Sabtu, 19 Desember 2009
MATHEMATICAL RESEARCH
To make or create a research, we need some ways that we should we do included in mathematical research. The first way, you need many references to support your research. One of references is browsing internet. Internet is broad network in the world. It save many information that can help you make easier do everything. You can find out many things in there. So, you can collect much information about your research from it to complete your research. And then, the second way, you should make a discourse about mathematics like The Nature of Mathematics that content of definition of mathematics. In the discourse, you should explain the definition of mathematics according to your own thinking. There are many definitions about mathematics, but everyone have different in make a definition of mathematics. They have different opinion and it according to their thinking severally and their experiences in learn mathematics. Such as, “Mathematics is a science or system which is constructed by deductive method composing definition, axioms, and theorems in such away that there is no contradiction in side. It is an example of formal mathematics or axiomatic mathematics. For the third way, you find out the definitions of mathematics. By definition of mathematical system, you will create a new theorem which is not available before yet. But to make it, you should construct mathematics system that have available. So, from much information about mathematical system, you can combine all if information becomes a theorem. After that, you can give your theorem’s name; in order to it can remember by everyone easily. There are some examples of mathematical system. Such as, Group Theory, Ring Theory, Fied theory, Numbers Theory, Euclidean Geometry, Non-Euclidean Geometry, Number System, and many more. You can take one of them to be a research. In make mathematical research, you must have a purpose of the research. It was done to clarify the research conducted. For example, the aim of mathematical research is to examine and establish new system of mathematics. Here, examine means to test existing theories of previous mathematicians. Whereas, establish means you create a new theory of mathematics that has not existed before. Therefore, you create a new something in mathematics. There are main aspects of mathematics, namely definition, axioms, theorems, and rule/law/procedure in mathematics. And then there are some factors which are supporting your research. For the first is your knowledge of mathematics. It will assist all to make a research like the matters learned in mathematics. You can apply it to help you develop your research. And then, the factor is your knowledge of the history of mathematics. History of some mathematicians theorems produced by mathematicians can expand your mathematical research. Learning from the history and the philosophy of mathematics also can create a new theorem. The theorem consists of two divisions; there is complete system of mathematics, but it is not consistent. And another is consistent system of mathematics, but it is not complete. But the proof of theorem is incompleteness. Other factor is your knowledge of the mathematicians. Mathematicians can be supporter to establish your spirit to create a new thing that useful for everybody in the world someday for study mathematics. Then the last is your experiences of developing mathematics. Many ways that can do to develop your skill in mathematics. Like a mathematical method in study mathematics. The steps of mathematical research consists of some step that can you do. First, in depth study references, then identify and formulate the problems. After that, develop method of research. And then process of research. Next is finding, then you can publish it to Journal.
Minggu, 06 Desember 2009
UNY Becomes the World Class University
UNY agreed to go to WCU as declared by the Chief of UNY in every opportunity or in the newspapers. These ideals are great ideals, lofty and noble. An effort to realize a university becomes world-class university concept (World Class University) requires many steps that must be done. One of them is increase the student competences pass through authority of foreign languages, especially English. The colleges usually seek for authority of foreign languages to students pass through using of English as the medium of language in a subject. To create UNY become a WCU is a long and hard struggle, so that needed a strategic and mature plan, and continuous and sustainable. Several steps and things that need be prepared:
1. the strong and complete intention from all of academic community. There is an intention that UNY will be concern to WCU, need to be socialized throughout the university components, so that appear optimism that is the capital base and a strong base for further steps.
2. Define a World Class University (WCU) and continued the socialization.
3. Explain the definition of WCU in a work program that measured in the time limit and specific achievements, such as: yearly or 3 yearly.
4. Cultivate all of the resources, tools, and available systems. The need for renewal and revision of systems of locally based, such as: writing and thesis examination is possible in English, renewal of regulations towards international discourse.
5. Increased cooperation between universities from within and abroad and with the community. This cooperation should not just more MOU, but with concrete action, for example: student exchange, delivery of academic staff, research cooperation.
But UNY also have to spend much money to support WCU programs. The money can use for finance the lecturer or someone that can support the programs. UNY can facilitate some lecturer to continued their study in abroad to support English learning. But in UNY only two majors that will be change into WCU now. There are mathematics education majors and accounting education majors. But not all of majors change to WCU yet. So, hope in order to the WCU programs can be successful, so that all of majors in UNY can change to World Class University.
