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Monday, 28 March 2011

Natural numbers

At the heart of Buddhism is the concept that stillness reigns supreme, that by virtue of stilling the mind and emptying it of its contents, one can become enlightened. What is mind-startling about this premise is the truth that rings loudly from its core. What we shall see here through a mathematical example is how the Buddha was indeed right: form does arise from emptiness and emptiness is actually form. It is all in the perception.
The famous mathematician, John von Neumann, created a method, known as von Neumann hierarchy, of generating the set of Natural numbers {1,2,3,...} from...essentially nothing. From this example, we see how form arises out of emptiness, and thus reinforces the precept of the Heart Sutra quoted above. To carry out this example, all we need is some basic knowledge of set theory.
A set is a group of objects. Thus the set A = {3, 5, 7, 9} comprises the odd numbers from 3 through 9 inclusive. We can also talk about the set {}, which is called the empty set. The empty set is the set which contains no elements; this set is sheer "emptiness." Now sets can contain sets as elements. For example, take the set A above and now add the element {12} which is the set which contains the element 12. Form the set B = {3, 5, 7, 9, {12}}. The set B contains five elements, one of which is itself a set.
When we talk about the union of two sets, we simply merge the elements of each set into one, not repeating any common elements. Thus if C = {1, 2, 3} and D = {3, 4, 5} then C union D, or CUD, in which the symbol "U" means union, is the set E = {1, 2, 3, 4, 5}. Now the example that follows is going to show how we create something from nothing, or form from emptiness. We have the following steps:
Step 0: {} Empty Set
Step 1: { {} } Set containing the empty set
Step 2: { {}, { {} } } Set containing the previous two sets
Step 3: { {}, { {} }, { {}, { {} } } } Set containing the previous three sets
Iterating in this way, we create a sequence in which the next element is the union of the two previous sets. Now at Step 1, we have a set with one element; at Step 2, we have a set with two elements, and so on. In this way, we can generate the set of Natural numbers {1, 2, 3,...}
Thus from emptiness, namely the empty set, which contains nothing, we have created form, that is the Natural numbers, which contain an infinity of numbers. The only difference is how we look at the two sets: our perspective. In mathematics, there is a very special word for what we have just done between the sequence generated by the empty set and the Natural numbers. We say the two sets are isomorphic, which basically means that the elements of each set are the same except in the way we perceive them. This is much the same as the isomorphism that would exist between the numbers 1,2,3... in English and the same numbers called by another name in a foreign language such as French or German, or even Macedonian, if you will.
Thus emptiness is form, depending on our perspective of course; and form, the Natural numbers, is emptiness, again depending on our perspective. Indeed the Buddha did know something about mathematics that he never told us; but now even we know some of his ancient secrets. Now maybe if we apply them to everyday living, everybody will be a lot better off.

Joe is a prolific writer of self-help and educational material and is the creator and author of over a dozen books and ebooks which have been read throughout the world. He is a former teacher of high school and college mathematics and has recently returned as a professor of mathematics at a local community college in New Jersey.

Joe propagates his Wiz Kid Teaching Philosophy through his writings and lectures and loves to turn "math-haters" into "math-lovers." See his website http://www.mathbyjoe.com/ for more information and for testimonials, and try out one of his ebooks here http://www.mathbyjoe.com/page/page/2924777.htm to achieve better grades in math.

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first and second grader

A key core competency of mathematics for your first and second grader is that of being able to count by twos and threes. As easy a task as this might seem to you or me, this competency often presents much trouble to youngsters and is often only learned after much repetition and painful experience. Yet there is a very easy and neat trick---might I add---to facilitate its learning so that your youngsters can focus their attention on other important learning skills.
In working with kindergarteners through second graders, I observed that counting, let us say, from one to twenty was usually learned quite well and usually presented little or no difficulty. Request, however, that this same youngster, who could rattle off effortlessly the numbers from one to twenty, start to count by twos or threes, and you entered a whole new realm of technical difficulty. Unless the pattern is memorized beforehand, this task is not so easy as it seems. What often happens is that the first or second grader starts and stalls, starts and stalls, in a haphazard and fruitless manner.
This does not have to be the case. There is an easy way to teach the counting by twos and threes so that your youngster does not have to struggle until the pattern has been memorized from repetitive performance. Let us demonstrate this method by twos and then extend it to threes. Tell the youngster to first count from one to twenty out loud. Then instruct the youngster to count from one to twenty silently to himself. What you do next is explain that counting by twos and threes is simply a combination of counting out loud and silently at the same time.
For example, to count by twos, have the youngster begin counting silently and then out loud, alternating in this manner up till twenty. Thus the count for the first six would be "one (silent), two (out loud), three (silent), four (out loud), five (silent), six (out loud)" all the way to twenty. After a few runs the student will get the natural rhythm and flow and after a few times will be able to do this so that it seems as though he were simply counting by twos without the alternating pattern.
Completely analogous would be by threes in which the first six would go "one (silent), two (silent), three (out loud), four (silent), five (silent), six (out loud)." Again, after a few runs, it will seem as though the youngster has mastered this task without any effort at all. In both cases, the twos and threes will be mastered after a number of repetitions of the outlined exercise.
Try this procedure out and you will see that this method provides a pleasant and fun alternative to the traditional method of rote learning. Your youngsters can then apply the time saved on such tasks as learning to count by twos and threes to perhaps mastering their multiplication facts. Happy learning!

