A. The Natures of Logarithm
a to the power of m times a to the power of n is equals to a to the power of m plus n in bracket. a to the power of m over a to the power of n is equals to a to the power of m minus n in bracket. Logarithm base a of b is equals to n, means that b is equals to a to the power of n. logarithm base g of a is equals to x, means that a is equals to g to the power of x. Logarithm base g of b is equals to y, means that b is equals to g to the power of y.
Logarithm base g of a times b in bracket is equals to? Let the logarithm base g of a is equals to x, so a is equals to g to the power of x. Logarithm base g of b is equals to y, so b is equals to g to the power of y. a times b is equals to g to the power of x times g to the power of y. a times b is equals to g to the power of x plus y in bracket. Logarithm base g of a times b in bracket is equals to logarithm base g of g to the power of x plus y in bracket. Its equals to x plus y in bracket times logarithm base g of g. We know that logarithm base g of g is equals to one. So the solution for logarithm base g of a times b in bracket is equals to x plus y.
Logarithm base g of a times b in bracket is equals to logarithm base g of a plus logarithm base g of b.
The Nature a.
Let the logarithm base g of a is equals to x, so a is equals to g to the power of x (equation I). Logarithm base g of b is equals to y, so b is equals to g to the power of y.
a over b is equals to g to the power of x over g to the power of y. Equals to a over b is equals to g to the power of x minus y in bracket. Logarithm base g of a over b is equals to logarithm base g of g to the power of x minus y in bracket. Equals to logarithm base g of a over b in bracket is equals to x minus y in braxket times logarithm base g of g. Logarithm base g of a over b in bracket is equals to x minus y in bracket, because logarithm base g of g is equals to one. So the conclusion is logarithm base g of a over b in bracket is equals to logarithm base g of a minus logarithm base g of b.


The Nature b.
Logarithm base g of a to the power of n is equals to logarithm base g of a times a times a times a times a times a times a until n times of a for each is a in bracket. Equals to logarithm base g of a plus logarithm base g of a plus logarithm base g of a plus logarithm base g of a until n quantifying tribes for each is logarithm base g of a. Equals to n times logarithm base g of a. So the logarithm base g of a to the power of n is equals to n times logarithm base g of a.
B. How To Find an Abc Formula
How to find an abc formula? First we know that the general equation of quadratic equation is a times x plus b times y plus c is equals to zero. And then from that formula we can dividing by a, so we will find other construction of quadratic equation. Then we will find new equation that is x plus b over a plus c over a is equals to zero. And then we used a completed square formula. We will found the quadratic form so we can find the x1 and x2. And finally we will find that x1,2 is equals to negative b plus minus square root of D all over by two times a. Which D is equals to b square minus 4 times a times c.
C. How To Find Phi Number
Phi number which we know is looking for by comparing the diameter and the circumference of circle. If we want to prove that, first we cut a string which has length of 22 cm, then we make it to the circle. We will get the diameter of the circle is 7 cm. from that experiment the phi number found.
D. The Square Root of 2 is Irrational Number
We know that hypotenuse of triangle (c) is the square root of quadrate of the two sides of triangle. When the triangle is right triangle with the same long of the side that is one, the long of the hypotenuse is square root of two. To prove the square root of two is irrational number we can used reduction ad absurdum or prove by contradiction. First we assumed that square root of two is rational number which has the form of m over n for m is integer number and n not both even. Then m square is equals to two times n square in bracket. Let m is two times p, so m is equals to 2 times n square, so 2 times p square is equals to n square, when n is also even. The contradiction is square root of two is irrational numbers.

My Difficult Words on English Learning

1. Equilateral : sama sisi
2. Segment : segmen
3. Scalene : sisi tak sama panjang
4. Inequalities : ketaksamaan
5. Perpendicular : tegak lurus
6. Circumcircle : kelililng lingkaran
7. Circumference : keliling
8. Altitude : ketinggian
9. Intersect : perpotongan
10. Perimeter : garis keliling
11. Quadrilateral : segi empat
12. Bricklayer : tukang batu
13. Marbles : kelereng
14. Axe/axes/axis : sumbu
15. Consecutively : turut
16. Proportion : proporsi
17. Slant : condong/miring
18. Truncated cone : kerucut terpancung
19. Indeterminate equation : persamaan tak tentu
20. Simultaneous : serentak
21. Constructability : kemampuan menciptakan/membangun
22. Subtraction : pengurangan
23. Finite number : bilangan terhingga
24. Infinite number : bilangan tak terhingga
25. Integer : bilangan bulat
26. Derivative : turunan
27. Heuristic : heuristis/menyelidiki sendiri
28. Method of exhaustion :metode pembuangan
29. Velocity : kecepatan
30. Slope : tempat miring
31. Measurable : dapat diukur
32. Arbitrary point : titik berubah-ubah
33. Approximate : perkiraan
34. Multiplied : mengalikan
35. Indefinite integral : integral tak tentu
36. Density : berat jenis
37. Whole number : bilangan bulat
38. Bijective function : fungsi bijektif
39. Inference : dugaan
40. Enumerate : menjumlahkan
41. Invariance : persamaan
42. Contradictory : kontradiktif
43. Summation : menyimpulkan
44. Inscribed : bersyarat
45. Computed : menghitung
46. Dawn : mulai jelas
47. Equal : sama dengan
48. Area : luas
49. Semicircle : setengah lingkaran
50. Radius : jari-jari
51. Solid : padat
52. Definite : tertentu

