 1.05946 or 464.18 Hertz. And so continues tuning with the next Note B by taking 2 ^ (2/12) * 440. Note that with the increase of twelfth power 2 by 1 every time the power 2 of 1 / 12, 2/12, 3/12, etc.

What is nice about this process is exactness, unlike inexactness of Pythagorean intonation method discussed earlier. Thus when we arrived at the octave note, almost on top of the standard A, which should vibrate twice the original frequency of 440 Hertz A, we get A octave = 440 * 2 ^ (12/12) 440 * 2 = 880 Hertz, as it should be — exactly. As we noted earlier, when the set of the Pythagorean method, this does not happen because of repeated use rate 3/2, and the accommodation must be made to bring into line the inexactness of this approach. These great cause noticeable dissonance between certain notes in certain keys.

This tuning exercise shows that math and music are closely intertwined, and indeed it can be said that these two disciplines are inseparable. Music truly is mathematics and mathematics is well, yes music. Since many people think of musical talent coming from “ creative” species and math capabilities come from “ nerdy ” or non-creative types, this article is in some part help disabuse these same people of this idea. Yet the question is: If two ostensibly different fields like music and mathematics are happily married, how many other areas out there that at first seem to have nothing to do with mathematics, are just as intricately linked to this most fascinating material. Consider that for a while.

If you really want to increase your odds of winning the lottery then you need to do two things. First, you can increase your chances of winning by working with law probability. To do this is relatively easy. You can also play more lottery numbers than you would normally. Using a mathematical system that you can take more numbers than usual and make sure they all end up together on the target.

Let’s look at how you can play more lottery number combinations in the lottery without having to spend a fortune to do it. Play more numbers than normal on the lottery and mix them so that you have all the possible combinations is called “wheeling.

Lottery Wheeling is a method you can choose more numbers than you normally would with a standard ticket. For example, 6 of 49 tie (like the UK lottery) you do not pick 6 numbers than a 7, 8, 9, or any amount you can afford to play.

You create the combination of these numbers so that every possible combination is on target. You’re there with a better chance of winning the prize. If you select the 6 winning numbers in the combination of numbers then you will definitely win the jackpot prize. Therefore, you have a better chance to select 6 winners because you’re picking more figures. However, it also means you win more prizes when you do the math winning numbers because they tend to fit in some of the target.

When the wheel numbers that you will be ready to buy more tickets. While you will be required to buy more tickets it is well worth the investment especially if you play the part of the coalition. For a measly £ 28 you can increase the number of bikes on the UK National Lottery and bring your odds of winning the jackpot prize down from 14 million to 1 only half a million to 1! The odds of winning smaller prizes are incredibly high.

Even though you greatly increases the chances of winning the top prize by using WHEELING system this is not their primary purpose. When using Wheeling with lottery numbers to ensure you win many smaller prizes when you select just a few of the winning lottery balls.

When you add Wheeling system to other systems designed to work with the laws of probability you increase your chances to win even more – sometimes amazing

Although there are very sophisticated methods to manipulating the law likely the easiest one for you to use now is to choose the lottery hot number. Hot numbers are the numbers that appear in the lottery more than usual. These numbers come up in the lottery draws much more to the rest and they can usually be found under the “hot numbers” on the lottery Web site or by searching the internet.

There are better lottery systems that have been designed to give you amazing chances to win, but now you can use Wheeling and likely to increase your chances.

If you are studying for the math part of the incoming Armed Services website vocational Aptitude Battery, or ASVAB test, you will probably face many calculations at first glance seem to require either a calculator (which is not allowed) or long handwritten form calculations to get the answer. My goal is to show you not only how to simplify the mathematical process, but also to show you some mathematical tricks. In particular, this article will focus on multiplying numbers that end in zero

If you are facing the ASVAB style question asks you to multiply two medium or large numbers, such as 22 times 37, you can find yourself spending too much time with a pen and paper. If instead you simplify the numbers to the point where your calculations are significantly shorter, you will find that you have more time to complete both Mathematics Knowledge (MK) and numbers reasoning (MR) parts

Check out the latest problem sample exam practice you and answer choices. Look at the answer choices given. The figures provided is not so close to each other to perfectly accurate calculation is required. Instead, the numbers will be far apart that even with some rounding and evaluation answer will still be close enough to just one of the answer choices.

With the above example, instead of calculating 22 times 37 the long way we can round each number to the nearest unit 10. Since 22 is very close to 20 to round it down. And 37 is very close to 40, so we round it up.