1. the strong and complete intention from all of academic community. There is an intention that UNY will be concern to WCU, need to be socialized throughout the university components, so that appear optimism that is the capital base and a strong base for further steps.
2. Define a World Class University (WCU) and continued the socialization.
3. Explain the definition of WCU in a work program that measured in the time limit and specific achievements, such as: yearly or 3 yearly.
4. Cultivate all of the resources, tools, and available systems. The need for renewal and revision of systems of locally based, such as: writing and thesis examination is possible in English, renewal of regulations towards international discourse.
5. Increased cooperation between universities from within and abroad and with the community. This cooperation should not just more MOU, but with concrete action, for example: student exchange, delivery of academic staff, research cooperation.
But UNY also have to spend much money to support WCU programs. The money can use for finance the lecturer or someone that can support the programs. UNY can facilitate some lecturer to continued their study in abroad to support English learning. But in UNY only two majors that will be change into WCU now. There are mathematics education majors and accounting education majors. But not all of majors change to WCU yet. So, hope in order to the WCU programs can be successful, so that all of majors in UNY can change to World Class University.
Kamis, 29 Oktober 2009
EVOLVING ENGLISH IN STUDY OF MATHEMATICS
Logarithms usually find out the exponential problem if known main numbers and product of exponential. There are several properties of logarithms. First, logarithms based b of x equals to y, b as based. To find out the value of x, can solve by b power y, y as the power. For example, logarithms based ten of one hundred equals to x. If we use the first properties of logarithms, so ten as based power x equals to one hundred. So that, we can find the value of x. the value of x is the positive numbers. In the same ways, if in fraction form, so the value of x is negative numbers. Second, logarithms based e of x equals to ln e, e as irrational numbers. ln e usually called by natural logarithms. Except that, there are three properties again about logarithms especially for characteristics in calculate about logarithms. First, logarithms based b of M times N, so the solution is logarithms based b of M plus logarithms based b of N. So that, in logarithms multiplication form can change to addition form. The same way, if it division form can change to subtraction form. So, logarithms based b of M divided by N equals to logarithms based b of M minus logarithms based b of N. And the last, logarithms based b of x power n. So, the solution is n as power can change as multiple numbers. So that, it equals to n times logarithms based b of x.
In common factors and grouping, we will recognize about product and factors. For example, three times five equals to fifteen. Three and five are factors, but fifteen is product of factors. Factoring means to have all factors are prime numbers. Usually to find The Greatest Common Factor (GCF), we have given two numbers. There are several steps that have to do. For the first step, find out the factors. The factors consist of prime numbers. After that, make it to be a simple form by use exponent. For example, the factors of forty five are five times three times three. If we write like that, it can so long. So, we can make it to be simple form. It will be three square. Then, find out the same factors from two numbers. And to solve it, look for the same factors that have the smallest exponent. After get it, multiply the factors. So, the product of multiply of factors is the greatest common factors.
Trig function usually related with triangle especially right triangle and angle that available in triangle. To solving problem in trig function, you need to know the value of sides in triangle to find measure of an angle. There are six basic in trig function. They are sine, cosine, tangent, cosecant, secant, and cotangent. The trig function defined by sides of a triangle and angle being measure. If there is a right triangle and it has an angle, example theta as an angle in a right triangle, so the sides in front of theta called by OPP (side opposite theta). And the sides beside of theta called by ADJ (side adjacent to theta). And the sides called by HYP (hypotenuse of theta). So, the six trig functions for the theta for sine of theta equals to OPP over HYP, for cosine of theta equals to ADJ over HYP, and for tangent of theta equals to OPP over ADJ. for cosecant, secant, and cotangent of theta, we can find by folding over from sine, cosine, and tangent. Cosecant is folding over of sine, so cosecant of theta equals to HYP over OPP. Secant is folding over of cosine, so secant of theta equals to HYP over ADJ. Then cotangent is folding over of tangent, so cotangent of theta equals to ADJ over OPP. For make us easy to remember it, we can called the short name is SOH CAH TOA.