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vector is nothing more than a directed

A vector is nothing more than a directed line segment. Technically speaking, a vector is defined as an object that has both a size, or magnitude, and a direction. Vectors have many applications in mathematics and are found abundantly in fields like physics and engineering. Examples of vectors are velocity, acceleration, and force.
Vectors are defined by their size and direction. For example, velocity is a vector because we can describe this quantity by both its size, that is speed, and its direction. Thus a car moving at 60 miles per hour in a direction due north exemplifies a velocity vector. Acceleration also typifies a vector because this quantity has both a size and direction. A truck accelerating at 10 feet per second per second moving due south exemplifies an acceleration vector. Force is another object which is modeled by a vector quantity. A force of 15 Newtons (on earth this is a weight of about 3lbs) exerted downward is an example of a vector.
In the Cartesian Plane---the grid on which we graph points, lines, and curves---a vector can be given as a point. For example, in two dimensions the point (1, 0) represents the vector starting at the origin (we say having its tail at the origin) pointing to the right and terminating (we say having its head) one unit from the origin. The point (0, 1) represents the vector having its tail at the origin, pointing straight up and having its head one unit from the origin. The point (1, 1) represents the vector having its head once again at the origin and its tail at the point (1, 1); this vector lies on the line which bisects the first quadrant.
Since we live in a three dimensional world, we need to introduce vectors in three-space. These are analogous to those given in two-space, except that now we use three values. That is, we specify the x, y, and z coordinates and thus give a vector as (x, y, z). For example, the vector (0,0,1) is that having its tail at the origin of our three dimensional coordinate system and its tail one unit straight up from the origin. Similarly, we can give other coordinates to generate vectors pointing in any direction in three space, and such vectors would correspond to such things as force or velocity in the real world.
Once we understand the basic definition of a vector, we can then talk about operations with them: these operations include addition, subtraction, and a special kind of multiplication called scalar multiplication. Such operations would come into play when, for example, combining (adding) or subtracting forces or accelerations.
The most important thing to remember is that a vector is simply a mathematical object that models such real world phenomena as force and speed. Vectors are directed line segments that can be plotted on a Cartesian Plane using two points in two dimensions, or three points in three dimensions. Other more expansive applications of vectors are studied in courses such as calculus, linear algebra, and physics.

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segment. Technically speaking, a vector is defined as an object that has both a size, or magnitude, and a direction. Vectors have many applications in mathematics and are found abundantly in fields like physics and engineering. Examples of vectors are velocity, acceleration, and force.
Vectors are defined by their size and direction. For example, velocity is a vector because we can describe this quantity by both its size, that is speed, and its direction. Thus a car moving at 60 miles per hour in a direction due north exemplifies a velocity vector. Acceleration also typifies a vector because this quantity has both a size and direction. A truck accelerating at 10 feet per second per second moving due south exemplifies an acceleration vector. Force is another object which is modeled by a vector quantity. A force of 15 Newtons (on earth this is a weight of about 3lbs) exerted downward is an example of a vector.
In the Cartesian Plane---the grid on which we graph points, lines, and curves---a vector can be given as a point. For example, in two dimensions the point (1, 0) represents the vector starting at the origin (we say having its tail at the origin) pointing to the right and terminating (we say having its head) one unit from the origin. The point (0, 1) represents the vector having its tail at the origin, pointing straight up and having its head one unit from the origin. The point (1, 1) represents the vector having its head once again at the origin and its tail at the point (1, 1); this vector lies on the line which bisects the first quadrant.
Since we live in a three dimensional world, we need to introduce vectors in three-space. These are analogous to those given in two-space, except that now we use three values. That is, we specify the x, y, and z coordinates and thus give a vector as (x, y, z). For example, the vector (0,0,1) is that having its tail at the origin of our three dimensional coordinate system and its tail one unit straight up from the origin. Similarly, we can give other coordinates to generate vectors pointing in any direction in three space, and such vectors would correspond to such things as force or velocity in the real world.
Once we understand the basic definition of a vector, we can then talk about operations with them: these operations include addition, subtraction, and a special kind of multiplication called scalar multiplication. Such operations would come into play when, for example, combining (adding) or subtracting forces or accelerations.
The most important thing to remember is that a vector is simply a mathematical object that models such real world phenomena as force and speed. Vectors are directed line segments that can be plotted on a Cartesian Plane using two points in two dimensions, or three points in three dimensions. Other more expansive applications of vectors are studied in courses such as calculus, linear algebra, and physics.

