Archive for the ‘Math tools’ Category

Famous Mathematical Theorems

For most famous mathematical theorems there already exists some published evidence – not so with Fermat’s, this type of theorem proof isn’t yet offered. Bayes’ theorem might be best understood via an example. Fermat’s theorem proved to be a mathematical statement. Use Pythagorean theorem to discover the hypotenuse.



The end result will be an enormous paradox that will show the theorem. There are specific sets of numbers which have a very special property regarding the Pythagorean Theorem. Clicking on the bigger equation will ensure it is understood straight away. A certifier is a far simpler tool when compared to a theorem prover.     If you struggle with any of these problems, there are some useful educational resources online – the BBC website has a lot of maths educational programmes some of which were linked with the Open University.  You can use this tool demonstrating how to watch TMS abroad to hide your location if required (BBC pages are not always available outside the UK).

The Pythagorean equation and also the cubic equation may be visualised in a couple dimensions. NUMBER theory is among the most abstruse elements of mathematics. Fermat’s last theorem was that a sure equation, under certain conditions, had no potential solution. Fermat’s last theorem is among the most famous mathematical puzzles ever posed.

Let’s take a glance at a fast example that uses Rolle’s Theorem. Fermat’s theorem is helpful as it suggests a way of finding local extrema. `We knew that Taniyama’s conjecture needed to be correct,’ he said. Let’s now have a look at two or three examples utilizing the Mean Value Theorem.

This theorem is known as as the bottom of the Fermat’s primality test. It’s therefore safe to say that Fermat is among the most critical figures in the creation of calculus. Compute the series of solutions for each.

Definitely, if one could actually locate a solution for some group of numbers, that will disprove the theorem and solve the issue. And So, the function doesn’t have an absolute maximum. While mathematics is absolutely not for everybody, the field’s practical use cannot really be contested. Essencially, it states the integral of the function is practically not possible to find.

It was shown within the proof the reason Eq. Despite the fact that the general problem isn’t computable, many specific instances are easily solved. A proof that’s unfinished is no proof whatsoever,” Dr. Ribet explained. There’s an overall proof by way of the Taniyama-Shimura theorem however it’s subject to specific conditions.

Fermat proves the area of the appropriate triangle cannot be a square. It seemed the solutions for any one of many infinite variety of elliptic curves could possibly be derived from among the infinite variety of modular forms. Here is an instance of adjacent, supplementary angles which work together to build a linear pair. This is really a remarkably popular region of active research at present, along with a number of the experts are tough at work attempting to prove generalizations.

Unlike a modern mathematician, who’ll publish her or his work at each opportunity, Fermat did not publish his work. Ever elusive, Dr. Wiles reported that was one thing he’d never reveal. The competitive type of mathematics of his own time was extremely much to state outcome and challenge others to prove them, as opposed to spreading wisdom. Have a guess based on your own intuition.

Therefore Fermat triples usually do not exist. As a good number of primes within the root number goes up, a good number of factors increases rapidly. There are really an infinite variety of Pythogorean triples.

Further Reading


Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Poisson Distribution and Probability

Inside this sense, lambda within the Poisson distribution is the exact same lambda within the corresponding exponential distribution. It is one of the important topics of statistics. The Poisson distribution relies on four assumptions. It is also sometimes referred to as the distribution of rare events.

There are four conditions it is possible to check to see whether your data will possibly arise from a Poisson distribution. Additionally, There are some empirical means of checking for a Poisson distribution. This distribution is known as normal since the majority of the all-natural phenomena follow the normal distribution. The exponential distribution subsequently is really an instance of the gamma distribution.



The Poisson Distribution can be a discrete distribution. Also enter 1 for an entire distribution.

Poisson’s father decided the medical profession would give a safe future because of his son. Few people may have achieved academic success as fast as Poisson did. Ergo, the Poisson distribution is more affordable to use because the amount of accidents is regularly recorded by the authorities department, while the total variety of drivers is not. It can be used to calculate the probabilities of various numbers of successes” based on the mean number of successes.  So for example if you wanted to calculate both the distribution and probability of an event, such as a VPN blocking algorithm you could introduce a known constant perhaps if you’re in Dublin the fact that you would have an Irish IP address for example.

