From that title that as a student english is very important especially for mathematics education. but its so embarrasing that a student have been has a competent for it. For the example on three times exam I only get score which still under the standard. It prove that I must increase my english competent. In fact, English is not hard, but only us which stiil less on practice so we difficult on english. English is very important for us. It is amust that we must study english hard. In education area like mathematics education english become one of the language which is used on teaching learning process.
Not only for lecturing, but also for high schools and elementary school even today english also become one of the subject on kindergarten. It prove that how important of english for us. Its embarrasing that a student can’t mastering english. Our child or grandchild next maybe must have competent of english since child because five or ten years to go english maybe has used for daily language in every country.
Books, magazine, even music which using english language can be a media of practicing english. More practice english can increase our english ability. Sometimes when we listening english music involuntary we try to imitating it and try to understanding the music by translating the lyrics by dictionary or so on. Then involuntary our english will increase. Our vocabulary collection will more and more
As we know that now is the globalization era. In this era english is used for international language. English is very important for us. And as a student, it is amust that having a competent for english. And on mathematics education english also used for daily communication. We can going around the world with english. Not nly that, english also used for teaching learning process. Today english usedsince on elementary school even on kindergarten.
What should be done in mathematics education students in the English language?
1. Learn every day
Try to allocate some time each day to learn English. Ideally the brain when we are able to receive well. Better to study 30 minutes per day than 3 hours per week. If it can provide time-per, try to share a 2 or 3 sessions. For those who work in office, may have only a few hours as in the rest. Most important is that we (students in mathematics education) can take the time to learn English even though the goods while.
2. Review regularly
Students repeat each material already learned several times. To give time to the brain for consider materials, but make sure that the distance of each material is not too long, for example, more than a few weeks. If not, students may concern forget what is learned. And ensure students have understood the content of the material before proceeding to the next.
3. Focus on things of interest
Once the students have to understand the basics of the English language, both flee practice reading / writing / speaking on matters of interest. In this way will be easier to remember words, phrases and grammatical. Because basically if we like something it will be easier to apply. For example through music. If you like to sing but not too interested in the English language, please start looking for songs that speak English well and we like singer well as voice and her or his face. If we pleased with the track, we will try to understand the meaning of music. Well, indirectly we have favor with the English language because that song.
4. Raise read books, articles, writing in the English language
At the beginning of the reading will have a lot of vocabulary that students do not know. Do not give up easily. interpret each word with the help of the dictionary, and write the meaning of the word underneath. If done continuously in a few weeks then we will stop to open the dictionary every 2 minutes to read any posts in kind.
5. Note sounding words
Indeed, sometimes very difficult to say a word the English language well, but not does not mean impossible. Slang will not be lost, but try to pay attention to pronunciation. The first must do is control of the alphabet, and then note that phonetik often included in the dictionary.
6. Raise vocabulary
Students spend approximately 15 minutes each day to learn new vocabulary. Can repeat with vocabulary obtained from the literature, tried consider song lyrics, or attempt to catch the film favored dialogue. Write a vocabulary that has been learned in a special book to write. With the vocabulary will not be lost.
7. Try write in English
No direct means must write articles or works of literature. Self-expression short sentences, followed by a short paragraph. Then try any posts in their own corrections. Do not always rely on Word Spelling Check, because this function can not be relied upon to check the grammar error.
Self-discipline and follow basic grammar rules with the patient. No need to hurry to write the sentence that is long and complex. Start with a short sentence with a simple vocabulary. For example in the task of the English language lecturers. Try re-write a story or conversation in the video that was shown when the lecturers teaching the English language course. Or try to write back to text speak Indonesian in the English language.
For increasing my english, I must reading more book, I must increasing practising listening, writting, and speaking skill. I still have a differenting on vocabulary. My vocabulary skill is still bad. I must getting more collection of words. And I must practising to translate some article or even book for increasing my vocabulary collection. From the statement brfore, we must read more books, magazine, and so on, and also we must try to note toaounding words, raise vocabulary and etc to increase our english ability and maybe we will success with english.
Tuesday, June 2, 2009
Sunday, May 24, 2009
What I Have Done and What I Will Do About English for Mathematics
English is one kind of subject which be taught on my lecture. Now on the 2nd semester, I get English 2 subject which be delivered by Mr. Marsigit. By this paper I will tell about my experience about english for mathematics and what will I do about english mathematics. English is very important for our life. English used to international language in almost country. This is my experience about my english for mathematics.