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Sunday, 27 March 2011

Sports enhance the multifarious abilities

Sports enhance the multifarious abilities of a school-going child, developing the spirit to become robust and energetic. A balance between academics and sports, when encouraged by the school enables students to understand the importance of caring for the body as well as the mind.

Most little ones are naturally active and enjoy activities which involve a lot of movement. Oberoi International School aims to enable its students to live life to the fullest through the sports activities offered.

The Oberoi International School's campus has world-class facilities for outdoor and indoor sports. Children are encouraged to take up sports and physical activities.

Playground is the place where kids let out their aggression; here they are able to release emotions like frustration and anger in a healthy manner. It teaches them to deal with disruptive emotions in socially acceptable manner.

Participating in sports is important for motor skill development, maintaining a healthy exercise program and provides for a release of anger when the academic stressors become overwhelming.High school sports presents an opportunity for an increased bonding between children and their parents when parents come to games to cheer their child or the school team.

Our students are trained by qualified experts. Tennis coaching in Oberoi International School is handled by the professional Mahesh Bhupathi Team Tennis. Likewise we have for Academic Year 2010-11 other organizations such as Indian Cricket Academy, Soccernova, Terence Luis Academy of Dance send in their professionals to coach our children.

In addition to helping achieve high-levels of physical fitness, active participation in sports is known to enhance focus and concentration, improve self-confidence and body language and sharpen the child's ability to handle challenges and take quick decisions.

We ensure that our students not only start reaping the benefits of exercise in their formative years but also have fun doing so.

The School plans to organize inter-house sports tournaments and activities to foster healthy competition and team spirit as also to help students improve the quality of their game.

Action activities offered by Oberoi International are aerobics, badminton, basketball, cricket, gymnastics, handball, indoor rock climbing, camping / pioneering, soccer, squash, swimming, table tennis, tennis, throw ball, track and field, trekking, volleyball, yoga.

Outdoor facilities include a 3-acre, professionally-maintained playground with a cricket pitch and an athletic track, 4tennis courts and an Adventure-Obstacle Course. While indooramenities include a physical education center, state-of-the-art gymnasium, 6 lane swimming pool, indoor rock climbing &traverse wall,basketball court, volleyball court, badminton courts, 2squash courts,table tennisgym, snooker, chess, carrom zone, sportszones with playing areas for juniors.

Sport activities can bring together the entire school, either in the form of participation in the game itself, or by support through applaud. It boosts school morale when students cheer for their team. When adults look back on their time in school,along with teachers and friends, they fondly remember the sports they participated either by playing or by cheering.Every schooling student can have a better overall school experience with the inclusion of a healthy sport structure.

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For more information on world school visit: http://www.oberoi-is.org