As an example, the standard 2-dimensional Poisson Cluster Process (PCP) is somewhat like an easy 2-D Poisson process since it starts with a random point collection. The complexity is far higher than the example of gamma-Poisson modeling. The conventional normal distribution is commonly used in hypothesis testing.

This only means that if we need to model the amount of discrete occurrences which take place during a given length, we have to first check whether the Poisson distribution gives a fantastic approximation. These resulting distributions have several different shapes which are determined by the kind of process which is being modeled. Poisson distribution may be used for various events in other stated periods like volume, area or space. The Poisson distribution might be used within the design of experiments for example scattering experiments where a small variety of events are seen.

It is often true for medical data the histogram of the continuous variable obtained from an individual measurement on various subjects will get a characteristic `bell-shaped’ distribution known as a Normal distribution. The normal distribution has a lot of features which make it popular. This might explain the overwhelming dependence on the standard distribution in practice, notwithstanding how most data usually do not meet the criteria required for the distribution to fit. Also an assumption is created that every sample follows a standard distribution curve despite the tiny sample size.

A fundamental knowledge of the binomial distribution is useful, but not needed. The binomial may be the acceptable distribution for bit-changes via an invertible substitution table or cipher.  It’s used online in lots of situation from powering search algorithms and even as a method that Netflix blocking proxies with.

Log linear regression doesn’t handle that issue, either. In such problems, we’ve frequently emphasized that Poisson conditions are frequently not met. 1 example of the natural phenomenon which can be modeled employing a Poisson distribution is radioactive decay. In reality, negative binomial regression did about too as Poisson regression.

As the function is just defined by one variable, maybe it doesn’t be surprising to get the standard deviation is, in addition, about the mean. In the geometric distribution, the conventional deviation was often near the mean. First figure out the mean.

Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Using Triangles in Trigonometry

There are just three primary functions in trigonometry and they’re called sin, cos, and tan. In regards to trigonometry, you’ll have to know how to solve trigonometric equations. Think about trigonometry for a toolbox. Now for both of the other trig functions.   The tangent could be the last of the 3 principal trigonometric functions. The height of the triangle are available via an application of trigonometry. This is accomplished by using basic trigonometry and of course using triangles.



In this composition, we’ll be continue discussing triangles. This definitely is an absolute spoiler, however, since it will provide you with the true WGS84 co-ordinates for both caches. Many troubles that handle right triangles yield decimal answers.

Thus the sides which make the equal angles will soon be proportional. Sometimes, a may be the identical length as b. All ideal triangles have a lengthiest side that is certainly directly across from the best angle. With time, however, trigonometry was adapted so the angles don’t necessarily represent angles in a triangle. An angle significantly less than one-forth of the circle 8.

We are almost prepared to explain what SOHCAHTOA actually represents, but there’s one point I need to stress that’s missed by the majority of Geometry students. Geometry is, in addition, near trigonometry along with the areas you must focus on include problems involving circles. Games and activities to allow you to learn trigonometry. You need to arrive in the drawing and also the formula shown here.  There are some useful programmes online which explain the more advanced functions of trigonometry, unfortunately some of these are region locked so you may have to change your IP address using a residential VPN service.

So, if you discover a basic Pythagorean Triplet, you can multiply all 3 sides by exactly the same number, and you’ll find another proper angled triangle with 3 entire number sides, along with the exact 3 internal angles as before. The real key to solving the of the correct angled triangle, would be to do as I’ve done here, which is to ensure the proper angle is at among the bottom corners. The most suitable angle triangles may also be of two sorts. An angle with its vertex in the center of the circle 14.

Insert within the diagram every one of the things you’re given. Listed below are the values shown within the diagram in addition to another frequent group of values for this particular triangle. The initial step is always to draw a diagram. Draw this suitable angle into the diagram.

