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Determination of the location of a point on a plane using two real number lines that intersect each other perpendicularly at the null point, a single flat (horizontal) and the other upright (vertical). A horizontal line called the X axis (abscissa), and a vertical line called the Y axis (ordinate). Two mutually perpendicular axes is called a Cartesian coordinate system perpendicular or also called Cartesian coordinates.

figure 1

Location of point P (figure 1) is associated with two numbers, ie numbers which specify the space O to the P1 and numbers stating the distance O to P2, respectively called the abscissa ordinate points P1 and P2 point, then pair the two distances is called the coordinates of point P

 figure 2

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In figure 2 it can be said that the point P 4 and berordinat berabsis 2. Furthermore, the coordinates of point P is said to be (4, 2). Coordinate axes, namely the X and Y axis, dividing the plane into four regions, each called a quadrant, that quadrant I, quadrant II, quadrant III, and IV quadrants, such as figure 3

Figure 3

Consider two points P1 (x1, y1) and P2 (x2, y2) in the following illustration

Figure 4

Then using the Pythagorean theorem, is obtained:

Given three points P (x1, y1), Q (x2, y2), and T between P and Q with comparison

| PT |: | TQ | = m: n, as shown below

Figure 5

Consider figure 5, since | PT |: | TQ | = m: n, then | P1T1 |: | T1Q1 | = m: n, so
(xt – x1) (x2 – xt) = m: n
m (x2 – xt) = n (xt – x1)
(m + n) xt = mx2 + Nx1
xt = (mx2 + Nx1) / (m + n)

Manner as above, then obtained:
yt = (my2 + ny1) / (m + n)
From the above description, we can conclude: If the known points P (x1, y1) and Q (x2, y2), and point T on the line segment PQ such that | PT |: | TQ | = m: n, then coordinates of point T are:
xt = (mx2 + Nx1) / (m + n) and yt = (my2 + ny1) / (m + n)

If known to the points P (x1, y1) and Q (x2, y2), and point T is the midpoint of line segment PQ, then | PT |: | TQ | = 1: 1, so the coordinates of point T are:
XT = (x2 + x1) / 2 and yt = (y1 + y2) / 2

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by: Geoff Ficke

One of the greatest literary and science works of the ancient world, rarely studied today, was the Opus Majus. The amazingly futuristic content of the Opus Majus was virtually a modern tutorial, written in the 13th century, on an array of literary, scientific and philosophical topics. The writer was the eclectic, brilliant Franciscan friar, Roger Bacon.

Bacon was born to a prosperous English family in the 13th century, attended Oxford University at the age of 13 and soon commenced a career as a teacher at Britain’s most famous university. He lectured on Aristotle and a wide range of philosophical and theological topics. He became a Franciscan friar late in life and a confidant of Pope Clement IV.

His study and observations on astrology, science, alchemy and medicine were advanced for the age, controversial and dangerous. It is widely believed that he was imprisoned for his presumed heresies while in Paris. His discovery of the “visible spectrum”, obtained while viewing a sitting glass of water preceded the discovery and observations of the same by Sir Isaac Newton by some four centuries.

During a long and varied life of study, observation and experimentation Roger Bacon was both adored and pilloried. His work was often under attack from Catholic Church theologians and competitive thinkers vying to supercede his growing reputation for modern, innovative thought. Nevertheless, his writings, lectures and theorems were widely studied and many became the under pilings for more advanced scientific and practical science that would evolve in the future in a more modern world.

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If Roger Bacon has produced nothing else, the Opus Majus would have secured his legacy for all time as an innovative, exciting thinker. The work is still considered a primer for inquiring minds seeking guidance in the vast galaxy of experimental science.

For many years we have been reading and hearing that the United States is not producing enough scientists, mathematicians, engineers and technicians. We live in a technological age. These work skills are needed by any economy hoping to stay cutting edge, grow rapidly and provide better living circumstances for all. Certainly the United States requires copious quantities of such skilled workers to maintain our economical edge.