The first is listening skill, I like music not only indonesian music but also foreign music so I usually listening music especially music on english language. I try to understanding the song by translate the lyrics. It can make my english ability increase. And when I saw a movie on english language I heard it and I try to understanding the way of the movie. Although I can’t understand what the meaning of the dialogue.
Then the speaking skill, I like repeat what the singer say by saw the lyrics of the song. I read carefully and sometimes I sounding it. I believe that it can increase my speaking skill on english.
And the last is reading skill, sometimes I read textbook or magazine which be written on english. I also like playing games and sawing international football match on english language, so that I can increase my vocabulary.
What I will do on next is I will practice my speaking, because I will become a teacher so I must have speaking skill. My speaking skill is still bad, so that I need more practice. Not only that, I also will increase my vocabulary. I got difficulty on vocabuary, because I only have a few meaning word that I know. I must attempt to search more difficult words and translate it. Not only that, I also got difficulty on tenses. Tenses can help me on speaking, so I think tenses is very important thing on english. I also insrease my reading skill by reading more book or magazine, see a foreign movie and go to internet café for searching information about english for mathematics.
The first is listening skill, I like music not only indonesian music but also foreign music so I usually listening music especially music on english language. I try to understanding the song by translate the lyrics. It can make my english ability increase. And when I saw a movie on english language I heard it and I try to understanding the way of the movie. Although I can’t understand what the meaning of the dialogue.
Then the speaking skill, I like repeat what the singer say by saw the lyrics of the song. I read carefully and sometimes I sounding it. I believe that it can increase my speaking skill on english.
And the last is reading skill, sometimes I read textbook or magazine which be written on english. I also like playing games and sawing international football match on english language, so that I can increase my vocabulary.
What I will do on next is I will practice my speaking, because I will become a teacher so I must have speaking skill. My speaking skill is still bad, so that I need more practice. Not only that, I also will increase my vocabulary. I got difficulty on vocabuary, because I only have a few meaning word that I know. I must attempt to search more difficult words and translate it. Not only that, I also got difficulty on tenses. Tenses can help me on speaking, so I think tenses is very important thing on english. I also insrease my reading skill by reading more book or magazine, see a foreign movie and go to internet café for searching information about english for mathematics.
Tuesday, January 13, 2009
THE HISTORY OF MATHEMATICS
Mathematic
Mathematic (Greek : μαθηματικά – mathēmatiká) is generally affirmed as a pattern research from structure, change, and room; someone may say that is research of numbers. On formalist view, mathematic is inspected the axioms which affirm the abstract structure used symbolic logic and notation of mathematic; other view is drawn on mathematic philosophy.
The specific structure whish been researched by Mathematician often coming from Science, generally in Physic, but mathematic also affirmed and investigate the structure to know the caused inside only until true science, because structure may providing, to occurrence, unifier generalizing for some chapter, or appliance assist for the habit calculation. Finally, many mathematician study the subject done their the aesthetic only, see the true science as a art shape than practical science or terapan.
The History of Mathematic
The History of Mathematic started when people must note more than one. The tribe of ancient Nomaden count and noting livestock folk though they do not have number system written. For counting, they collecting seed and gravel and including it into the sack. For big number, they used finger to symbolizing the number of 10 and 20. They developing number concept as separated from device of calculating object. In the early middle ages, swipoa from east emerge in Timur Tengah. The appliance in the form of box framework with seeds on a bar of number. Swipoa or Abacus now still used widely in East Asia and Timur Tengah.
Anything That Could I Found About Mathematic Concepts, Problem Of Mathematics, And Solution Of Mathematics At Ancient Times Which Still Wearied Until This Time.
Abul Wafa Muhammad Al Buzjani, inventor of the base of Trigonometri Formula.
The feathers of ancient Islamic tempo is marked by the hoisterous of science tradition. The Moslems masters, specially who stand on Baghdad and Andalusia, playing the interesting part for grow and expanding the doctoral science, mathematic, chemist, and other science which still expanding until this time. Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani, is one of many Moslem scientist who participate to expand the past time science. He notes as an expert of science on mathematic and astronomy. He help many sciences privately to expand many interesting theory on mathematic, especially geometry and trigonometry. On geometry, he gave significant contribution to resolving problems of geometry with compass; equivalent construction for any problem; comon polyhedral; a half side hexagon construction from isosceles triangle; parabola construction by dot and solution of geometry for equation.