Cache 2 was also put in a hole in the base of the tree. Speed, distance and time could be calculated utilizing a magic triangle. This box just includes a Zip-Loc bag which then contains quite a few envelopes. Place a stick figure in the angle for a point of reference.

The fundamental right triangle rule may be the Pythagorean theorem. In Euclidean geometry, any 3 non-collinear points determine a distinctive triangle plus an exceptional plane. This value may be found utilizing the Pythagorean theorem.

The 3 medians intersect within a point, the triangle’s centroid. The 2 pots aren’t the exact same distance from both reference points but they’re very close, just a few meters away. The 3 altitudes intersect in one point, known as the orthocenter of the triangle. This last example has a Cos value supplied, but it’s for the very best angle within the Triangle.

There are still formulae for finding the 3 entire number sides of the appropriate angled triangle. Hipparchus developed what’s known as the very first trigonometric table. Each one of the above combinations represent the 3 lengths of the proper triangle.

Further Reading

John Harris, Online IP changer, Haber Press:2015

Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Time to Change How We Teach Mathematics

There is often a presumption that some people can ‘do maths’ and others simply can’t. The idea that many people are destined to fail in maths whatever their intentions, is rather an outdated belief but amazingly one that is often prevalent in mainstream schools.


There is of course no doubt that some pupils are able to learn maths much more easily than others, but many academics are beginning to believe that this is more to do with how they are taught than any intrinsic mathematical ability.  Could  it be that our maths teaching methods are actually to blame in why some people feel left out of mathematical knowledge?

One academic from Stanford believes that there is a big problem in how pupils in most of the world are taught maths.     One of the issue that Jo Boaler highlights is that many children simply believe that mathematics is a subject where the answers are either right or wrong.  This is perhaps because the school classroom environment focuses on coming up with ‘right’ answers quickly rather than truly understanding the subject.

She suggests in her book Mathematical Mindsets that there should be much less focus on testing in maths, less worrying about failure and a much wider use of visual representation and manipulatives.  These manipulatives are items which can be used to explain concepts that can be handled like blocks, cubes and shapes, best used in group work.

There is definitely an idea that in maths, there is only right or wrong, success and failure as opposed to other subjects which have a much more widespread definitions.  There is also a significant perception that maths success doesn’t need hard work – if you are a mathematically minded individually everything will come very easily.

The concept works towards a growth mindset which encourages children to believe that they are all capable of achieving anything and it is not a talent that you are simply born with.   Many educators are now buying into this vision and changing the way they teach maths including using video presentations using products like Content Samurai.

The Professor’s ideas are often controversial, even recently she complained that schools should ban the learn by rote of times tables.  The focus she says was wrong and that the goal of maths education should be greater than simply learning these by memory.  These views were not popular and many teachers pointed out that actually times tables were extremely important and should be viewed at the very least an educational entitlement.

For Further reference

Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Mathematicians Find Perfect Shape

There is often a criticism leveled at mathematicians that much of their work has limited real world applications.   Mathematicians can often spend years pondering complex equations and defining complicated proofs to see their work greeted with a sigh of ‘so what’ from their non-mathematician colleagues.

However the latest discover in the realm of geometry will actually have a host of real-life applications which could affect all of us.  The discovery is that of a pentagon which can actually completely tile a floor without overlapping or leaving any gaps.



It’s the result of work by three Washington based maths researchers working together in a field often referred to as ’tiling the plane’, this discovery is only the 15th type of non-regular pentagon which has ever been discovered.  The news has caused great excitement in the maths world, one colleague described it as the equivalence of discovering a new atomic particle for physicists.

The scientists responsible include Professor Casey Mann, his wife Jennifer Mcloud-Mann and an undergraduate researcher David Von Derau.  There are more details on their websites and on the Washington University site although you may need an American IP address to access.

So why a Pentagon?