Now we have a new example reads 20 times 40. Once again you have a chance to figure out this long way, which will still be more or you can take this one step further and actually do the math the head

How?

is not the number 20 actually just 2 times 10? And is not the number 40 really only 4 times 10? If we think of two digit numbers that end in zero as the number times 10, we can simply get these problems requires a calculator, that does not even have a pen and paper

instead of 20 times 40 we have now trouble les 2 times 10 times 10 4 times multiplication allows us to rearrange the order of the numbers, so let’s look at this example 2 times 4 times 10 times 10

Is not everything one look so much simpler? 2 times 4 is 8, and 10 times 10 is 100 That leaves 8 times 100 is 800

Actual answer for 22 times 37 is very near 814th Since the ASVAB will not give you a choice of close to real In response, 800 will still be the closest value. Was it worth doing all that extra math for differences 14?

Many people seem to have a distorted and incorrect definition of the word “ remission ,” as it is used in conjunction with cancer patients. Most people seem to believe that going to remission means that the patient is treated and safe.

However, according to the American Cancer Society, remission of cancer is a “period when the cancer is responding to treatment or is under control. The most cancer remission , all signs and symptoms of the disease disappear … complete remission of cancer may continue for several years and considered cured. “

So, someone who goes cancer remission does not show signs of cancer. It does not matter how many cancer cells are still going strong and growing in the body of the patient, for the time it does not cause “symptoms” patient is said to be in remission.

Oddly enough, there is not much covered in advertisements for traditional cancer treatments for an extension of the length of life for the patient. And there are not many discussions about the quality of life of the patient.

These two concepts are not a factor in when talking about “ remission of cancer ” in patient.Typically speaking, cancer remission direction shrinkage in tumor size or altering some of the tumor markers. Tumor markers are substances, usually proteins, which are produced by the body in response to cancerous growth or tissues. However, much of the markers also found in non-cancerous conditions so they are not really a good diagnostic tool for cancer.

Traditional cancer therapies are successful in shrinking tumors and reducing tumor markers. For this reason, after the administration of cancer is used as an indicator of “successful” cancer.

Cancer remission does not necessarily mean the patient does not die. For example, a patient is said to have been treated for cancer if the therapies put them into remission, even if they die from pneumonia. Despite the fact that the pneumonia was only fatal cancer treatments, because cancer remission hand, it was successful treatment.

most people, no treatment that still results in death should be considered successful. But when it comes to cancer remission , that’s exactly what can happen when they pursue only traditional cancer treatment options.

Visit www.alternative-health-ebooks.com for more information and free articles. This article is available for reprint for your website and newsletter, provided that you maintain its copyright integrity and include the signature tag.

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~ S. Gudder

Actually, math State of brains get rankled and hearts seem to lose their grip on reality. Even in this seemingly senseless world, simplicity Metamorphoses from the complex; natural unfolding of irrationality and floral order from chaos. If you doubt these proposals, then observe the bizarre environment by following numerical calculations, and then see if you are still skeptical that God does in fact indwell numbers and math.

follow the symmetrical and enjoy!

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 987 65

123456 x 8 + 6 = 987 654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

And now with the number 9:

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111 111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

But the number 9 still has a magic to it. To wit:

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888 888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888 888 888

number 1 is one of the five most important numbers in mathematics. Not only is 1 of Multiplicative identity , number 1 dazzles us with some amazing multiplicative properties contained in this repunits (a repunit number consists of all 1 ‘s)

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12,321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 11111111 x = 123456787654321

111111111 x 111111111 = 12345678987654321

After witnessing this array of numbers of juveniles, it is difficult to imagine that the supreme deity was not able to control such magic. Maybe if the teachers implemented bit symmetric razzmatazz like to start a class, students could perk up and listen for a change. Then true study would have a shot at the beginning and all kinds of positive results could be achieved. After all, when God is in charge, everything else goes well. Try it out and have fun.