One way to find factors polynomial is use algebraic long division. To find out factoring polynomials, we can use arranged division. We can find out the factors of polynomial. We can use algebraic long division to calculate polynomials that have more than one degree equation. So, we can solve polynomials that have two, three, etc degree by use algebraic long division. For example, x cube minus seven x minus six divided by x minus three. We can solve this problem by use arranged division have learned in elementary school. In x cube minus seven x minus six, the second degree term no has value or zero. X cube divided by x minus three. The product is x square. Then x square multiply x minus three, so x cube minus three x square. Do the same step until get zero. Here x minus three as the factors. But it’s only one of them. For third degree equation have three roots. The degree of polynomial equation always limits the number of roots. For second degree equation always have two roots. For fourth degree equation have four or fewer roots. To solve long division for a third order polynomials are find a partial quotient of x square by dividing x into x cube to get x square, then multiply x square by the divisor and subtract the product from the dividend. Repeat the process until reach a remainder. Polynomials consist of odd and even degrees.
A function is an algebraic statement that provides a link between two or more variables. Use to find the value of one variable if you know the values of the others. For example, y equals to two x. If you know x, you can find y. So that, to solve this problem, we consider that the value of x is a numbers. Such as, if the value of x is five, so y equals to two times five. It’s ten. The value of y is ten. Function is relation in which each element of one set is paired with one and only one, element of the second set. There are two kinds of relations, equations and inequalities. For example, one plus five equals to six. It’s an equation. But it’s different for inequalities. For example, eight is more than five. Function of x usually called by f(x), f of x. f(x) equals to y. for example, y equals to three x plus four. Three x plus four called by function of x. So, y equals to f(x) equals to three x plus four. It is standard form of function of x. f(x) =3x+4. Many alphabets that can use for sign a function. If given an equation g(x) = x^2-3x+2 and x equals to five. So we can substitute the value of x have known into an equation. We will find out the product or the value of function.
Parallelogram has four sides. But it has special thing. If a quadrilateral is parallelogram, then opposite sides are parallel. If side AB is parallel to side CD and side AC is parallel to side BC. So, it’s called by parallelogram. (AB ) ̅ || (DC) ̅ , (AD) ̅ || (BC) ̅.
In common factors and grouping, we will recognize about product and factors. For example, three times five equals to fifteen. Three and five are factors, but fifteen is product of factors. Factoring means to have all factors are prime numbers. Usually to find The Greatest Common Factor (GCF), we have given two numbers. There are several steps that have to do. For the first step, find out the factors. The factors consist of prime numbers. After that, make it to be a simple form by use exponent. For example, the factors of forty five are five times three times three. If we write like that, it can so long. So, we can make it to be simple form. It will be three square. Then, find out the same factors from two numbers. And to solve it, look for the same factors that have the smallest exponent. After get it, multiply the factors. So, the product of multiply of factors is the greatest common factors.
Trig function usually related with triangle especially right triangle and angle that available in triangle. To solving problem in trig function, you need to know the value of sides in triangle to find measure of an angle. There are six basic in trig function. They are sine, cosine, tangent, cosecant, secant, and cotangent. The trig function defined by sides of a triangle and angle being measure. If there is a right triangle and it has an angle, example theta as an angle in a right triangle, so the sides in front of theta called by OPP (side opposite theta). And the sides beside of theta called by ADJ (side adjacent to theta). And the sides called by HYP (hypotenuse of theta). So, the six trig functions for the theta for sine of theta equals to OPP over HYP, for cosine of theta equals to ADJ over HYP, and for tangent of theta equals to OPP over ADJ. for cosecant, secant, and cotangent of theta, we can find by folding over from sine, cosine, and tangent. Cosecant is folding over of sine, so cosecant of theta equals to HYP over OPP. Secant is folding over of cosine, so secant of theta equals to HYP over ADJ. Then cotangent is folding over of tangent, so cotangent of theta equals to ADJ over OPP. For make us easy to remember it, we can called the short name is SOH CAH TOA.
One way to find factors polynomial is use algebraic long division. To find out factoring polynomials, we can use arranged division. We can find out the factors of polynomial. We can use algebraic long division to calculate polynomials that have more than one degree equation. So, we can solve polynomials that have two, three, etc degree by use algebraic long division. For example, x cube minus seven x minus six divided by x minus three. We can solve this problem by use arranged division have learned in elementary school. In x cube minus seven x minus six, the second degree term no has value or zero. X cube divided by x minus three. The product is x square. Then x square multiply x minus three, so x cube minus three x square. Do the same step until get zero. Here x minus three as the factors. But it’s only one of them. For third degree equation have three roots. The degree of polynomial equation always limits the number of roots. For second degree equation always have two roots. For fourth degree equation have four or fewer roots. To solve long division for a third order polynomials are find a partial quotient of x square by dividing x into x cube to get x square, then multiply x square by the divisor and subtract the product from the dividend. Repeat the process until reach a remainder. Polynomials consist of odd and even degrees.