While a  triangle and square can be arranged to tile in virtually limitless sizes and structures.  It has been proven mathematically that any irregular convex, polygon which has more than six sides  cannot.  This has led to the challenge of creating non traditional pentagons to be used in tiling, a difficult and complex task.  It was nearly a hundred years ago in 1918 that a German mathematician discovered that you can in fact use pentagons to tile.  Not many have been discovered so far though, a San Diego housewife discovered five of them and this is only the 15th and the first one for over thirty years.

These particular mathematicians specialize in this area of tiling and knot theory (an equally practical related area).  They did however begin to doubt that any other shapes could be found, computer models were used to research possibilities which were then investigated by the mathematicians themselves.

Further Reading:

Proxy Unblocker –




Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

UK Firms Need Migrant Math Skills

Maths has never been one of the trendy subjects to be studied in further education. For a variety of reasons, it’s often perceived as difficult with limited direct links to good employment opportunities. This unfortunately is highly misleading as maths is in huge demand among employers in all sorts of areas. So much so that Uk firms say that there is a genuine shortage of maths skills and they are having to rely on UK migrants rather than employ British candidates.


A recent report has said that there is an urgent need to improve ‘post 16’ maths skills in British students. Particularly in areas which require statistical and quantitative skills (QS), there is a shortage of people with the relevant skills. Maths is often seen as a subject to be studied up until 16 and then switched in preference to other subjects. The report calls for the UK Government to encourage more students to study maths at a higher level in order to keep up with other countries like the US for example.

In the UK, many of the top UK QS jobs are filled with people who were born outside the United Kingdom. In fact two thirds of those covered in the survey, had arrived in the UK over the last ten years. This situation differed from most other employment sectors which suggest there is a specific problem attracting UK candidates with the requisite skills.

The opportunities for the economy to tap into the ‘big data’ revolution are increasing every year, yet without a supply of skilled maths graduates then the UK could start falling behind. The potential needs to be highlighted particularly to students who are considering options for advanced study.

The challenges for the UK education sector to meet that demand are evident, however the rewards are also there too. There is a report on the BBC News Online education sector site, see this to access from the Centre for Economic and Business Research Unit who suggest that nearly 60,000 new jobs which require specific mathematics skills will be created up until 2017.

Dame Jil Matheson, chair of the British Academy project, said: “For our ambition to be fully realised within a generation, we must not underestimate the cultural change that is required – starting now – primarily, but not entirely, with the UK’s education systems.”

Further Reading:

BBC Australia – Source


Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Maths Pioneer Remembered – University College Cork

George Boole was a remarkable man, who was born 200 years ago and became the first professor of Mathematics at Queen’s College, Cork.  He is being honoured over the year with a series of events and readings designed to mark the anniversary of his birth.


George Boole was definitely born in the wrong time, in the wrong location and without all the benefits of class that many of his contemporaries enjoyed.  There was little chance of him climbing the ladder of mathematics, but he managed it anyway.  He was born in Lincoln at that time at the heart of the industrial revolution.  His first piece of real luck was to have a father who had a love of maths which he passed on to his children.

His father was soon outstripped in his maths skills though and by 8 years old, was in need of more advanced help.  A family friend helped take over some tutoring and took him through basic latin, but by 12 years old the friend was also overtaken.  By 14 years old, George was fluent in German. Italian and French, by 16 years old he became an assistant teacher.  Four years later, still aged  only 20 he had opened his own school.

At this time he started to take mathematics very seriously, studying all the most revered texts of the day.  From Isaac Newton to Laplace and Joseph Lagrange, he studied and mastered all the techniques and the latest techniques.  It was then he started to push the boundaries, and by 24 he published his first paper – Research on the Theory of Analytical Transformations.  Some of these papers were covered in the Maths festival  programmes that were covered on the ITV recently, it may be able to catch up with them on ITV player though – here’s how.

By 1844 he was concentrating on the uses of joined algebra and calculus to process big figures and infinitely little, and, in the exact same year, received a Royal Society medal for his contributions to evaluation.