And yet, our educational system is not producing technologically advanced graduates at a rate anywhere near our industrial requirements. Managers at tech giants MicroSoft, Dell, Hewlitt-Packard and Oracle complain loudly, and publicly, that they are hamstrung by the serious decline in the ability of our educational system to train and produce enough engineers to satisfy the demands of a technologically based economy. They must seek candidates for high paying tech centered jobs from India, China and Korea; all countries where mathematics and science courses are pre-eminent in their educational curriculum.

Roger Bacon was predictive of the consequences of a lack of concentration on mathematics and sciences. The following is one of the most famous quotations from Opus Majus:

“Mathematics is the gate and key of the sciences. Neglect of mathematics works injury to all knowledge, and he who is ignorant of it cannot know the other sciences or things of this world”.

Roger Bacon was a 13th century visionary whose observations are most prescient today. The United States has lost a generation of potential talent in the scientific fields by watering down the curriculum and minimizing the importance of chemistry, calculus, algebra, physics and trigonometry. Our security, both militarily and economically is being imperiled by the lack of importance placed on these essential building blocks of scientific knowledge.

Knowledge of mathematics disciplines is color-blind. Understanding the Pythagorean Theorem is not politically correct or incorrect. It is the same proof in Zimbabwe as in Sacramento, Athens or Beijing. Roger Bacon offers a wonderful reference to one of history’s truisms: He who does not learn the mistakes of history is doomed to repeat those mistakes. Will we learn?

Continue reading »]]> Fishes are one of the most beautiful gifts of nature. They boast of beauty, grace and cheerfulness. Well coming to the point, fishes as pets makes you admire beauty with a very trouble-free handling. Maintaining fish tanks is not an ardent task as assumed by many. It is in fact one of the simplest and easiest way to have beauty and poise in your home. Maintaining your fish tank requires some tips to be noted. First of all, a bigger tank is always better depending upon your room space.

It gets cleaned properly and the fish mortality rate is also very low. As long as the fish gets more space to swim, it has a longer life. Further, the cleaning of tank and changing of water is also effortless in bigger fish tanks. Second important thing is selecting the fish breeds. The fresh water fish are easy to maintain as they can very well adapt to the environment. The fishes chosen must not harm each other.

Now, coming to one most popular myth of having fish aquariums, i.e. change the water of the fish aquarium every day. This is not right since experts’ advice that water should be changed once in a week and that too not completely. Fresh water should be added to the tank in the ratio of 70:30. Another thing is placement of the tank. Appropriate sunlight must reach the tank so that the fishes can live a healthier life. Next thing is to take care of the food for the fish which comes separately. Never over feed the fish which may even be fatal. More food means more excreta and you will need to clean the tank more often.

With these small and important tips, you can maintain a healthy fish tank. They are loved by children and adults. Their movements are so lovely and graceful that you feel at peace when you see them. Further, it is advised for heart patients to have an aquarium as the movements created by a fish in the water produces vibrations which are good for health. So if you want to maintain pets that too hassle free, without any doubt you must buy a fish aquarium. Sit and watch the fishes gliding in the water and you get what you want the most i.e. inner peace. You feel calm and composed.

Continue reading »]]> Neo,  in “The Matrix” movie, needed his brain to be plugged into a supercomputer, so he could learn martial arts in minutes, and Trinity in the nick of time, could fly a chopper so they could get away from the “agents”. Using encoded mandalas is the closest working model to this science fiction,  that proves that old adage, there is nothing new under the sun. 

Mandalas have been used as far back in time as we can remember. Most people today, when visiting ancient ruins, like pyramids, can see images, of geometric patterns and designs in the decoration, even in early Christian Churches. Or are they merely decoration? 

The first time I ever seen a symbol like a mandala,  it was a pentagram, and  I was scared to death of it  because of course it was in a horror movie and I was a small child at that time. It wasn’t until much later, that I learned in geometry, that Pythagoras, of the famous Pythagorean theorem, was also a numerologist. This numerology is all about the numbers and subtle meanings that had nothing to do with mathematical formulas, i.e.  [a squared + b squared = c squared]  and I did confuse me. Why wasn’t this taught as well? If his theorems worked, why wasn’t this other aspect of his contributions taught in High School math? 