Education Is Compulsory For Your Child's Life

Directly or indirectly the prospect of a family or a country depends on the future of a child. So, initially it appears to be an obligation for a family and the country to provide a child, almost every chance to grow or to prosper physically as well as mentally. This is because the future of a country and a family is subjected to the present of a child. We have seen that the countries, which fall in the category of under-developed, are facing the major problem of illiteracy.
Countries like Africa, South Africa, and Afghanistan etc have not progressed yet because they have the lowest ratio of education. Whist, countries like America, United Kingdom, Canada, Australia etc are in the race of developed countries. The major reason behind their development and progress is their standardized educational system. If we only take an example of the UK, she has the high literacy rate of 99%.
The above mentioned statistics show the significance of education in the life of a country. It not just contributes to a country's development and growth but also revolutionizes a young's mind to civility.
Undeniable strength of a foundation
Not even a single thing can stand or maintain its position without the support of a solid foundation. Every young mind requires stable nourishment for its growth in the shape of education. In this process, formal education plays a fundamental part, which a child acquires from schools like primary schools, prep schools, private schools or secondary schools.
School is the initial home of education, where one gets familiar with the basic principles of a right and a wrong. Country like UK has made education a compulsion for all children.
We observe that in many countries acquiring education formally has not become a necessary part as it should have become up till now. Parents should admit and realize the deep-seated strength of education for his/her child because education is as important as a healthy diet for a proper physical and mental health. It is such a strength and vigour which, itself empowers the keeper.
Many ancient thinkers, philosophers, and writers like Aristotle, Plato, and Einstein, etc have written books in the significance of education. Aristotle's writing encompasses morality and aesthetics, logic and science, politics and metaphysics. This wide range of study reflects that acquiring education or knowledge is being honoured by the ancients, who have excelled almost in every field of the study.
Why to choose a good educational institution for your child?
The major reason why a school is regarded as a significant part of a child's growth is that it gives high precedence to enhancing young child's social development. This is so because social behaviourism and interaction of a human child begins in the early years.
Put briefly, it is appropriate to introduce your child with the regular and formal rules or terms of living in a society in educational institutes like school.
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Written by basiliskt
Freelancer Content Writer /Blogger/ Academic Writer

best tools for children

Toys are the best tools for children and also play a very important role for learning and either we said toys is an essential of kids learning as well as playing.

Good toys not only enhance a physical action, attention, observation but also can enhance imagination power, thinking ability.

Parents are not also hesitating to give a toy as a gift because toys help to increase a creativity of child.

Toys help to know a child interest if child playing with guns toys than his/her interest on army or police side.

Wooden toys are the best gift for children, they helps to enhance the imagination power, children mental health, environment health and also physical health.

Wooden toys is made by wood so they are safe and also long lasting toys

Educational toys are the combination of playing and as well as learning. They help to problem-solving technique, or mathematical proposition. Parents want to teach a child but child wants to play so educational toys resolve this problem and this helps to save time for playing and learning together.

Toys motivate kids. Kids will do a work if parents make it rewarding for them the answer is money but remember every time the child not picking the money than you have to promise that if u work than I give u toy(Barbie doll or soldier toys etc). The toys play a two role playing as well as learning. The most demandable toys for girls are Barbie doll toys and for boys are soldiers' toys, guns, etc.

Like a puzzle toys helps to do a work fast on time and also enhance the reasoning aptitude solve.

This puzzle toys provide a good deduction skills.

Most of the toys are good for children like puzzle for developing a children mind and marble, jackstone and balls also developing a children development. The kids' toys are basically made by plastic, wooden, cotton, stones.

Always try to give a more toys to infant because they help to increase a identification power, more of the toys more of the identification power.

Best infant toys are balls, stuffed animal, musical toys, nesting toys, baby mirror, rattles.

Best toys for boys are build and paint a bird house, shadow magic kit, etc

Best toys for girls are kitchen sets, Barbie dolls etc,

"Kids toys help to children life happy and learnable"

Decimals

Decimals are a method of writing fractional numbers without writing a fraction having a numerator and denominator.
The fraction 3/10 is written as the decimal 0.3.

Decimals are fractional numbers. The decimal 0.3 is the same and equal to fraction 3/10,the number 0.23 is a decimal that represents 23/100.
Adding Decimals is just like adding other numbers.in simple adding operation
Always line up the decimal points when adding decimals. means point of decimal are lie in same place like

                    22.33 add 2.3 then written as
                         22.33        +
                           2.3
                     .....................
                       24.63
                  ........................

Remember to put the decimal point in the proper place in your answer.

Decimal numbers, such as O.8766, have fiver digits after the decimal point. Each digit is a different place value. as 8 7 6 6
The first digit after the decimal point is called the tenths place value.

The second digit tells you how many hundredths there are in the number.

The third digit is the thousandths place.

The fourth digit is the ten-thousandths place .

Rounding decimals is very similar to rounding other numbers. If the thousandths place of a decimal is four or less, it is dropped and the hundredths place does not change. For example, rounding 0.843 to the nearest hundredth would give 0.84.
If the thousandths place is five through nine, the hundredths place is increased by one. The decimal 0.846 rounded to the nearest hundredth is 0.85.