Boole shortly started to see the chances for using his algebra. Boole’s 1847 work, ‘The Mathematical Analysis of Logic’ enlarged on Gottfried Leibniz’ earlier conjectures on the correlation between math and logic, but claimed that logic was primarily a subject of mathematics, rather than philosophy.

It was this newspaper that gained him, not only the admiration of the eminent logician Augustus de Morgan (a mentor of Ada Byron’s), and also a position on the faculty of Ireland’s Queen’s College.


James Hemmings


Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Students Enjoy Vedic Mathematics

It takes 11-year old Aditya Ray only seconds to multiply a five-digit number using a four-digit one, thanks to Vedic mathematics, which he claims makes it quicker and accurate. By traditional method, he would have significantly more than a minute to get the answer.

“It takes me around one plus a half minutes to multiply such large numbers utilizing the conventional technique. However, if I take the Vedic maths course, I could solve it in 30 seconds,” the Class 6 student explained.


The Kolkata-based Ray added that while his school anticipates him to solve problems using the traditional manner, he at times uses Vedic maths.

Discovered by Hindu seer Swami Bharati Krishna Tirthaji in the early 20th century, additionally it is said to not be difficult to consider, creates inquisitiveness, offers multiple ways of doing precisely the same computation and improves analytic thinking.

According to the School of Vedic Maths (SOVM), Tirthaji was born in Tirunelveli in Tamil Nadu in 1884. After finishing his Master of Arts he was a faculty principal. The college principal quit that to embrace a religious path. It was during deep meditation that he got inner revelations on the 16 sutras from the appendix of Atharva Veda, one of the four vedas, the primeval Indian scholastic and religious texts.

Tirthaji declared that any mathematical problem can be solved using them.
Gaurav Tekriwal, president of the Vedic Math Forum India, said Vedic maths was a collection of techniques to calculate faster when compared to the traditional systems.
“With just a little practice in Vedic maths one can make routine computations easier, simpler and quicker so much so that you can call it ‘World’s Fastest Mental Maths System’. It’s applications mainly in arithmetic and algebra and therefore is a favorite of competitive exam aspirants who wish to handle maximum problems in less time,” Tekriwal told IANS.

On-line courses spread over 30 hours for pupils and 40 hours for teachers are held by the Forum. The classes are one on one.

Pradeep Kumar, founder director of Magical Methods, which supplies training shared that using such calculations, choosing the square of any number ending with five becomes incredibly simple.

“Say you are looking for square of 85. You multiply 5 by 5 and set 25 as your right part of the solution. Then, multiply 8 and set 72 as your left element of the solution. Your answer is 7,225,” he said, including the same formula can be used to locate square of any number ending with five.

The division is slowly gaining popularity among students “because it’s quite useful, especially for anyone planning to consider competitive examinations”, Kumar said.

“Nowadays, there is a large number of competitive exams. Speed is really one of the factors that are key to crack any assessment which tests numeric ability. Vedic maths is an excellent instrument.

Nair added that from a teacher’s perspective, it gives “tremendous possibilities to research learning mathematics from many positions as well as in innovative ways”.

“It has little importance. We might as well forget it. Though it may have a few useful bits, the aura around it makes it very damaging on the whole,” Dani told IANS over email.

Retired 85-year-old teacher and educationist Dinanath Batra, who got American scholar is batting for the debut of Vedic maths in universities and schools.

Those people who have profited from Vedic Maths and want it introduced in the schooling system favour it. Teachers of conventional mathematics and school principals we  spoke to agreed that it should be formally introduced.  It was interesting to see that there were examples on the internet, including in Japan and accessible using a Russian proxy – in schools in Moscow.

“There is no damage in introducing it in the primary level in schools, at least some parts of it. It’ll only make the pupils’ base stronger. It has been seen that pupils take interest when new techniques are taught,” Rekha Dwivedi, a mathematics teacher at a government school in Dwarka in Delhi.

She added that teachers ought to be first trained.