From Wickipedia

“In various spiritual traditions, mandalas may be employed for focusing attention of aspirants and adepts, as a spiritual teaching tool, for establishing a sacred , and as an aid to meditation and trance induction. According to David Fontana, its symbolic nature can help one “to access progressively deeper levels of the unconscious, ultimately assisting the meditator to experience a mystical sense of oneness with the ultimate unity from which the cosmos in all its manifold forms arises.”  The psychoanalyst Carl Jung saw the mandala as “a representation of the unconscious self,”[ and believed his paintings of mandalas enabled him to identify emotional disorders and work towards wholeness in personality.

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In common use, mandala has become a generic term for any plan, chart or geometric pattern that represents the cosmos metaphysically or symbolically, a microcosm of the Universe from the human perspective” 

Take away all the esoteric stuff, and you still don’t have much you can use here. Most people are spiritual but not inclined to seek out the cosmos or metaphysics. However, something of value is here if we take the time to apply what could be a new beginning, and  a transformation of human learning and understanding. 

Do you remember that scene in “The Matrix” movie? when Neo learned martial arts in an instant…  think about it… what would that application look like in real life? 

Brain Mirror neurons, a recent discovery, are said to operate and/or fire signals through the brain.. whether the person is completing an activity or simply watching the activity. This  has serious implications, to what we call learning and what is possible in regards to  Matrix Style Learning (training). 

Of course some variant of this is possible otherwise I wouldn’t be writing this article.

Four years ago, I was amazed at my own brain mirror neurons being trained a sequence of Chi Gung movements and instantly getting the benefit of that training.

This training would otherwise taken years of practice. Not only that, the use  of Mandalas and sacred geometry was explained to me in a way I never heard before.   Brain mirror neurons can actually understand  like some type of computer Operating System (OS), sacred geometric shapes, images and patterns and by looking at these images… hmmm just  like  the ancient spiritual practicioners, suggested,  esoteric or not, benefits can be derived. 

Fast forward to Dec 16th, the  day I launched  the I Chi Power App on Itunes (www.i-chipower.com) I  codesigned an app for Iphone that actually works with brain mirror neurons providing an instant benefit.   I called this the I Chi Power App, because you the user get to experience what I had experienced over the years instantaneously in this App.  Check out the You Tube demo to see first hand one of the benefits of this app and you might find yourself on a journey to unlocking your true potential.

Continue reading »]]> The key to a good math education starts very early at the elementary years period. Nevertheless, it has been found out that students are not learning math in a way which will help them love it, hence often times, they try to look for help with math.As a consequence, it is not unusual that students simply turn their back to math, and don’t end up assimilating basic mathematical skill which would help them tremendously in the professional careers, in almost every field.

One of the main reasons why some people hate numbers and would probably scour for help with math is that it has been taught differently during their early years. One capital mistake is the tendency to entice memorization instead of critical math reasoning, which certainly leads to failure, since memorization doesn’t provide the reach that true mathematical understanding does. Using this kind of teaching method, it does not help the students that much with math. Take for example the case of Pythagoras Theorem.

The Pythagorean Theorem in geometry states that, in a triangle with which one angle is a right angle (having 90 degrees or also known as a right angle), the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two other sides of the triangle. In equation form, it is often expressed as a2 +b2 = c2

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In this example, instead of just asking the students to memorize a formula, the teacher should be able to discuss on how the formula came about. The teacher should go for a historical contextualization of why the theorem is true and why how it was developed. Kids would probably find more appealing a historical reference than the mere memorization of it. As we probably have experienced before, a good story usually makes it up for a difficult concept, because it makes math much more enjoyable

Another fun way of educating kids in mathematics is through online games. There are quite a number of websites which offer interactive games that help your kid understand the concepts of mathematics while at the same time, making learning an enjoyable experience. You can also acquire education materials that are readily available in book stores, computer shops, and electronic stores. This will surely help you with your math challenges.

In today’s world it is clear that not all the responsibility of math learning is on the teachers. As a matter of fact, parents may even have a more important role, because they have access and decide on the external tools the kids will use which could make the difference between learning and not learning. There is this story about a parent who was trying to teach her kid about the value of different money denominations. Using her imagination, she created a game about an imaginary toy store, where she would need to buy toys from her little sister. . This creativity and ingenuity did not only allow the kid to learn fast, but also made her understand the idea far better than the typical classroom scenario.