A function is an algebraic statement that provides a link between two or more variables. Use to find the value of one variable if you know the values of the others. For example, y equals to two x. If you know x, you can find y. So that, to solve this problem, we consider that the value of x is a numbers. Such as, if the value of x is five, so y equals to two times five. It’s ten. The value of y is ten. Function is relation in which each element of one set is paired with one and only one, element of the second set. There are two kinds of relations, equations and inequalities. For example, one plus five equals to six. It’s an equation. But it’s different for inequalities. For example, eight is more than five. Function of x usually called by f(x), f of x. f(x) equals to y. for example, y equals to three x plus four. Three x plus four called by function of x. So, y equals to f(x) equals to three x plus four. It is standard form of function of x. f(x) =3x+4. Many alphabets that can use for sign a function. If given an equation g(x) = x^2-3x+2 and x equals to five. So we can substitute the value of x have known into an equation. We will find out the product or the value of function.
Parallelogram has four sides. But it has special thing. If a quadrilateral is parallelogram, then opposite sides are parallel. If side AB is parallel to side CD and side AC is parallel to side BC. So, it’s called by parallelogram. (AB ) ̅ || (DC) ̅ , (AD) ̅ || (BC) ̅.
Sabtu, 23 Mei 2009
My Small Dictionary about English for Mathematics
1. Sudut : Angle
2. Persegi : Square
3. Persegi panjang : Rectangle
4. Lingkaran : Circle
5. Tegak lurus : Perpendicular
6. Sebanding : Proportional
7. Keliling : Circumference
8. Akar : Root/Radical
9. Pangkat : Exponent/ Power
10. Kubus : Cube
11. Kubik : Cube
12. Sejajar : Parallel sides
13. Alas : Base
14. Tinggi : Altitude
15. Lancip : Acute
16. Tumpul : Obtuse
17. Sebangun : Similar
18. Sama dan sebangun : Congruent
19. Bola : Sphere
20. Luas : Area
21. Panjang : Length
22. Lebar : Width
23. Rusuk : Lateral edges
24. Sepusat : Concentric
25. Garis singgung : Tangent
26. Berpotongan : Intersection
27. Definisi : Concept
28. Bukti : Proof
29. Arsir : Shadow
30. Kurva : Curve
31. Permukaan : Surface
32. Puncak : Top
33. Pernyataan : Argument
34. Ruang : Space
35. Himp. Bagian : Subset
36. Trapesium : Trapezoid
37. Jari-jari : Radius
38. Derajat : Degree
39. Bidang datar : Plane
40. Bil.bulat : Integer
41. Bil.khayal : Imaginer
42. Persamaan : Equation
43. Himp.penyelesaian : Set solve
44. Cabang : Branch
45. Melambungkan : Throw
46. Persekutuan : Common
47. Perkalian : Multiple
48. Pembagian : Divided
49. Volume : Volume
50. Garis lurus : Straight line
51. Segitiga siku-siku : Right triangle
52. Segitiga sama sisi : Equilateral triangle
53. Garis potong : Secant
54. Juring : Sector
55. Sisi miring : Apothema
56. Bersilangan : Crossing
57. Rata-rata : Mean/Average
58. Membulatkan : Rounded
59. Kosong : Empty/Blank
60. Bergeser : Move/Transform
1. Sudut : Angle
2. Persegi : Square
3. Persegi panjang : Rectangle
4. Lingkaran : Circle
5. Tegak lurus : Perpendicular
6. Sebanding : Proportional
7. Keliling : Circumference
8. Akar : Root/Radical
9. Pangkat : Exponent/ Power
10. Kubus : Cube
11. Kubik : Cube
12. Sejajar : Parallel sides
13. Alas : Base
14. Tinggi : Altitude
15. Lancip : Acute
16. Tumpul : Obtuse
17. Sebangun : Similar
18. Sama dan sebangun : Congruent
19. Bola : Sphere
20. Luas : Area
21. Panjang : Length
22. Lebar : Width
23. Rusuk : Lateral edges
24. Sepusat : Concentric
25. Garis singgung : Tangent
26. Berpotongan : Intersection
27. Definisi : Concept
28. Bukti : Proof
29. Arsir : Shadow
30. Kurva : Curve
31. Permukaan : Surface
32. Puncak : Top
33. Pernyataan : Argument
34. Ruang : Space
35. Himp. Bagian : Subset
36. Trapesium : Trapezoid
37. Jari-jari : Radius
38. Derajat : Degree
39. Bidang datar : Plane
40. Bil.bulat : Integer
41. Bil.khayal : Imaginer
42. Persamaan : Equation
43. Himp.penyelesaian : Set solve
44. Cabang : Branch
45. Melambungkan : Throw
46. Persekutuan : Common
47. Perkalian : Multiple
48. Pembagian : Divided
49. Volume : Volume
50. Garis lurus : Straight line
51. Segitiga siku-siku : Right triangle
52. Segitiga sama sisi : Equilateral triangle
53. Garis potong : Secant
54. Juring : Sector
55. Sisi miring : Apothema
56. Bersilangan : Crossing
57. Rata-rata : Mean/Average
58. Membulatkan : Rounded