The Logic of Mathematic
The logic of mathematic is the branch of Logic and mathematic which containing logic mathematic study and the application of the study for another subjects out of mathematic. The logic of mathematic related with computer science and the logic philosophy. The special theme on the logic of mathematic such as the power of expressive from formal logic and the power of deductive from formal verification system. The logic of mathematic often divided into the branches of gathering theory, model theory, recurcy’s theory, verification theory, and constructive theory. This subjects has the same base of logic.
Logic
Logic was coming from ancient Greek word λόγος (logos) which means the result of consideration of mind which is phrased by word and expressed by language. As a science, logic called by logike episteme (logica scientia) or logical science (science) which study about efficiency of thinking diametrical, precise, and regularly. Logic which used here could means with sensibility.
Logic started since Thales (624 BC - 548 BC), the first Greek philosopher who leaving of fable, takhayul, and spurious stories and looking away to kindness mind to solving the secret of universe. Aristoteles then defining logic as a science, which then called logica scientia. Aristoteles said that Thales conclude that water is arkhe of universe with the reason that water is soul of life.
On 370 BC – 288 BC Theophrastus, the pupil of Aristoteles become master of Lyceum, continuing the development of logic. The term of Logic for the first time defined by Zeno from Citium 334 BC – 226 BC the exponent of Stoa Clan. The systematic of logic happened on Galenus era (130 C – 201 C) and Sextus Empricius 200 C, two medical doctor who develop logic with applying the geometry method.
Porohysus (232 – 305) making a preface (eisagoge) for Categoriae, one of the Aristoteles book. Boethius (480 – 524) translated Eisagoge Porphyrius into Latin Language and adding the comments. Johanes Damascenus (674 – 749) publishing Fons Scientieae.
Ibnu Ismail al Jazari, The inventor of Modern Robotika Concept
Al Jazari giving an interesting contribution for science in the world specially on Mathematic and Physic. Water pump machine which presented on his book, become the one of inspirational masterpiece. The ancient society has exploiting a lot of thing to get water. That is, Shaduf and Saqiya. Shaduf is consist of long log which sustained between two pillars with horizontal wood log. While Saqiya is animal machine energetic. Mechanism as central as consisting of two tooth. The animal energy which used is ass or camel.
The Theorem of Pythagoras
On mathematic, Theorem of Pythagoras is relation on Euclid between three sides of isosceles triangle. This theorem called by philosopher and Greek mathematician on 6th century that is Pythagoras. Pythagoras didn’t the inventor of this theorem but he is the first people who proved this theorem mathematically. In the fact, this theorem has been founded many years before Pythagoras born. The facts of this theorem has known by mathematician from India, Greek, Tionghoa, and Babylonia.
Anything That Could I Found About Mathematic Concepts, Problem Of Mathematics, And Solution Of Mathematics At Ancient Times Which Didn’t Wearied By This Time.
The Oldest Calculator
The ancient Abacus from Salamis Island in Greek in the form of block of marmer as long as 1,5 metre and estimated by have been used on a temple by all money changer. This article enlisting number values and currency name like drachma, talent, and obol.
Sabak Numerator Of Romawi
Since wearing with using gravel which residing in to the top and bottom of winnow line marked by Romawi number according to the columns. Every gravel in the bottom of line in column on extreme right counting as a unit, and every gravel in the up of line valued by five. If the count valued as 10, a gravel bring in to the right. The table in the bottom view the count equal to 256.317 sheeps.
Anything That Could I Found About Mathematic Concepts, Problem Of Mathematics, And Solution Of Mathematics At Ancient Times Which Has No Relation With Mathematic.
Open-ended Problem
Like another science like social sciences, problems or any question on mathematics can classified by 2 parts. First is the problems of closed problems. And the second is problems of open problems. That during this time is taught on many schools is problems of closed mathematics problems. Where really on the solving of the mathematics closed problems, procedure which used almost can said standard. While, open mathematics problems almost doesn’t touched, almost never comes and be assumed for the process of mathematics studied. Open problems can divide by two kinds that is open ended problems, and pure open problems. Open ended problems can divide again by : 1) Problems with one answer and many solving, and 2) problems with many solving and also have many answer.