For mathematics to be exciting, and to assist you deal with math with your kids, mathematics should be introduced in such a way that kids would remember the concepts and formulas easily. The major challenge for educators is to entice and appeal to the exciting side of math.

Related Pythagorean Theorem Articles

Continue reading »]]> If you consider adding a special touch to your property a gazebo is definitely a very good choice. Now, there are various new gazebo styles that you can choose from. Since its invention the gazebo has been morphed into a variety of materials. They include the stone, wood, metal and even concrete. Among all, the wood gazebo is the most popular one. A good amount of experience in woodworking and artisan is essential to select your ideal gazebo. While choosing a gazebo make sure to find out if it is water resistant or not. Now we will discuss the important tricks and information that is required when choosing gazebo plans to suit your need. The first step is to find the websites that usually recommends and offers valuable information regarding choosing the best plan, and then using them successfully in constructing the gazebo.

If you spend a good amount of time and do a thorough job, you will be acquainted with more than sufficient enough information and tips, which in turn will help you with building your favorite gazebo. Once you choose your favorite gazebo plan you are ready to start the building process. It is important that you integrate the size of the gazebo in addition to a minimum of 2 feet for walkway. This will provide enough space for movement. In case you decide to buy the gazebo plans, you will get certain tricks and tips along with them. This will help you in achieving great success. In any case, you may also buy ready-made gazebos. An important point to keep in mind when building the gazebo of your choice is, you need to have the right foundation. It should be somewhat similar to the one we use for solid house building. You can`t make the blunder of ruin everything in case the foundation is not strong enough and steady.

For your information, there are three important steps to ensure success with your gazebo project. You can make use of the old gazebo plans to get a design, this particular guide and these gazebo plans will help you a lot as you proceed with your work. It will also help you in deciding and choosing the equipment and the tools that are required. If you have woodworking skills and experience, you can work on large gazebo projects, including the building of a strong foundation, a perfect layout and of course an attractive design. The most beautiful gazebos are the standalone gazebos. It will be a wise decision to review the gazebo plans you have at your disposal.

In order for you to personalize the gazebo you can add a fire pit or a hot tub. It can also reflect your taste and living style, as well. It is not necessary that you restrict your creativity on my advice only. Use your imagination and consider something unique. Try and create something unique and remarkable. The garden gazebo can actually be a fantastic feature for any outdoor entertainment. You can choose to invite some friends and relative to enjoy, and also to admire your skills.

Continue reading »]]> What is skimboarding? Often people confuse skimboarding with surfing, as they are very similar to each other. The basic difference is the board. The surfboard is about 6 feet tall whereas the skimboard would reach the chest of the skimboarder when made to stand on one of its ends. Skimboarding goes way back to the 1920′s when it originated at the Laguna Beach. This sport gained momentum in the 1960′s.

Originally the skimboards were made out of wood but the modern ones are made of either fiberglass or carbon fiber. The modern boards are more advisable as they float better. They are also available in various shapes such as hyperbolic, swallowtail, pintail, etc. Selecting a skimboard according to your weight is the primary requirement. Also for being able to balance properly and stay and the board you will have to apply a specific wax. Another option is to use tail pads identical to the ones used by surfers. These too will prevent you from slipping off the board.

Skimboarding is not as easy as it looks. It takes years of practice, dedication and occasional bruises to be good at this sport. Balance is the basic key to even attempt skimboarding. First you need to learn how to get on to the board. You should stay on the shore with the skimboard in your hand and wait for the waves to break. The moment you see the perfect opportunity you run towards the ocean with the board in your hand. Once you reach the wet sand you drop the board and jump on to it. Remember you have to just drop your board and not throw it. The board will be taken by the waves as soon as you drop it so try balancing yourself on it. Stand upright so that the board does not lose its momentum. To slide you will have to bend your knees.

It will take a fair amount of practice to be able to perform this task the way it has been mentioned. However, once you master this part you can move on to boarding on the waves farther from the shore and eventually even try some tricks and stunts. Some highly experienced skimboarders are capable of performing tricks like the ones professional skateboarders perform. Some highly gifted skimboarders can also perform aerials. If you are a person who loves beaches and water sports, skimboarding is a sport you should try out. Who knows, you could actually become a master at the sport!