59. Kosong : Empty/Blank
60. Bergeser : Move/Transform
Selasa, 14 April 2009
On Wednesday, March 25 2009, Mr. Marsigit explained about graph of quadratic equation. He told us how to design a graph. In drew a graph of quadratic equation, there are elements, the first is graph intersection point with fuse coordinate, second is coordinate top hyperbola point, and the last is equation of symmetry fuse. The value of x or roots that fulfilled quadratic equation depend on the value of discriminate .If D>0, so quadratic equation intersect fuse of x in two different point. If D=0, so quadratic equation intersect fuse of x in one point or tangency fuse of x. And if D<0, so quadratic equation not intersect fuse of x. Quadratic equation and quadratic function was different. Form quadratic equation , but form quadratic functions .
Mr. Marsigit also told us about how make a book. He had made many books. Started from book for junior high school, and now he is preparing a book for senior high school. He is so creative. The first method in made a book was made a curriculum. According to him, philosophy mathematics and junior high school was different. Mathematics spoke about pattern and relation. Mr. Marsigit also explained about Nature of Mathematics. Mathematics consists of:
• Pattern and relation
• Mathematics is a means of problem solving(mathematics should able to applied in living)
• Mathematics is a means of research
The Nature of Mathematics is tools for communication. With mathematics, we could communicate with human.
Mr. Marsigit also told us about how make a book. He had made many books. Started from book for junior high school, and now he is preparing a book for senior high school. He is so creative. The first method in made a book was made a curriculum. According to him, philosophy mathematics and junior high school was different. Mathematics spoke about pattern and relation. Mr. Marsigit also explained about Nature of Mathematics. Mathematics consists of:
• Pattern and relation
• Mathematics is a means of problem solving(mathematics should able to applied in living)
• Mathematics is a means of research
The Nature of Mathematics is tools for communication. With mathematics, we could communicate with human.
1. Get numbers of phi
The quadrature problem is the computation of phi, the ratio of the circumference of a circle to its diameter. We have seen that in the ancient orient the value of phi was frequently taken as three and for the Egyptian quadrature of the circle given in the Rhind papyrus, we have phi equals to three point one six. The first scientific attempt to compute phi, seems to be that of Archimedes with his achievement. To simplify matters, suppose we choose a circle with unit diameter. Now the (length of the) circumference of a circle lies between the perimeter of any inscribed polygon and that of any circumscribed polygon. According Archimedes, phi is between twenty two seventh or in decimal places, phi is given by three point fourteen. In the work are found same remarkable rational approximations to irrational square roots. The method of computing phi by using regular inscribed and circumscribed polygon is known as the classical method of computing phi. Except Archimedes, still more scientist attempt to compute the value of phi.
2. Get the formula of ABC
• Change all of segment to be a coefficient x
• Eliminate Constanta of left segment or both of joint minus with c/a
• Add both of joint with a half of quadrature from coefficient x
• Change the left join to be a complete quadratic
3. Find out the area
There are two lines equation. So, to find out the region bounded is the first lines equation should be equals to the second lines equation or y1=y2. After that, we will get the value of x. the value of x is the region bounded. Then to find out the area, we use the formula of integration with the region bounded among negative one until two. After calculate it, we will get result is negative thirteen sixth unit of area.
4. To decided the volume of cone
Cone is pyramid that have base plane curved circle. The volume of cone equals to the volume of pyramid. If known a cone with base radius r and altitude t, then to find the volume of cone equals to one third from the base’s area times the altitude. The base’s area equals to phi times the quadrature of radius. Thus, the volume of cone is one third from phi times the quadrature of radius times cone’s altitude.