Agreed Nair, who said that introducing Vedic maths will be good notably in Courses 6 to 9, “but with no suitable pedagogy in teaching and appropriate training to teachers, it mightn’t be quite powerful.”
In fact, vedic maths got the attention of Japan over a decade ago and it could establish an international occurrence like the Chinese abacus if channelized properly.

Additional Information

Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Using the News to Learn Maths

Students frequently request examples they can relate to when will they make use of the math they are learning, and teachers often struggle to show real-world applications of the math they are teaching. Yet a rich source of material for both pupil and teacher is located every day: current events. The belief of Math in the News is the idea that each relevant narrative (the weather, sports, space travel, the market, etc.) can be recast as a math narrative. Let’s look with a good example.

All students go to pictures and therefore are accustomed to prices for other costs, food at the concessions, and tickets. They know there is an effective movie on the basis of the number of tickets sold as well as the amount of cash it makes. It is a topic that pupils already are interested in. You are halfway toward creating a lesson.


There are several Web sites that keep an eye on data on all films released in a given year. Start by asking students when they understand just how much cash was made in 2013 from all pictures. Write their guesses on the board. Arrange the numbers from least to greatest. From these speculations you are able to start to develop the concepts of median range, and mean of a group of data.

All of a sudden a data-gathering task has a real and private relevance for pupils.

After that you can show the students the top movies for the entire year. Ask exactly how many pupils watched every one of the 10. See whether the most notable movie was watched by more pupils. You can then break it down further – ask who watched it on ITV player or using a UK VPN perhaps.  Then ask them to think the amount of money each film brought in in ticket sales. Have students find the average of the guesses, then compare them to the specific numbers from the Web site.

You don’t have to work with only historical data. At just about any certain time of the entire year, a group is always of films about to be released, and one marquee movie which gets a great deal of promotion. Then have the particular numbers are gathered by the students once the weekend box office numbers are understood. Ask them to compare their predicted values with the actuals. And all of a sudden the mathematics has taken on real meaning for the students.

Current events offer an endless chance for mathematics-related stories. Identify the themes that interest your students. Have a day of collecting news articles, then possess the pupils find the underlying math story.

Article Citation

Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather

Adding Up Web Server Resources

There is a side to using math in a practical sense that can reveal a whole lot about the way in which this website and a whole brace of others are hosted and given the visibility that surfers need to see them. Many website owners fail to figure out for themselves just what the numbers are in regard to web hosting and that can be a mistake especially when a site is expected to receive a lot of visitor traffic.

In its simplest terms, the number of websites hosted on any given server will differ markedly from the next. If a website owner thinks about the host their site lives on at all, it might be concerning the actual number of sites inhabiting the same server.

But it is not just that basic number that the site owner needs to be aware of and concerned about. While a server may host thousands of individual websites, it is the statistical information about those sites that should be of concern and not just the raw site population.

You can take two identical servers hosting exactly one thousand sites each, but one will perform much better than the other. This is typically because the bulk of the sites that occupy one might be smaller and less resource hungry than the bulk of those occupying the other.

A typical resource hog would be the kind of site that uses a content management system (CMD) such as WordPress and that has a lot of internal pages each with lots of social interaction (comments), streaming video and large images. Such a site may not necessarily attract a lot of visitor traffic but may still use a large amount of system resource just by being there.

On the other hand, a resource friendly site would be a static html site with little or no php, javascrpt or other programmatic processing, fewer, lower resolution images and few if any video embeds. Such a site may attract rather more traffic and still use far fewer system resources than its CMS powered housemate. You can read more about webhosting at:

For the site owner that is keen to ensure their pages load quickly and enjoy the maximum amount of up time the server can provide, their primary concern should be over the mathematical statistics surrounding other sites occupying the same server as itself. If they are predominantly low resource users, you can probably be fairly sure your site will perform to its maximum potential, which is the most important statistic of all. Find more information here:

Facebooktwittergoogle_plusredditpinterestlinkedinmailby feather