Continue reading »]]> College Math CLEP

The College Mathematics CLEP exam covers material taught in a one-semester course. This CLEP test requires students solve straightforward problems as well as problems requiring an understanding of concepts and skill application. Questions on the College Math CLEP exam include the real number system, logic, sets, equations, functions and their graphs, probability, statistics, and data analysis. A few questions on this CLEP test involve complex numbers, logarithms and exponents, and applications from algebra and geometry. Students taking this CLEP exam should be familiar with current math vocabulary, symbols, and notations.   

The College Math <a rel=”nofollow” onclick=”javascript:_gaq.push(['_trackPageview', '/outgoing/article_exit_link/1135922']);” href=http://www.speedyprep.com/clep_exam_procedure.aspx>CLEP exams</a> includes probability and statistics, involving counting problems, permutations and combinations, simple and compound probability events, measures of central tendency, and standard deviations.  The real number system section of this <a rel=”nofollow” onclick=”javascript:_gaq.push(['_trackPageview', '/outgoing/article_exit_link/1135922']);” href=http://www.speedyprep.com/clep-test.aspx>CLEP test</a> consists of prime and composite numbers, odd and even numbers, factors and divisibility, rational and irrational numbers, absolute value and order, and open and closed intervals.  The functions and their graphs section of the College Math CLEP exam covers properties, domain and range, and the composition of functions and inverse functions.  The College Math CLEP test also contains additional algebra and geometry topics and applications including complex numbers, logarithms and exponents, perimeter and area of plane figures, properties of triangles, circles, and rectangles, Pythagorean Theorem, parallel and perpendicular lines, algebraic equations, systems of linear equations and inequalities, and the Fundamental Theorem of Algebra and Remainder and Factor Theorems. The Logic section of this CLEP exam encompasses truth tables, conjunctions, disjunctions, implications, negations, conditional statements, converse, inverse, contrapositives, hypotheses, conclusions, and counterexamples. The last part of the College Math CLEP test includes sets and covers unions and intersections, subsets, Venn diagrams, and Cartesian products.

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College Algebra CLEP

The College Algebra CLEP exam covers material taught in one-semester introductory undergraduate college algebra course and contains routine problems using basic algebraic skills and those that require a demonstration of concept comprehension for solving.  The College Algebra CLEP exam includes questions on algebraic operations, linear and quadratic equations, inequalities, and algebraic, exponential, and logarithmic functions. Students taking this CLEP exam should know current algebraic vocabulary, symbols, and notations.  

The College Algebra CLEP test involves functions including definition, interpretation, properties, algebraic, graphical, numerical, symbolic, and verbal representations and models of functions, domain and range, intercepts, symmetry, and transformations. Algebraic operations represented on this CLEP test include factoring and expanding polynomials, operations with algebraic expressions and exponents, and properties of logarithms. The College Algebra CLEP exam also covers equations and inequalities, including linears, quadratics, absolute values, exponential, logarithmic, and systems. The remaining portion of this CLEP test determines students’ understanding of number systems and operations with real and complex numbers, sequences and series, determinants of 2-by-2 matrices, and the Factorials and Binomial Theorems.

CLEP Test Details

Both of these multiple-choice CLEP exams place little emphasis on arithmetic calculations and do not contain any questions that require CLEP testers to use a calculator. However, an online non-graphing scientific calculator is available to students during the CLEP exam, as part of the testing software. Each of these <a rel=”nofollow” onclick=”javascript:_gaq.push(['_trackPageview', '/outgoing/article_exit_link/1135922']);” href=http://www.speedyprep.com/clep-test-study-guides.aspx>CLEP tests</a> allows 90 minutes for completion and contains 60 questions.