5. To prove that in immaterial triangle then the totally of angel is one hundred eighty degree
The first, we make an immaterial triangle then make stretch of lines from point everywhere. For example, point of C collinear with AC. Then, exceed the point of C; make lines that parallel with AB. The angle of DCE equals to the angle of CAB because it’s opposite each other. The angle of BCE equals to the angle of ABC because it’s on both sides. The angle of ACB plus the angle of BCE plus the angle of ECD lie in one line equals to one hundred eighty degree, so the angle of ACB plus the angle of ABC plus the angle of CAB equals to one hundred eighty degree is proved.
6. To decided probability appear sum of figure more than six from two dices threw entirely
To make easier us to find out probability with make a table of probability. If there are two dices, then it has thirty six sample spaces. Whereas the probability appear two dices is twenty one. Thus, the probability appear figure more than six is twenty one over thirty six.
7. To decided the lines equation exceedingly (10,0) and tangent of circle
We should find the value of gradient. To find it, we should make equation inform Ax+By+C=0. To get equation like that, we should use roots of the equation known and the equation should be equals to zero. After that, to find the gradient, we use the formula is m= . So, the line equation also use the formula, the formula is . For the value of x and y, we used exceed point is ten and zero. Ten as x and zero as y. The equation can inform y equals to or the lines equation equals to zero.
8. To prove the theorem of Pythagoras
The Pythagorean Theorem only used for right triangle. In a right triangle, with sides a and b, and hypotenuse c, then power of c equals to power of a plus power of b. A right triangle is a triangle with one right angle has an angel ninety degree. And sides a and b perpendicular mutually. The simplest proof is an algebraic proof using similar triangles. Similar triangle has proportional sides.
9. To find out the sum of odd numbers two hundred first
With use arithmetic series, first term is one, with difference is two and there are one hundred terms. Then, sum of odd numbers two hundred first equals to a half times one hundred multiple two times the first term plus the hundred terms minus one times two, the answer equals to ten thousand.
10. Paint or make the cube that known lateral edges
For example, we will make the cube ABCDEFGH, the base ABCD and vertical lateral edges AE, BF, CG, and DH. With the length of lateral edges is six cm, the angle is thirty degree and the proportion projection is two over five. The steps:
• Design line of AB along six cm horizontal
• At point of A, paint the angle thirty degree, AD is segment orthogonal line because the length of projection two over five, then the length of AD equals to two cm
• Gradient projection of square ABCD shaped parallelogram, then the base can solve
• The middle of lateral edges shaped vertical line segment, so that the point of angle E, F, G, H can draw, and then produced the cube ABCDEFGH
The quadrature problem is the computation of phi, the ratio of the circumference of a circle to its diameter. We have seen that in the ancient orient the value of phi was frequently taken as three and for the Egyptian quadrature of the circle given in the Rhind papyrus, we have phi equals to three point one six. The first scientific attempt to compute phi, seems to be that of Archimedes with his achievement. To simplify matters, suppose we choose a circle with unit diameter. Now the (length of the) circumference of a circle lies between the perimeter of any inscribed polygon and that of any circumscribed polygon. According Archimedes, phi is between twenty two seventh or in decimal places, phi is given by three point fourteen. In the work are found same remarkable rational approximations to irrational square roots. The method of computing phi by using regular inscribed and circumscribed polygon is known as the classical method of computing phi. Except Archimedes, still more scientist attempt to compute the value of phi.
2. Get the formula of ABC
• Change all of segment to be a coefficient x
• Eliminate Constanta of left segment or both of joint minus with c/a
• Add both of joint with a half of quadrature from coefficient x
• Change the left join to be a complete quadratic
3. Find out the area
There are two lines equation. So, to find out the region bounded is the first lines equation should be equals to the second lines equation or y1=y2. After that, we will get the value of x. the value of x is the region bounded. Then to find out the area, we use the formula of integration with the region bounded among negative one until two. After calculate it, we will get result is negative thirteen sixth unit of area.
4. To decided the volume of cone
Cone is pyramid that have base plane curved circle. The volume of cone equals to the volume of pyramid. If known a cone with base radius r and altitude t, then to find the volume of cone equals to one third from the base’s area times the altitude. The base’s area equals to phi times the quadrature of radius. Thus, the volume of cone is one third from phi times the quadrature of radius times cone’s altitude.