Fractions

Fraction in math is like part of any one part it define as fraction is part of an entire object. e g if one part consist f 3 parts then one part is red and 2 parts are black then fraction of black is 2 parts as a whole part and wright as 2/3 and similary for red 1/3
fraction having two parts in given example like 2 and 3 in 2/3 example

. The top number is called the numerator that is 2. The bottom number is called the denominator that is 3
numerator
denominator

=2/3

Equivalent fractions are fractions that have the same value or represent the same part of an object. If a square is cut into two pieces, each piece is also one-half of the it. If a square is cut into 4 , then two pieces represent the same amount that 1/2 and as a whole fraction is 2/4 that in lowest form is 1/2 thus as we say that 1/2 is equivalent to 2/4.
Fractions are determined to be equivalent by multiplying the numerator and denominator of one fraction by the same number. This number should be such that the numerators will be equal after the multiplication. For example if we compare 1/2 and 2/4, we would multiply 1/2 by 2/2 which would result in 2/4 so they are equivalent.

examples are :

Fractions equivalent to 2/5 are 4/10, 6/15, 8/20, 10/25, ...
Fractions equivalent to 2/6 are 4/12, 6/18, 8/24, 10/30, ...
Fractions equivalent to 2/7 are 4/14, 6/21, 8/28, 10/35, ...
Fractions equivalent to 2/8 are 4/16, 6/24, 8/30, 10/36, ...

Improper fraction is a fraction that has a numerator larger than or equal to its denominator. eg are 4/3 ,5/4,10/3........

Proper fraction is a fraction with the numerator smaller than the denominator.
e g are 2/3,5/4,1,2.......
Fraction to a Decimal
It is also simple process just do as follow:
For example: Convert 3/5 to a decimal

Divide the numerator of the fraction by the denominator ( 3 ÷ 5=0.6)

Round the answer to the desired precision that is not in this case

Fraction to a percentage
It is like above example continue
For example: Convert 3/5 to a decimal

Divide the numerator of the fraction by the denominator ( 3 ÷ 5=0.6)

Round the answer to the desired precision that is not in this case

In last just multiply 0.6 to 100 to find percentage that is 60

Use percentage sign like 60%

Percents

Hello to find percentage in math is too easy it define as

Fraction , ratio with 100 as the fixed and understood denominator.

how to find percentage let see example if we find percentage of 90 out of 150 then

Divide the first number by the second (e.g. 90 ÷ 150 = 0.60)
Multiply the answer by 100 (Move decimal point two places to the right) (e.g. o.60*100 = 60)
Round to the desired precision ( if )
Follow the answer with the % sign (e.g. 90 is 60% of 150)

Similary to find fraction percetage is easy like if we find ther percentage of 2/3 then first divide 2 by 3 ,2nd then answer will be 0.66667 ,then multiply the answer by 100 and we get 66.6667,3rd Round to the desired precision 67 from 66.6667 , in last 4rth wright the answer with the % sign 67%

Exponents

Exponent is a number that tells how many times the base number is used as a factor. For example, 3² indicates that the base number 3 is used as a factor 2 times. To determine the value of 3², multiply 3*3 which would give the result 9.similary 4*4=16 ,6*6=36 that is 6²

Squares shows that it has value of two. . To find the area of a square or rectangular , multiply width with length and in case of cube mutiply lenght by width by widht ,and also haing power of three as exponents for ex, 3³
Exponents are written as a superscript number (e.g. 3²) or preceded by the caret (^) symbol ,it can be seen in any calculator
Some facts about exponents:

Zero squared (e.g. 0² = 0)

seven squared (e.g. 7² = 49

perfects aquare

                                               1 x 1 = 1
                                                2 x 2 = 4
                                                3 x 3 = 9
                                              4 x 4 = 16

5 x 5 = 25

                        10 x 10 = 100

                        11 x 11 = 121

                        12 x 12 = 144
                        13 x 13 = 169
                        14 x 14 = 196

15 x 15 = 225

                        16 x 16 = 256
                        17 x 17 = 289
                        18 x 18 = 324
                        19 x 19 = 361