The Big Secret: Do not think about the problem until you write down all of the elements

Sounds too easy, right.? But that’s where all the sticks. Start by carefully reading the entire question from the beginning to the end and read important. Then go back and you can read it again, to write down only the necessary elements. Components are not just numbers, but also things like days, percent sign, pm or what will help keep it straight to you. . Also neat writing numbers below or above numbers will be added to or subtracted from the set up any part of

Write equate where it belongs

This is important; logo is like switch in our brains that we have been taught since third grade. Now the problem is what written with an equal sign instead, the light will generally go on and you will start working on the problem. From here, the only hang-ups you may encounter are things like did not trade or have to change all such factors. Even if you write down the elements wrong the first time, you’ll likely see how to re-arrange them and start

Sloppy writing is not allowed in mathematics :.

success in mathematics is subject to write all the factors neat and organized. When you come across a math word problem, the first thought that should come in the head is to take a piece of paper to write it out. As you jot it down, write neatly and leave you some space between lines.Beware: Exam writers prey on bad habits

When I create practice math word problem for free practice exams, I have to think up. three dummy answers. How do I do it? It may sound sadistic, but I try to consider what answers would come up if someone was sloppy. I think about things like if the element was left out, or if someone did equation in a hurry, or their heads. Exam writers who write for public exams do the same. After all, the test used to weed out unqualified applicants. If you want to pass the exam, actually get to write it down completely, neat and organized.

When you get a question of math word problems.

First, relax and know that all the facts are available to you to resolve it. Then take a deep breath and follow these steps: Do not try to speed up or used to shorten

Read it at least twice

writing down only the necessary elements

Add equate where it belongs

math

Need more Pharmacy Tech math practice?

For FREE help with pharmacy technician math, visit http://www.pharmacy-tech-study.com . You’ll find a complete review of the mathematical calculations including violations strength ratio, algebra, and much more.

As a teacher for 11 years and middle-school math teaching consultant, I’ve seen a wide array of differentially math programs and classes. I’m sharing here the 10 best teaching tips I’ve compiled over the years.

1. Provide compelling content to study.

Years ago, a colleague I was working with said, “Maybe class Can be fun, but I can not make compelling class. I have to Teach math!” It’s an assumption worth exploring.

Take Ron Berger’s middle-school math project to study radon levels in Their own homes. Studying radon is boring. But Berger’s class project has got to be one of the most compelling projects in math class history. What if his students discovered dangerous levels of radon in the homes of one geographic area and published the results as They had superintended? What would happen to real estate values ​​in That area? What he found is that students were highly Engaged in mapping, Taking aver ages, looking at standard deviations- students That heretofore did not care one bit about radon or the other concepts.

So what’s the trick? The trick is that there is not one. You can not trick students Into finding something compelling if it is not. Take a little bit of time to developping a few topics of study Throughout the year That you find compelling- the Economy, the Presidential Campaigns, the Human Body, etc. Find an authentic way to present your result- the paper, the web, a magazine. Keep the project small, authentic and do-CD.

Students of teachers That do take this kind of time have better outcomes on state tests than students of teachers WHO only stick to the text. Almost Any social studies context Provides a Backdrop for learning That adds depth.

Even teachers WHO hold a math “topics” class only once a month see real benefits, so you do not have to abandon your regular class. And, you’ll find That students are more Engaged When regular class is held.

If you want to go really deep and have solid support administrator, look Into the school reform movement of Expeditionary Learning Schools WHO have an excellent Thematic approach to teaching.

2. Do not use extraneous rewards Such as candy, purchase points, stickers, etc.

There is nothing more certainties than seeing the culture of a math class decline over a period of years When a teacher briber theme. The intent of the teacher, of course, is good. A teacher cares about his or military students and wants the very best for themself. “I do not care how They Learn math,” one teacher said to me. “I just want Them to Learn it so thatthey are prepared.” The teacher Cared enough to purchase candy out of her own pocket, but the real message to students is this: the “positive reinforcement” of candy means “math is not worth doing on its own.” The research is clear on the matter too, and shows us That extrinsic, non-Related rewards hurt learning.

Even if the effects are not immediate, over time so called “positive reinforcements” Like These mentioned above Erode Otherwise an high-quality math program. As a teacher, you are much better off Trying to createTextNode inherently compelling curriculum than buying candy.

3. Build a culture where students Teach eachother.

For Many teachers, one student helping another is called cheating. But I found That Actually the better middle-school math programs all Encouraged students to team together at times certainties Throughout the week. The activities were usually Graded as complete or not-complete, and When tied to meaningful Tasks, such as building a survey together and collecting original data, student comprehension was greater than on individual Tasks.

Building the kind of culture That works for student pairs or groups takes years and lots of practice. But before you give up and Decide it does not work, determiner if you are Following tips # 1 and # 2 first.