Right triangles and the Pythagorean Theorem
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Continue reading »]]> Geometry formulas play an integral role in the learning of Geometry, the science of spatial relationships. It may frighten you at start, but once you master them you will feel fascinated applying them in math problems. The formulas are not only used in maths but also in other major subjects such as physics, engineering, navigation etc. That is the reason tutors always stress the importance of learning the basic formulas of Geometry. History Of Geometry The term Geometry has been coined from the two Greek words Earth (Geo) and measure (metria). The science that is extensively studied by students and widely applied in many areas nowadays had been invented and used for the first time by the Greeks. It is evident from the ruins they have left behind that they had a very good understanding of the science related to measuring shapes, angles, areas and distances. Based on the geometric principles employed by different groups of ancient people, the science is broadly classified into early geometry, Egyptian geometry, Babylonian geometry, Greek geometry, Hellenistic geometry, Indian geometry and Chinese geometry. Brain And Geometry According to a May 23, 1988 report entitled “Plane Facts on Geometry,” in the Los Angeles Times, “The brain apparently uses simple geometric calculations to instantly figure out depth and distances, but researchers say they do not know if the ability is learned or inherited.” In the post, Times staff and wire reports have been quoted as having said, “Scientists at the Smith-Kettlewell Eye Research Institute in San Francisco, who are studying how the nervous system enables people to see in three dimensions, have found that the brain uses either innate or learned geometric principles.” Geometry In Real Life Geometry formulas that help in making variety of engineering or navigation based calculations are sometimes very helpful in real life situations also. For instance, when you plan to paint your living room, you need to know the area of the wall that has to be painted so that you can purchase the paint accordingly. Here is another instance. Farmers that want to buy fertilizers for their farm land need to know the area of the land that needs fertilizers. Therefore, people that belong to all sectors need to have a sound knowledge of basic geometry formulas and how to apply them practically. Here is a list of basic formulas that one needs to know for sure: 1.Perimeter of triangle, rectangle, square and circle 2.Area of triangle, rectangle, square, circle, parallelogram and trapezoid 3.Volume of cube, sphere, cylinder, cone and pyramid 4.Surface area of cube, sphere, cylinder, cone, pyramid and trapezoid. Some of the theorems of geometry that students may find useful are Euclid’s First Theorem, Line Intersection Theorem, Betweenness Theorem, the highly reputed Pythagorean Theorem and Right Angle Congruence theorem. The knowledge of Geometry is believed to be very important in life. When students get used to applying geometry formulas in their mathematical/science/engineering curriculum at various evaluation levels, their analytical and logical thinking improves gradually. So, learning and applying the formulas will help you excel mentally as well as mathematically.

A quick overview of how the pythagorean theorem can be used

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Continue reading »]]> If you have a pet dog then naturally you have to treat him like a family member. You have to give him the facilities of roaming around in the house at its will and fancy. He should have the freedom to go and come out of the house as when he likes, without bothering you or disturbing you in your work. Nevertheless, this is impossible, as he is not a human being but an animal after all. Well we have one benefit of keeping a pet dog and that is dogs are extremely intelligent and are quick to learn. Hence we can arrange to attach dog doors to our house. By doing so, we save the trouble of getting up and opening the main door each time the wants to go out or come in and he in turn does not have to disturb you in your sleep or work.

Either a dog door is a small door which is attached to your main door by means of hinges or it is a flap which opens and closes by itself whenever the dog moves in or out of the house. These doors are adjustable and can be arranged in such a way that they do not hinder the main structure of the dog door. These doors can be temporary or permanent according to your need. If you are residing temporarily at this residence then there is no need to fix the door on the hinges but you can just arrange the flap door which can be easily fixed or removed as per your need. These doors are available in various materials like aluminum, venial, and nowadays even plastic doors are available.

One more thing one should keep in mind is the size of the dog. This is very important; if it is smaller than the dog size then the dog will not be able to use it, as he will get hurt while moving in and out. If it is bigger than the dog then other stray animals can cause a nuisance. Since dogs are not kept just as pets but also to guard our house, it is very important that they should remain outside the house.

Dog doors are most beneficial when we are not around the house and the dog has to be left alone to keep guard. At such times, the dog will need to go inside the house for his meals on his own. Thus it is necessary to have dog doors fixed. The latest dog doors are electronic doors, these doors work in such a way that the door opens automatically only when the dog approaches the entrance of the door, because it has a key attached to its collar.