5. To prove that in immaterial triangle then the totally of angel is one hundred eighty degree
The first, we make an immaterial triangle then make stretch of lines from point everywhere. For example, point of C collinear with AC. Then, exceed the point of C; make lines that parallel with AB. The angle of DCE equals to the angle of CAB because it’s opposite each other. The angle of BCE equals to the angle of ABC because it’s on both sides. The angle of ACB plus the angle of BCE plus the angle of ECD lie in one line equals to one hundred eighty degree, so the angle of ACB plus the angle of ABC plus the angle of CAB equals to one hundred eighty degree is proved.
6. To decided probability appear sum of figure more than six from two dices threw entirely
To make easier us to find out probability with make a table of probability. If there are two dices, then it has thirty six sample spaces. Whereas the probability appear two dices is twenty one. Thus, the probability appear figure more than six is twenty one over thirty six.
7. To decided the lines equation exceedingly (10,0) and tangent of circle
We should find the value of gradient. To find it, we should make equation inform Ax+By+C=0. To get equation like that, we should use roots of the equation known and the equation should be equals to zero. After that, to find the gradient, we use the formula is m= . So, the line equation also use the formula, the formula is . For the value of x and y, we used exceed point is ten and zero. Ten as x and zero as y. The equation can inform y equals to or the lines equation equals to zero.
8. To prove the theorem of Pythagoras
The Pythagorean Theorem only used for right triangle. In a right triangle, with sides a and b, and hypotenuse c, then power of c equals to power of a plus power of b. A right triangle is a triangle with one right angle has an angel ninety degree. And sides a and b perpendicular mutually. The simplest proof is an algebraic proof using similar triangles. Similar triangle has proportional sides.
9. To find out the sum of odd numbers two hundred first
With use arithmetic series, first term is one, with difference is two and there are one hundred terms. Then, sum of odd numbers two hundred first equals to a half times one hundred multiple two times the first term plus the hundred terms minus one times two, the answer equals to ten thousand.
10. Paint or make the cube that known lateral edges
For example, we will make the cube ABCDEFGH, the base ABCD and vertical lateral edges AE, BF, CG, and DH. With the length of lateral edges is six cm, the angle is thirty degree and the proportion projection is two over five. The steps:
• Design line of AB along six cm horizontal
• At point of A, paint the angle thirty degree, AD is segment orthogonal line because the length of projection two over five, then the length of AD equals to two cm
• Gradient projection of square ABCD shaped parallelogram, then the base can solve
• The middle of lateral edges shaped vertical line segment, so that the point of angle E, F, G, H can draw, and then produced the cube ABCDEFGH
Jumat, 20 Maret 2009
THE NATURE OF MATHEMATICS
Challenging of mathematics is complexity and puzzle that appears in mathematics problem. Many people consider that mathematics is so frighten. They always think that mathematics is very difficult because it’s always related with numbers. Maybe for them, mathematics make dizzy. Many people know that mathematics is important for their life. But a part of them don’t know that mathematics is important for their life. Mathematics is very required in life. With mathematics, we can solve many problems in our life. For example, with use mathematics, we can calculate many of object’s size. Such as when we will build house or place. We can approximate it with mathematics. And still more examples again. Mathematics is abstract science. With this, mathematics is interesting and full of challenging so much. A learn in mathematics such as Algebra, Geometry, Calculus, Arithmetic, etc. Mathematics also have structure pattern. The structure of pattern is very need. In solve mathematics problem, we must answer structurally.
In mathematics don’t need answer that true or wrong, but how we can solve this problem with use step structurally. Such as, in solve problem about triangle, square, etc. We can make a construction and a pattern for solve this problem. And that’s will make we easier. Mathematics is also communication. With mathematics, we can communicate with human being. From Mr. Marsigit’s article about “Elegi Hakikat Matematika ke Satu”, have explain that every human being have different conception about mathematics severally. There explained how the mathematics come from. Mathematics is very complete. The basic knowledge is mathematics. Mathematics is knowledge from all of knowledge. All of knowledge should base with mathematics. Before we solve our problem in mathematics, as good as possible we investigate it. That will make us easier for answer. In solve mathematics problem can’t only see. We should try and try for solving this problem. And after we can solve it, we will feel satisfied. In mathematics very need creativity for solve problem. The creativity can give us advantage and make easier in answer mathematics question. And we can make a smart solution for solving it. Such as make the formulas simply. Learning of pure mathematics and mathematics education is different. In mathematics education more pressed to teach method. Whereas mathematics non education learn about realized. I hope from there, I can be a mathematician. And I can more improve my skill in realized theorems or definition in solve mathematics problem.