4. Give less, but more meaningful work, Including homework.

The Trends in International Mathematics and Science Study labels the curriculum in the United States as “a mile wide and an inch deep.” Their review of math texts in middle-school found That some were almost 700 pages long. With heavy pressure to Teach to the standards, as a teacher you might be Tempted to skip and jump to Many topics Throughout the text. Do not. It ACHIEVE little learning.

Choose the most Important pieces Before the beginning of the year, and keep it simple. Teach the concepts you do Teach with depth.

The national advisory Counsel is formed from the study recommended “put first things first” and Suggested That indeed, less is more. Take the time to cull the curriculum to a manageable size for your students, and present themself with only that. If you have to “cover” standards, find out what standards and document When you indeed Teach Them in class. You’ll find That teaching with Oftel depth reaches to a broad array of standards.

It’s helpful to know what’s driving the breadth. As the national study panel concurs, publishers are Trying to meet Demands of Hundreds Of Different districts by Including everything That Any school might want. And while publishers have been attempting custom publishing, it is just as Difficult to Create a math curriculum for a small district as a large one. Thus, the challenges of book publishing lead to a single, uniformly created overarching textbook. Oftel this is a very large text or an entireties series.

In the classroom, teachers and students become overwhelmed and seems to handle the scope or breadth of learning in this form. As teachers, we have to recognize That predominantly negative emotions surround math in middle-school, and anything That we Can Reduce Those emotions will go a long way toward gains in learning learning. Placing a 500 page text in front of a 7th grade student is Unlikely to help, so use it sparingly and build little, home-made notebooks for daily use.

5. Model thinking, not solutions or answers.

Do not show a student how to Solve something. Instead, “Think Aloud”. For example, you might have a whiteboard with a problem up, and start by saying, “ok, I notice That the 4 numbers I am to some are all in the thousands category, and That the first is near 3,000, the second near 5,000 , and the third … I am confused about … “Model exactly what you thinking Including confusion, emotions, skills, Strategies and more.

When you do this, also let your students know how mathematician think . One piece of research That is helpful to know is that mathematician spend a long time thinking about how to set up a problem, a little bit of time doing the problem, and a long time “looking back” by asking the question, “Does this make sense? ‘ Model That for your students, by Putting up a complex problem on the board and spending time not just jumping Into a solution, but just talking about what Strategies you might use to Solve the problem.

6. Provide feedback That is immediate, Related to the task, non-comparative, and leads the way to next steps.

Many teachers believe That grading is a form of feedback. It is not. Grading, When done well, Can Be a form of assessment of learning, but the distinction shouldnt be clear. Grades are not an Effective tool as assessment for learning. Grades are the end of the road, When You assessable what has been learned, but They should not be superintended to inform a student where to go next.

Take, for example, three groups of students WHO received differentially kind of “feedback” on math papers They had “turned in.” The first group received only narrative feedback (no score) informing themself where and how They made mistakes. The second group received a grade (or score) and narrative feedback. The third group received just a grade. Not surprisingly, the students received WHO narrative feedback improved When re-Tested. Those WHO had received only a grade did not have the information to Improve, and Performed the joint When re-Tested. But here is the surprising part. There was no difference between “grade-only” group and the group That received the grade and narrative feedback. Why? The students received WHO Both a grade and narrative feedback completely ignored the written suggestions and only Looked at the score. “I got a blah, blah, blah … what did you do?”

Because we live in a world where Grades and formalized Assessments are so Important, work with the system by differentiating assessment for learning and assessment of learning.

When you are grading, one guide is to reference Rick Level Gins Strategies of assessment for learning. That way, When you are conducting an assessment of learning (ie grading), you’ll notice That you are momentarily stepping out of the role of Improving a student’s learning and will not have the conflict of Trying to do two things at once.

7. Change mimeographed sheets to problems you and your students Personally developable.

A pervasive aspect of our culture is to give out page after page of information. In faculty meetings, business meetings and Conferences, Hundreds of pages of documents are handed out. It Makes us look organized and prepared. It’s also a way to “cover” content. But for a middle-school math student, it also Makes it hard to determiner what is Important. Was it the fractions part? Was it the decimals section? Was it the number line? Was it the triangle puzzle problem? Was it the cartoon?

Instead of another mimeographed page, have your student write Their own story problems. Tell them to add artwork for comprehension. Give Them the Latitude to make themself fun. Celebrate Them by posting themself in class. Give Them 5 home-made story problems They createTextNode for homework Instead of a mimeographed sheet with 30 problems, and really Dive Into Improving themself through revision.

