poster

mathematical research

THE RESEARCH OF MATHEMATIC
THE APPLICATION OF DIFFERENTIAL EQUATION IN POSITION, VELOCITY AND ACCELERATION




Arranged by:
Name : Anis Septiana Sari
NIM : 08305141039









YOGYAKARTA STATE UNIVERSITY
2009

PREFACE

In the name of Allah SWT, the Author want to say thanks to God, because only God help I can finished my mathematical research which have a title “The Application of Differential Equation in Position, Velocity and Acceleration” on time and without matter problem.
This mathematical research made for completed the final task in the English II in Yogyakarta State University..
This mathematical research explain about the function of possibly theorem in our life. It can help our to calculate the possible a happening.
Hopefully this mathematical research can be useful to whosever read this report, specially to the students. For sure the author need developed critics and suggestions for the author reports in the future can be better.
In this case the Author would say thanks to :
· Allah SWT
· My Parents and my sister, who support me until now
· Mr Marsigit as my lecture
· My friends
· And the last is for all who did help the author, and the author can’t put their name in this report because the spaces











BACKGROUND

We often go to somewhere by kind of transportation. We can use motorcycle, bicycle, car or another transportation. We can arrive at somewhere more quickly by motorcycle than by bicycle. It approve that each transportation has different velocity. Velocity influence arrival in somewhere. Courese, we will choose a transportation that have quicker velocity tha another transportatio.
In Physics, especially in Mathematical method in phisical science position, velocity and acceleration be studied. If we study it, we can know the relation of them. The relation of position, velocity and acceleration is very important to be studied because it’s all be needed in our life. Velocity can be gotten from position. Acceleration can be gotten from velocity. It’s all be gotten use differential equation.
From the reason above,I arrange the reasearch of mathematics with the tittle “The Application of Differential Equation in Position, Velocity and Acceleration”.















CONTENTS
A. Introduction
Mr. Marsigit’s opinion at Wednesday, December 16th 2009, The aim of reasearch of amthematics is to examine and develop mathematic. Mr. Marsigit also explain tah the nature of mathematics consist of three parts. They are formal mathematics/axioms mathematics/pure mathematiscs, applied mathematics and school mathematics/concret mathematics/real mathematics. Mathematics is a deductive system consist of definition, axioms, and theorem in which there is no contradiction inside. Formal mathematics consist of number theory, group theory, Ring Theory, Filed theory, Eudidion Geometry, Non Eudid Geometry, etc. applied mathematics can be found in our life. In this my mathematics research I take “The Application of Differential Equation in Position, Velocity and Acceleration”
B. The Definition of Position, Velocity and Acceleration
Position
Ÿ In physics science, position and removal are the different meaning. Removal is vector mulberry. Position is scalar mulberry. So, removal have direction and position haven’t direction. But, they have same large. In the physics science, two different points have position and removal.
Ÿ Velocity is defined by position of somethhing and interval of time which is needed to cover a distance.
Ÿ Acceleration is defined by change of velocity intime interval.
Ÿ The symbol of position is s, the symbol of velocity is v , the symbol of acceleration is a.
C. Establish The Velocity and The Acceleration from Position Function
Ø From definition of velocity, we can write
, for approach nol
To interval of time approach nol


So
Ø From definition of acceleration, we can write
, for approach nol
To interval of time approach nol



So or

D. Application of Position, Velocity and Acceleration in daily life
we can use the formula ofposition, velocity and acceleration to solve the daily problem. For example:
s=(3t2 + 9t + 6) m. determine the velocity and the acceleration from it!
Solution:
Given: s=(3t2 + 9t + 6) m
Ask: v=…?
a=…?
Solve:
m/s
So the velocity is 6t +9 m/s. The graph of velocity is
9
O
s
t






m/s2
So the velocity is 6 m/s2. The graph of velocity is
6
O
a
t




























BIBLIOGRAPHY

Boas, Mary. L. Mathematics Method in The Physical Methode. Canada, Depsul University : 1983.
Kamajaya. Fisika SMA. Bandung, Grafindo Media Utama: 2004.

mathematic problems and the solution

PROBLEMS (by Anis Septiana Sari)
1.If |z = xy + x + y , x = r + s + t , y = rst

Determine
∂z/∂s |r=1,s=-1,t=2

2.A lawyer, every day, go for work from his house to his office. In average, the trip takes 24 minutes with standard deviation of 3,8 minutes. Assume that the time of the trip spread normally. Count the opportunity that 2 of three next trips to the office will spent more than 30 minutes.