Challenging of mathematics is complexity and puzzle that appears in mathematics problem. Many people consider that mathematics is so frighten. They always think that mathematics is very difficult because it’s always related with numbers. Maybe for them, mathematics make dizzy. Many people know that mathematics is important for their life. But a part of them don’t know that mathematics is important for their life. Mathematics is very required in life. With mathematics, we can solve many problems in our life. For example, with use mathematics, we can calculate many of object’s size. Such as when we will build house or place. We can approximate it with mathematics. And still more examples again. Mathematics is abstract science. With this, mathematics is interesting and full of challenging so much. A learn in mathematics such as Algebra, Geometry, Calculus, Arithmetic, etc. Mathematics also have structure pattern. The structure of pattern is very need. In solve mathematics problem, we must answer structurally.
In mathematics don’t need answer that true or wrong, but how we can solve this problem with use step structurally. Such as, in solve problem about triangle, square, etc. We can make a construction and a pattern for solve this problem. And that’s will make we easier. Mathematics is also communication. With mathematics, we can communicate with human being. From Mr. Marsigit’s article about “Elegi Hakikat Matematika ke Satu”, have explain that every human being have different conception about mathematics severally. There explained how the mathematics come from. Mathematics is very complete. The basic knowledge is mathematics. Mathematics is knowledge from all of knowledge. All of knowledge should base with mathematics. Before we solve our problem in mathematics, as good as possible we investigate it. That will make us easier for answer. In solve mathematics problem can’t only see. We should try and try for solving this problem. And after we can solve it, we will feel satisfied. In mathematics very need creativity for solve problem. The creativity can give us advantage and make easier in answer mathematics question. And we can make a smart solution for solving it. Such as make the formulas simply. Learning of pure mathematics and mathematics education is different. In mathematics education more pressed to teach method. Whereas mathematics non education learn about realized. I hope from there, I can be a mathematician. And I can more improve my skill in realized theorems or definition in solve mathematics problem.
Minggu, 15 Maret 2009
The First Meeting with Mr. Marsigit
Last Wednesday at 7.00 am was first meeting with Mr. Marsigit in Jaika’s room. Mr. Marsigit was our English’s lecturer this semester. On this first time, we introduced our self that name and come from. After that, Mr. Marsigit introduced himself. He told us about his life experience. Started from he studied S-1 earlier until got scholarship to London for continued his study S-2 and his journey to abroad for presentation an essay about international study. He told all of it so enthusiastic and completely. He had done journey to several country. Such as Australian, Singapore, Japan, etc. he also told us that a student from California University will come in Indonesia at August for research. He explain that English is communication. In English there are 5 skills. There are speaking, hearing, writing, understand, translate. English need courage. If we don’t have courage in speak English, we won’t able to speak English. And we always should improve our English. After he explains all of it, he gave task for us to made a blog. He commands us for posting comment in his blog.
And we continued again on second meeting at 3.00 pm on the same room. There, he continued his story about the journey to abroad. After that, he gave us exercise about our knowledge with the word of mathematics. And after enquired, I got the bad score. I feel embarrassed got bad score. And I will try for improve my English skill in mathematics English I.
Last Wednesday at 7.00 am was first meeting with Mr. Marsigit in Jaika’s room. Mr. Marsigit was our English’s lecturer this semester. On this first time, we introduced our self that name and come from. After that, Mr. Marsigit introduced himself. He told us about his life experience. Started from he studied S-1 earlier until got scholarship to London for continued his study S-2 and his journey to abroad for presentation an essay about international study. He told all of it so enthusiastic and completely. He had done journey to several country. Such as Australian, Singapore, Japan, etc. he also told us that a student from California University will come in Indonesia at August for research. He explain that English is communication. In English there are 5 skills. There are speaking, hearing, writing, understand, translate. English need courage. If we don’t have courage in speak English, we won’t able to speak English. And we always should improve our English. After he explains all of it, he gave task for us to made a blog. He commands us for posting comment in his blog.
And we continued again on second meeting at 3.00 pm on the same room. There, he continued his story about the journey to abroad. After that, he gave us exercise about our knowledge with the word of mathematics. And after enquired, I got the bad score. I feel embarrassed got bad score. And I will try for improve my English skill in mathematics English I.
Langganan:
Postingan (Atom)