8. Use story to Teach math.

Write a story, a real story with Characters and plot, and add the math problem set. Write about wizards That need to use angles they began Sorcery. Write about spice trading ships on the deep seas. Write a story That Last a whole page Before Even getting to the math portion. You’ve Engaged the right-side, or less analytical, part of the brain and you’ll see a powerfulness effect of enhanced engagement.

9. Get math tutor volunteers once a week for two-months beforehand state testing.

As a teacher or administrator, spend time during the fall months by planning for and Scheduling a single day Each week during the months of February and March (right testing beforehand) to have volunteers come in to Teach math in small groups. But what’s nice is that if Developed correctly, These volunteers do not need to have special training in Any math.

Start with a simple plan. Each student has 10 skills They have chosen to work on during the whole class tutoring session and have written down Their practice problems in class. The phone calls are made, the specific planning with an administrator is done, and volunteers come in and help the students answer the 10 questions during class with support. Schedule tutoring once the every week for two months beforehand testing and see your scores greatly Improve.

10. Work with the emotions your students have for math.

10a. Ask your students how They feel about math. Use a bit of class time periodic ally to gain a better sense of where They are. And, just let themself feel how They feel. If They like math, They like it. If They are bored, empathize. If your students can not stand math, Will you gain far more ground by seeing Their perspective than Trying to prove They are wrong. As a teacher this is hard Because we are so accustomed to Trying to “fix” the situation, and of course, our ego is tied to student emotion. If our students are bored, we feel like we are not doing the right thing. But the larger truth is that there is an ebb and flow in all of us for the topics we are learning. When the boredom, frustration and negativity does emerge, try understanding it. Perhaps class does feel a little boring. That’s o.k. Sometimes it Will. And then slowly, over a period of years, build Those compelling pieces Into your classes so That you punctuate boring times with excitement and joy.

10b. Go slowly. Changing the direction of your math class is like Trying to change the direction of a large ship, especially When dealing with emotions. Even once everything is place for the changes to occur, you Will notice the “ship’s” momentum going in the Same Old direction before you sense Any real Shifts. This is part of the process. It took me three years to developping a Coherent math program at my middle-school and Even then, we occasionally slipped in to old Patterns. Good luck!

Probably the most important fundamental branch of mathematics is algebra. No matter what anyone tells you folks, if your kid is not good at algebra, there is no shot he will excel in any of the above sectors. In fact, the famous calculus is actually a form of “glorified” algebra and this is what I used to tell my college students all the time. Therefore, if you want your kids to have the opportunity to learn and enter the beautiful intellectual domain calculus, then be sure they have the tools to learn algebra.

Algebra is a branch of mathematics that deals with solving equations with letters to represent unknown quantities. The difficulty with algebra is that for most students in the many letters and symbols created abstract that it is difficult to see through clearly. After all, when you see a bunch of X and Y and other expression that includes a number of mathematical symbols, footing can quickly be lost and your head might start reeling off track. To fend off this experience, which I call “algebra syndrome,” students being taught algebra in a way that removes unnecessary abstraction and paves a clear-cut way through the fog of confusion.

If students are shown ways to deal with the inevitable abstraction in algebra, you learn quickly to correct them, and are not intimidated when they encounter expression or problems they have never seen before. By learning some tricks or short cuts, students gain confidence and are better equipped to take on the challenges that algebra will always be present. In one of my ebooks, I talk about some new ways of handling and solving equations with “light switch property.” Another shortcut I teach to solve equations is called “bridge toll process.” By giving meaningful names to abstract methods, the teacher lets students visualize the procedure and think about it in a way that makes it more concrete. After a lot of abstraction is removed, students get algebra skills in a short span of time.

Most people believe that Albert Einstein won the Nobel Prize for his famous work on the theory of relativity. But he actually received the award for his discovery of the laws of the photo electric effect.

discovery Einstein

Einstein won a Nobel in physics in 1921. Photo electric effect is a phenomenon in metals emit electrons from their surface when the light shines on them. Einstein explained this phenomenon as follows:

– Light consists of small particles called photons. They carry energy in proportion to the frequency of the light. – When light shines on the metal, electrons absorb energy from photons and they get rejected due to the energy difference. This causes the electrons to flow.

discovery led Einstein to understand that light behaves as both a particle and a wave.

Applications

Detecting photo electric effect led to the development of solar cells, now useful as an alternate source of energy for us. Similarly photo diodes are other programs that find wide use in light detection in the field of fiber optic, telecommunications and other fields.