References :
http://id.wikipedia.org/wiki/Logika
http://id.wikipedia.org/wiki/Logika_matematika
http://id.wikipedia.org/wiki/Matematika
http://arifperdana.wordpress.com/
http://id.wikipedia.org/wiki/Teorema_Pyhtgoras
http://www.rumahislam.com/
http://mathematicse.wordpress.com/
Mathematic
Mathematic (Greek : μαθηματικά – mathēmatiká) is generally affirmed as a pattern research from structure, change, and room; someone may say that is research of numbers. On formalist view, mathematic is inspected the axioms which affirm the abstract structure used symbolic logic and notation of mathematic; other view is drawn on mathematic philosophy.
The specific structure whish been researched by Mathematician often coming from Science, generally in Physic, but mathematic also affirmed and investigate the structure to know the caused inside only until true science, because structure may providing, to occurrence, unifier generalizing for some chapter, or appliance assist for the habit calculation. Finally, many mathematician study the subject done their the aesthetic only, see the true science as a art shape than practical science or terapan.
The History of Mathematic
The History of Mathematic started when people must note more than one. The tribe of ancient Nomaden count and noting livestock folk though they do not have number system written. For counting, they collecting seed and gravel and including it into the sack. For big number, they used finger to symbolizing the number of 10 and 20. They developing number concept as separated from device of calculating object. In the early middle ages, swipoa from east emerge in Timur Tengah. The appliance in the form of box framework with seeds on a bar of number. Swipoa or Abacus now still used widely in East Asia and Timur Tengah.
Anything That Could I Found About Mathematic Concepts, Problem Of Mathematics, And Solution Of Mathematics At Ancient Times Which Still Wearied Until This Time.
Abul Wafa Muhammad Al Buzjani, inventor of the base of Trigonometri Formula.
The feathers of ancient Islamic tempo is marked by the hoisterous of science tradition. The Moslems masters, specially who stand on Baghdad and Andalusia, playing the interesting part for grow and expanding the doctoral science, mathematic, chemist, and other science which still expanding until this time. Abul Wafa Muhammad Ibn Muhammad Ibn Yahya Ibn Ismail al-Buzjani, is one of many Moslem scientist who participate to expand the past time science. He notes as an expert of science on mathematic and astronomy. He help many sciences privately to expand many interesting theory on mathematic, especially geometry and trigonometry. On geometry, he gave significant contribution to resolving problems of geometry with compass; equivalent construction for any problem; comon polyhedral; a half side hexagon construction from isosceles triangle; parabola construction by dot and solution of geometry for equation.
The Logic of Mathematic
The logic of mathematic is the branch of Logic and mathematic which containing logic mathematic study and the application of the study for another subjects out of mathematic. The logic of mathematic related with computer science and the logic philosophy. The special theme on the logic of mathematic such as the power of expressive from formal logic and the power of deductive from formal verification system. The logic of mathematic often divided into the branches of gathering theory, model theory, recurcy’s theory, verification theory, and constructive theory. This subjects has the same base of logic.
Logic
Logic was coming from ancient Greek word λόγος (logos) which means the result of consideration of mind which is phrased by word and expressed by language. As a science, logic called by logike episteme (logica scientia) or logical science (science) which study about efficiency of thinking diametrical, precise, and regularly. Logic which used here could means with sensibility.
Logic started since Thales (624 BC - 548 BC), the first Greek philosopher who leaving of fable, takhayul, and spurious stories and looking away to kindness mind to solving the secret of universe. Aristoteles then defining logic as a science, which then called logica scientia. Aristoteles said that Thales conclude that water is arkhe of universe with the reason that water is soul of life.
On 370 BC – 288 BC Theophrastus, the pupil of Aristoteles become master of Lyceum, continuing the development of logic. The term of Logic for the first time defined by Zeno from Citium 334 BC – 226 BC the exponent of Stoa Clan. The systematic of logic happened on Galenus era (130 C – 201 C) and Sextus Empricius 200 C, two medical doctor who develop logic with applying the geometry method.
Porohysus (232 – 305) making a preface (eisagoge) for Categoriae, one of the Aristoteles book. Boethius (480 – 524) translated Eisagoge Porphyrius into Latin Language and adding the comments. Johanes Damascenus (674 – 749) publishing Fons Scientieae.