THE NATURE OF MATHEMATICS

Mathematics is one of the knowledge which is in the world. Mathematics is quite near from our life. Mathematics cannot be dissociated from our life, we life in a mathematics environment. Most of us known and recognizing, but there are many of us who didn’t know what is the nature of study mathematics.
The nature of school mathematics.
The nature of school mathematics is consist of :
1. Mathematics is pattern
Mathematics has a characteristic which differentiating with the other science. Mathematics doesn’t study about molecules, or cell, but mathematics concern about number, manipulated of number, type of number although the history of mathematics.
2. Mathematics is communication
Mathematics is used to communication for each other people. Communication in mathematics during learning, listening, teaching and etc. We usually used logic to approximated the something which will be happened.
3. Mathematics is investigation
Mathematics is universal science, mathematics is able to used in many place. In the mathematics, we usually prove some problems with the induction method. Mathematics also used in other knowledge. For example in the economic, we can count the profit and loss with the mathematics.
4. Mathematics is problem solving
Mathematics can be a solution for the problem. Mathematics studying problem closed with the single solution, problem opened with the solution is not single, and problem variously solution. Mathematics also used to solve the problem in other science, mathematics involved in calculating the results of research or experimental physics. And mathematics also used in chemistry, engineering, technique, etc. On the mathematics learning, mathematics study started with the problem recognition matching with situation ( contextual problem).
The nature of student of mathematics
The nature of student of mathematics is :
1. Student needs motivation and spirit
Motivation is the important thing on the student. Teachers must giving motivation to their students. Teachers must giving spirit to their students and to make their dreams come true. Motivation and spirit can come from inside and outside of people. From inside people has have a characteristic which differentiating with other. From outside people usually get the motivation from other people. This is important because people will not stay in high performance but sometimes people will down and make a spirit to get up back.
2. Student is unique
No ones in the world have the same behavior, although the twin. Every people have a characteristic which differentiating for each other. Also student, student is differentiate for each other. Each student doing something according to their habbit. If the students have a bad habbit, teachers must make the students change their habbit smoothly. Student doesn’t like hardness. So the uniqueness must be developed well.
3. Student have competence
Every student must develop their competence, because it can make them easy to continue their study and easy to get success. Competence have there inside the people, but it must be developed.
4. Students is contextuality.

My Comment

Sir, Your article is very good and right for the student of junior High School. The language is easy to understand. it can increase the Mathematics and English ability of the Student of Junior High School. It also can increase my Mathematics and English ability. Sir, your book is very good, I wish that your next book will be better and useful. I'm really proud having a lecture like you. Thank you Mr. Marsigit.
(February 28, 2009 5:30 AM)

Wow..that's great idea sir. .
It can make your article better than before and easier to understand by the readers. .
And thank you Sir for your comment to me. .
(March 12, 2009 7:12 AM)

MY PREPARATION IN PARTICIPATING ENGLISH II LESSON BY Mr. MARSIGIT

On the 2nd semester of my study in Mathematics Education of The state University of Yogyakarta, I gave the English II lesson. The lecture who teach this subject is Dr. Marsigit. To participate this lesson, the student must have a blog and then they must posted their task to the blog. On the rirst meet he said that the topic of this subject for this semester is how to communication mathematics education in English. There are some words on that sentences such that : Communicate, Mathematics, Mathematics Education, and English.
Communicate
Hear : sometimes I heard a music with English language.
Talk/say: sometimes I try repeating to say / sing the song which I heard.
Write : to fulfilling the task especially English task I must write the task on English language, and it can increase my English ability.
Read : sometimes I read some books or a pamphlet on English language.
Translate: when there is some English words on my book, sometimes I try to translated it, and then I can understand what the words mean.
Mathematics
On mathematics we can see many chapters such as Algebra, Arithmetics, Geometry, Calculus, etc.
Mathematics Education
There are some parts on the Mathematics Education, that are Teachers, students, method, resources ( facilities and teaching aid ), classroom, etc.
English
English consist of 2 that is Formal and Informal. Both divide into 2 that is Writing and Speaking.

Teaching learning process
o Motivation
o Apperception
o Competence
 Will
 Attitude
 Knowledge
 Skill
 Experience
o Indicators
o Evaluation / assessment
o Preparation
o Lesson plan
o Student Worksheet
o Discussion
o Classical teaching
o Paradigm
o Theory
o Constructivist

Marsigit’s Lesson :
 Participation
 Class, Discussion, Exercise
 Assignment, paper, internet, web/blog.
Self effort :
 Text book
 Active learner
 Reference seeker

WELCOME

Welcome to my blog..