World year of physics

1905 delegates. a very important year in physics with four groundbreaking works by Albert Einstein in that year

These four publications are:

1) the photo electric effect

2) Brownian motion

3) Special Relativity

4) The famous mass and energy equation E = MC2

These publications especially special theory of relativity completely changed physics in recent years. Mass and energy equation led to the development of the atomic bomb as well as constructive nuclear energy. Highlighting the importance of 1905 as an important milestone in physics, 2005, it was recognized as the world year of physics at the occasion of the 100th anniversary of Einstein’s writings.

subsequent years

In later years, Einstein also added another publication ‘general theory of relativity “and won the unified field theory of his. The general theory of relativity was not accepted by many at the time that he published in 1915. The terms and calculations behind the theories were quite complex and it was not understood by many. He suggested that his calculations can be verified at a solar eclipse. After several years, the eclipse, observations were reported that proved his theory right. This made him even more famous.

mass energy Einstein’s equation was used to develop an atom bomb. Einstein was not involved in making the bomb. He spoke against the war and continued to use the technology peace until his death in 1955.

Most mathematical concepts we encounter every day – numbers, addition, subtraction – seems so basic, so hard to avoid discussing reality on even the most basic level, it is hard to imagine someone having to sit down and find them. Who was the first person to look at the two rocks and think, “Two more and I’ve got four?” The very idea seems almost absurd

But mathematics is, in part, language -. Do not just put a logical connection and entailments that seems deeper than words, but a set of symbols that allow us to discover those relationships. You can not see it twice two makes four, until you sign for the “two” of the brain can operate. And they sign – the language – did develop, strange as it may seem. (Prehistoric artifacts seem to indicate that in the first place had only four “numbers” at “No”, “one”, “two” and “many” – shows just how much our ability to talk about numbers depends on to have the right words for them.)

We do not know which culture was the first to develop a number of systems elaborate than “One, two, a lot!” A 20,000-year-old bone found near the Nile seems to show a series of prime numbers – which would indicate a fairly sophisticated mathematical knowledge from fairly early. Then the Harappan civilization of the Indus Valley in present day northern India and Pakistan. As far as we know, these people were the first to use decimals, among many other important concepts.

Archaeology also seems to find evidence of a sophisticated numbering of the Shang Dynasty in China, 1,600 years before Christ. Archaeologists often turn up new discoveries off the history of human knowledge – so it’s hard to say who was the first to develop this or that idea with certainty

But many mathematical ideas -. Like many other things – starting with the Sumerians. This culture – considered by some historians the cradle of civilization – flourished near the present-day Iraq between three and five thousand years ago, and in addition, provide the first known works of world literature (still-moving story of Gilgamesh), they developed a numerical system based on sixes. If you’ve ever wondered why the hour has sixty minutes, minute sixty seconds – after all, it would be much simpler if everything went 100 (such as the basic unit of our time was 100 smaller units, rather than sixty seconds, sixty minutes) – it is partly due to the lingering effects of Sumerian. As the culture of Sumer fell, it was absorbed into the Babylonian Empire, which also seems to have produced a mathematical way of thinking, if a handful of Babylonian mathematics writing yet to us provides suggested.

Babylonians, Egyptians and ancient Indians all seem to share at least one important discovery – the so-called Pythagorean theorem, the rule has to do with how to calculate the length of the sides of certain types of triangles. (Clearly, this discovery was of use to the culture that built the Pyramids.) The fact that this phrase was common to all three major ancient cultures suggests the traffic they may have had with each other, although some historians’ proposal that each culture was mainly closed off to other places. And the fact that we know the statement that the Pythagorean theorem – after the much later Greek mathematician and philosopher Pythagoras – shows the well-known, and often criticized the tendency of many historians to want to give the ancient Greeks credit for everything.

not that the Greeks did not understand enough. Greek mathematics grew up with Greek philosophy and Greek science – indeed, three subjects were not really understand; for the ancient Greeks, all branches of knowledge was one. Thales, for example – you will often found quoting the first Western philosopher – use geometry to calculate the height of the pyramids, among other things. In any case, the Greek thinkers began in the art of mathematics to a new level of sophistication. Euclid wrote a geometry textbook so percipient be useful today, Aristotle defined the laws of logic, and Archimedes still near the top of some mathematical historians – all-time greats list. Fixed link between mathematics and philosophy in Greek is well described by the inscription on the door of Plato Academy “. Let no one ignorant of geometry enter here”