Ibnu Ismail al Jazari, The inventor of Modern Robotika Concept
Al Jazari giving an interesting contribution for science in the world specially on Mathematic and Physic. Water pump machine which presented on his book, become the one of inspirational masterpiece. The ancient society has exploiting a lot of thing to get water. That is, Shaduf and Saqiya. Shaduf is consist of long log which sustained between two pillars with horizontal wood log. While Saqiya is animal machine energetic. Mechanism as central as consisting of two tooth. The animal energy which used is ass or camel.
The Theorem of Pythagoras
On mathematic, Theorem of Pythagoras is relation on Euclid between three sides of isosceles triangle. This theorem called by philosopher and Greek mathematician on 6th century that is Pythagoras. Pythagoras didn’t the inventor of this theorem but he is the first people who proved this theorem mathematically. In the fact, this theorem has been founded many years before Pythagoras born. The facts of this theorem has known by mathematician from India, Greek, Tionghoa, and Babylonia.
Anything That Could I Found About Mathematic Concepts, Problem Of Mathematics, And Solution Of Mathematics At Ancient Times Which Didn’t Wearied By This Time.
The Oldest Calculator
The ancient Abacus from Salamis Island in Greek in the form of block of marmer as long as 1,5 metre and estimated by have been used on a temple by all money changer. This article enlisting number values and currency name like drachma, talent, and obol.
Sabak Numerator Of Romawi
Since wearing with using gravel which residing in to the top and bottom of winnow line marked by Romawi number according to the columns. Every gravel in the bottom of line in column on extreme right counting as a unit, and every gravel in the up of line valued by five. If the count valued as 10, a gravel bring in to the right. The table in the bottom view the count equal to 256.317 sheeps.
Anything That Could I Found About Mathematic Concepts, Problem Of Mathematics, And Solution Of Mathematics At Ancient Times Which Has No Relation With Mathematic.
Open-ended Problem
Like another science like social sciences, problems or any question on mathematics can classified by 2 parts. First is the problems of closed problems. And the second is problems of open problems. That during this time is taught on many schools is problems of closed mathematics problems. Where really on the solving of the mathematics closed problems, procedure which used almost can said standard. While, open mathematics problems almost doesn’t touched, almost never comes and be assumed for the process of mathematics studied. Open problems can divide by two kinds that is open ended problems, and pure open problems. Open ended problems can divide again by : 1) Problems with one answer and many solving, and 2) problems with many solving and also have many answer.
References :
http://id.wikipedia.org/wiki/Logika
http://id.wikipedia.org/wiki/Logika_matematika
http://id.wikipedia.org/wiki/Matematika
http://arifperdana.wordpress.com/
http://id.wikipedia.org/wiki/Teorema_Pyhtgoras
http://www.rumahislam.com/
http://mathematicse.wordpress.com/
Tuesday, December 23, 2008
FOUNDATION OF MATHEMATICS
The Foundation of Mathematics consist of 2 part, that is Constant Foundation and Inconstant Foundation. The mean of Constant Foundation is implant the strong foundation on mathematic. For example, in English geometry is as the Foundation of Mathematic. While the Inconstant Foundation means that the foundation is epistemologic foundation. The knowledge learned about science.
Mathematics built as the foundation of critical idea that is synthetic apriory character. The figure who believe this foundation theory is Immanuel Kant.
Synthetic apriory means can explain something although never found before (idea). The opposite of the synthetic apriory is analytical synthetic. It means that mathematics appropriate with the law of identity.
Synthetic apriory for Immanuel Kant is a contradiction in idea, that is knowledge. While a contradiction an the heart make people like a ghost.
INTUITION
Intuition for common people is something about feeling in the heart, but intuition on mathematic is a container where mathematic placed. The person who believed about the theory is Brower. Brower said that the plan of intuition consist of 2 that is time and place. The idea about mathematic branched with time and place.
Plato said that Mathematic is only idea. Mathematic is only inside of the head (brain). Its only an idea. But his theory was opposed by Aristoteles. Aristoteles is a eksperimentalist, he said that mathematic is on the top of experience. Mathematic is come from experience, not only on the idea.
Mathematics built as the foundation of critical idea that is synthetic apriory character. The figure who believe this foundation theory is Immanuel Kant.