3.Prove that 1 ≤ ∫ from 0 until 1 √(1+x4) dx ≤ 6/5
Clue : 1 ≤ √(1+x4) ≤ 1+x4

4.Prove if a|(b-1) so a|(b4-1)

5.How to find the distance between two parallel planes?



SOLUTION (by Endah Ayu Wardani)

1.To find the solution of problem number 1, there is a theorm that can helps us, it is theorm of chain rule :
For example x=x(s,t) and y=y(s,t) have a first differential at (s,t) and for example z=f(x,y) can be differentiated at (x(s,t),y(s,t)) so z=f(x(s,t),y(s,t)) has a first partial differential that be given by :

i.∂z/∂s = ∂z/ ∂x . ∂x/∂s + ∂z/∂y . ∂y/∂s

ii.∂z/∂t = ∂z/∂x . ∂x/∂s + ∂z/∂y . ∂y/∂t


From that theorm, we know that the way to solve it is
∂z/∂s = ∂z/∂x . ∂x/∂s + ∂z/∂y . ∂y/ ∂s ………Eq.1


Find each first differential:
∂z/∂x = y+1 ∂x/∂s = 1 ∂z/∂y =x+1 ∂y/∂s=rt


Subtitude them to Eq. 1
∂z/∂s = (y+1)(1) + (x+1)(rt)

∂z/∂s = y + 1 + rtx + rt

Subtitude x = r + s + t and y = rst
∂z/∂s = rst + 1 + rt(r+s+t) + rt

∂z/∂s = 2rst + r2t + rt2 + rt + 1

When r=1, s=-1, and t=2
∂z /∂s | r=1,s=-1,t=2 = 2(1)(-1)(2) + (1)^2(2) + (1)(2)^2 + (1)(2) + 1 = -4 + 2 + 4 + 2 + 1 = 5


2.The opportunity cannot be found in a way. First, find the opportunity when the trip spent more than 30 minutes.

For example X is the normal random variable with µ (median) = 24 minutes and σ(standard deviation) = 3,8 minutes.
P(X>30) = P(Z>z1)
z1 =(30 - µ)/σ = (30 – 24)/3,8 = 1,58
P(X>30) = P(Z>1,58) = 1 – P(Z<1,58) = 1- P(ZSo, the opportunity of the trip spent more than 30 minutes is 0,0571

Then, we bring it to binomial deviation.
• The success opportunity is p = 0,0571
• The failure opportunity is q = 1 – 0,0571 = 0,9249

The opportunity when twice success from three times repetition :
b( 2 ; 3 ; 0,0571 ) = 3C2 . (0,0571)2 . (0,9429)3-2 = 3 . (0,0033) . (0,9429) = 0,0092

So, the opportunity that twice of three times next trips spent more than 30 minutes is 0,0092.


3.From the clue, we know that 1≤√(1+x4)≤1+x4. Then, integral all of them in limit [0,1] toward x, become :
∫01 1 dx ≤ ∫0 until1 √(1+x4) dx ≤ ∫01 (1+x4) dx
<=> 1 ≤ ∫ from 0 until 1 √(1+x4) dx ≤ [x+(1/5) x5]01
<=> 1 ≤ ∫ from 0 until 1 √(1+x4) dx ≤ (1+(1/5)-0)
<=> 1 ≤ ∫ from 0 until 1 √(1+x4) dx ≤ 6/5 PROVED!!