                        20 x 20 = 400

think of time

When we think of time, we often assume time always was and always will be. Yet time is a man-made construct, bounded only by the limits of our minds. According to astrophysicists, the universe is fourteen billion years old. Earth is a mere five billion years old. To motivate this discussion of the limits of time, I ask a simple question: where were you five billion years ago when the earth was formed?
The answer you probably uttered immediately was, "I wasn't born yet;" as before you were born, time had no meaning to you. Indeed time only exists for those in this world, and even then only man really has any use for it. To understand this idea better, ask yourself whether your dog or pet cat have any perception of time. Does your dog know how many years he has been alive? Does your cat look to the future for an expected occurrence? Okay maybe the treat he knows he gets every afternoon at about 2:00 P.M. But this aside, your cat or dog does not keep track of time. While these considerations may seem trivial---even nonsensical to some---they do prod us to contemplate the fascinating implications of eternal time.
To bring time in line with something more concrete---or abstract, depending on your viewpoint---we digress to mathematics. Let us take the real number line, which is a man-made construct as well, much like time. One assumes that the one dimensional real number line projects itself infinitely in both directions, and thus only has the dimension of length, no width. With this construct, we can associate time to the real number line. For example, for each day or year or second or even millisecond, we can associate a point on the infinite real number line. In this manner, we can think of time as ticking away right along our line. Since the number line never ends time would not seem to either under this association; and since the number line is infinite in the so-called negative direction as well, we can think of time as always being.
Yet like time, the real number line is created by man. Without any sentient beings to perceive these constructs, the argument breaks down. Whether time is infinite or not depends on whether there are minds to fathom such an elegant creation. So in a sense, time can be both infinite and finite. What? That is right. If nobody is there to witness the passing of time, then time does not exist and therefore cannot be deemed infinite. Yet if someone is there to perceive its passing, time does not stop and thus can be considered infinite, or having no end.
If there is anything we can take out of this weighty discussion, it would have to be that the only really important thing is the current moment, as the past is dead and the future is unborn. Whether we consider time infinite or finite is not so important as whether we stay present in the current moment, unburdened by either past or future inconveniences. From this perspective, whether time be viewed as infinite or not, we can rest assured that the eternal present is more valuable than either of time's two faces, and only in this state can we appreciate this extraordinary man-made construct.

integration

when the derived function or diffrential coefficient of a function is known,then the aim to find the function itself can be achieved.The tecnique or method to find such a funtion whose derivative is given involves the inverse process of diffrentiation called anti derivation or integration

Ellipse

Ellipse.

In continuation of the "Why Study Math" series of articles, here we look at another conic section: the ellipse. The four conic sections, in order from most popularly known to least, are the circle, the ellipse, the parabola, and the hyperbola. Remember that these shapes can all be obtained by slicing a right circular double-napped cone with a plane. As a visual exercise, picture an ice cream cone-without the ice cream-upside down standing on a table. This is a single-napped right circular cone. (To get a double-napped cone, add another cone on top, right-side up, balanced at the point.) To get the circle, take an imaginary plane (picture a piece of paper) and intersect the cone parallel to the base. The plane has just cut out a circle on the cone. Similarly, to get the ellipse tilt the plane slightly up or down and intersect it with the cone. What you have then is an elongated circle, or ellipse.

Probably the most famous application of the mathematical curve called an ellipse is in the description of planetary orbits. Johannes Kepler, the famous German mathematician and astronomer, used the position of the planet Mars and the sun to work out the orbit of the earth. After twenty years of painstaking work and analysis, Kepler was finally able to put forth his three planetary laws of motion. The first of these laws states correctly that the planets move about the sun in elliptical orbits. This was a revolutionary breakthrough which finally put an end to the Copernican idea of circular orbits.

Even though some might know that the planets revolve in elliptical orbits about the sun, a far less common application of this conic section is in machinery. The ellipse finds itself intricately involved in the manufacture of cams, which are rotating pieces of machinery that serve to transform rotating motion into up-and-down or back-and-forth motion. Examples of this are seen in the sewing machine, which uses the cam to generate up-and-down motion of the sewing needle. The punch press is another example that utilizes the cam. This machine is used in generating dies for the manufacture of metal objects. Because of the features of the ellipse, the punch press can function to produce all kinds of intricate metal objects running the gamut from rifle barrels to triggers to nuts and bolts to wire.

Of course, let us not forget the use of the cam in the automobile engine. The car engine has to be one of the most important inventions of all time. Because of knowledge of the ellipse, man was able to design the engine, relying on the cam and camshaft to generate the up-and-down motion from the elliptical cams moving in a rotary manner. This up-and-down motion is intricately involved in the complicated tasks of the internal combustion engine. Not bad for a simple mathematical idea such as the ellipse!

So the next time you hop in that new spit-shined Mercedes of yours and start to rev the engine, remember that had it not been for the study and application of the ellipse, you might be picking up your sexy date in a horse and buggy. Till next time...
Joe Pagano