Synthetic apriory means can explain something although never found before (idea). The opposite of the synthetic apriory is analytical synthetic. It means that mathematics appropriate with the law of identity.
Synthetic apriory for Immanuel Kant is a contradiction in idea, that is knowledge. While a contradiction an the heart make people like a ghost.
INTUITION
Intuition for common people is something about feeling in the heart, but intuition on mathematic is a container where mathematic placed. The person who believed about the theory is Brower. Brower said that the plan of intuition consist of 2 that is time and place. The idea about mathematic branched with time and place.
Plato said that Mathematic is only idea. Mathematic is only inside of the head (brain). Its only an idea. But his theory was opposed by Aristoteles. Aristoteles is a eksperimentalist, he said that mathematic is on the top of experience. Mathematic is come from experience, not only on the idea.
Friday, November 28, 2008
PYTHAGORAS, IRRATIONAL NUMBER, AND PYTHAGORAS THEOREM
A. PYTHAGORAS
Pythagoras is a Greek mathematician at the same time ancient a philosopher for the 6th century. He is very influence for science especially in mathematics. One of his famous omission is Pythagoras Theorem which almost people have ever heard it. Pythagoras Theorem said that hypotenuse of right triangle is sum of square of 2nd other side from the right triangle. Because of his omissions in mathematics, he also called as “The Father of Number”.
One of the pupils which so called Hippasus said that √2 which is hypotenuse of isosceles triangle which having length each feet is 1 is the irrational number. However, Hippasus then murdered because Pythagoras cannot argue evidence raised by Hippasus.
Hippasus is a pupil of Pythagoras coming from Metapontum. He also a mathematician at the same time ancient Greek philosopher about the 6th century. He considered to be inventor of irrational number, especially prove that square root of 2 √2 is irrational number. Ironically, the invention exactly cause the death. Pythagoras argue existence of irrational number. Pythagoras and the other pupils assumed that all nmber are rational number and there is no irrational number. Hippasus prove this theorem by using reductio ad absurdum (prove by contradiction) proving number that it is irrational number. Pythagoras cannot argue this statement and assume that Hippasus is errant teaching follower so that he set mind on to engulf Hippasus.
B. IRRATIONAL NUMBER
Irrational number is a real number which cannot divided (result for its have never desisted). In this case, irrational number cannot expressed as a/b, with a and b as integer, and b unlike null. So irrational number is not rational number. The example for irrational number such as π, √2, and e number. Phi number (π) which during the time we recognizing, actually imprecise 3,14 but 3,1415926535897932…. Also √2 number which if we formulate becoming 1,41421356237309504880….And e number that is 2,71828182….
The irrational number can be proved with using reductio ad absurdum or in english called proof by contradiction. It is logic argument started with an assumption, then from the assumption found an absurd result, illogical, or contradictive, so the conclusion of the assumption will to be wrong valuable and the deny will become correct valuable. A mathematical statement sometime be proved by reductio ad absurdum that is by assuming the deny (negation) from the statement which will be proved, then from the assumption degraded a contradiction. When contradiction reachable logically, then the assumption have proven fault, so that the statement is correct.
Proved by contradiction or reductio ad absurdum is not wrong argument, but if done truly will be valid argument. If prove by contradiction yield a mistake, the mistake lay at the process degradation of contradiction, not at may of the prove.
The classical example for the prove by contradiction at ancient Greek era is prove that square root of two is irrational number (cannot expressed as comparison of integer). This statement is provable by the way of assuming on the contrary that 2 is rational number, so that can expressed as comparison of integer a/b in simplest fraction. But if a/b = √2, so a2 = 2b2.It means a2 is even number. Because square from odd number is not possibly even, then a is even number. Because a/b is simplest fraction, b surely anomalous (because fraction of even/even number still can be made moderate). But because a is even number (assume 2r = a, mean a2 = 4r2) is fold number of 4, and b2 is fold number of 2 (even). This mean b is also even number, and this is contradiction to conclusion before all that b surely anomalous. Because assumption early that 2 is rational number result the contradiction, the assumption surely wrong, and the deny (that 2 is irrational) is correct statement.
C. PYTHAGORAS THEOREM
One of the Pythagoras omission that very popular is Pythagoras Theorem. The theorem called as the ancient Greek mathematician and philosopher, he is Pythagoras. Pythagoras is not the inventor of the theorem but he is the first people who proved the truth of the theorem so he given appreciation with give name the theorem like his name.
This theorem express that summing up wide squares at foots a right triangles equal broadly squares in hypotenuses. Right triangle is triangle having a right angle (90o0); the foots are two sides which the bevels angular shapes, and hypotenuse is third side dealing with the right angle. The formula of this theorem is a2+ b2 = c2, where a and b is the sides of the right triangle, and c is the hypotenuse.
Pythagoras is a Greek mathematician at the same time ancient a philosopher for the 6th century. He is very influence for science especially in mathematics. One of his famous omission is Pythagoras Theorem which almost people have ever heard it. Pythagoras Theorem said that hypotenuse of right triangle is sum of square of 2nd other side from the right triangle. Because of his omissions in mathematics, he also called as “The Father of Number”.
One of the pupils which so called Hippasus said that √2 which is hypotenuse of isosceles triangle which having length each feet is 1 is the irrational number. However, Hippasus then murdered because Pythagoras cannot argue evidence raised by Hippasus.
Hippasus is a pupil of Pythagoras coming from Metapontum. He also a mathematician at the same time ancient Greek philosopher about the 6th century. He considered to be inventor of irrational number, especially prove that square root of 2 √2 is irrational number. Ironically, the invention exactly cause the death. Pythagoras argue existence of irrational number. Pythagoras and the other pupils assumed that all nmber are rational number and there is no irrational number. Hippasus prove this theorem by using reductio ad absurdum (prove by contradiction) proving number that it is irrational number. Pythagoras cannot argue this statement and assume that Hippasus is errant teaching follower so that he set mind on to engulf Hippasus.
B. IRRATIONAL NUMBER
Irrational number is a real number which cannot divided (result for its have never desisted). In this case, irrational number cannot expressed as a/b, with a and b as integer, and b unlike null. So irrational number is not rational number. The example for irrational number such as π, √2, and e number. Phi number (π) which during the time we recognizing, actually imprecise 3,14 but 3,1415926535897932…. Also √2 number which if we formulate becoming 1,41421356237309504880….And e number that is 2,71828182….
The irrational number can be proved with using reductio ad absurdum or in english called proof by contradiction. It is logic argument started with an assumption, then from the assumption found an absurd result, illogical, or contradictive, so the conclusion of the assumption will to be wrong valuable and the deny will become correct valuable. A mathematical statement sometime be proved by reductio ad absurdum that is by assuming the deny (negation) from the statement which will be proved, then from the assumption degraded a contradiction. When contradiction reachable logically, then the assumption have proven fault, so that the statement is correct.
Proved by contradiction or reductio ad absurdum is not wrong argument, but if done truly will be valid argument. If prove by contradiction yield a mistake, the mistake lay at the process degradation of contradiction, not at may of the prove.
The classical example for the prove by contradiction at ancient Greek era is prove that square root of two is irrational number (cannot expressed as comparison of integer). This statement is provable by the way of assuming on the contrary that 2 is rational number, so that can expressed as comparison of integer a/b in simplest fraction. But if a/b = √2, so a2 = 2b2.It means a2 is even number. Because square from odd number is not possibly even, then a is even number. Because a/b is simplest fraction, b surely anomalous (because fraction of even/even number still can be made moderate). But because a is even number (assume 2r = a, mean a2 = 4r2) is fold number of 4, and b2 is fold number of 2 (even). This mean b is also even number, and this is contradiction to conclusion before all that b surely anomalous. Because assumption early that 2 is rational number result the contradiction, the assumption surely wrong, and the deny (that 2 is irrational) is correct statement.
C. PYTHAGORAS THEOREM
One of the Pythagoras omission that very popular is Pythagoras Theorem. The theorem called as the ancient Greek mathematician and philosopher, he is Pythagoras. Pythagoras is not the inventor of the theorem but he is the first people who proved the truth of the theorem so he given appreciation with give name the theorem like his name.
This theorem express that summing up wide squares at foots a right triangles equal broadly squares in hypotenuses. Right triangle is triangle having a right angle (90o0); the foots are two sides which the bevels angular shapes, and hypotenuse is third side dealing with the right angle. The formula of this theorem is a2+ b2 = c2, where a and b is the sides of the right triangle, and c is the hypotenuse.
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