4.There is a theorm in numeric theory contain :
If a|b => a|mb for every m is round number
From that theorm, we can solve it when (b4-1) is m(b-1)
•b^4-1 = (b^2+1)(b^2-1) ; b^2-1 = (b+1)(b-1)
<=> b^4-1 = (b^2+1)(b+1)(b-1)
Assume that (b2+1)(b+1) = m so
<=> b^4-1 = m(b-1)
a|(b-1) => a|m(b-1), when m=(b^2+1)(b+1) so a|(b^4-1) PROVED!!


5.For example, plane-α // plane-β
The steps to find the distance between plane-α and plane-β :

1)Investigate plane-α as same as plane-β or not, if they are same, the distance is zero (0).
2)When plane-α is different with plane-β, the ways to find the distance are :

2.1 Choose a point in plane-α, for example A(xA,yA,zA)
2.2 Find the normal vectors of both planes, because they are parallel, the normal vectors are same. For example the vector is k.
2.3 Find the perpendicular plane-α passing A. For example line g.

g = x = xA + ρk ; ρ is parameter
y yA
z zA
2.4 Find the passage point of line g with plane-β by equating the right side of equation g with the right side of plane-β equation. We will get system of linear equation, solve it and get the value of parameters and then subtitude them to equation g or equation of plane-β, so we get the passage point, for example point B(xB,yB,zB).
2.5 Find the distance between A and B.
Distance(A,B) = √((xA-xB)^2 + (yA-yB)^2 + (zA-zB)^2)
The distance between A and B is the distance of plane-α and plane-β.

PROBLEMS (by Anis Septiana Sari)
1. If |z = xy + x + y , x = r + s + t , y = rst
Determine
∂z
∂s r=1,s=-1,t=2

2. A lawyer, every day, go for work from his house to his office. In average, the trip takes 24 minutes with standard deviation of 3,8 minutes. Assume that the time of the trip spread normally. Count the opportunity that 2 of three next trips to the office will spent more than 30 minutes.

3. Prove that 1 ≤ ∫01 √(1+x4) dx ≤ 6/5
Clue : 1 ≤ √(1+x4) ≤ 1+x4

4. Prove if a|(b-1) so a|(b4-1)

5. How to find the distance between two parallel planes?

SOLUTION (by Endah Ayu Wardani)
1. To find the solution of problem number 1, there is a theorm that can helps us, it is theorm of chain rule :
For example x=x(s,t) and y=y(s,t) have a first differential at (s,t) and for example z=f(x,y) can be differentiated at (x(s,t),y(s,t)) so z=f(x(s,t),y(s,t)) has a first partial differential that be given by :
(i) ∂z = ∂z . ∂x + ∂z . ∂y
∂s ∂x ∂s ∂y ∂s
(ii) ∂z = ∂z . ∂x + ∂z . ∂y
∂t ∂x ∂t ∂y ∂t
From that theorm, we know that the way to solve it is
∂z = ∂z . ∂x + ∂z . ∂y ...... Eq. 1
∂s ∂x ∂s ∂y ∂s
Find each first differential:
∂z = y+1 ; ∂x = 1 ; ∂z = x+1 ; ∂y = rt
∂x ∂s ∂y ∂s
Subtitude them to Eq. 1
∂z = (y+1)(1) + (x+1)(rt)
∂s
∂z = y + 1 + rtx + rt
∂s
Subtitude x = r + s + t and y = rst
∂z = rst + 1 + rt(r+s+t) + rt
∂s
∂z = 2rst + r2t + rt2 + rt + 1
∂s
When r=1, s=-1, and t=2
∂z = 2(1)(-1)(2) + (1)2(2) + (1)(2)2 + (1)(2) + 1 = -4 + 2 + 4 + 2 + 1 = 5
∂s r=1,s=-1,t=2


2. The opportunity cannot be found in a way. First, find the opportunity when the trip spent more than 30 minutes.
For example X is the normal random variable with µ (median) = 24 minutes and σ(standard deviation) = 3,8 minutes.
P(X>30) = P(Z>z1)
z1 = 30 - µ = 30 – 24 = 1,58
σ 3,8
P(X>30) = P(Z>1,58) = 1 – P(Z<1,58) = 1- P(ZSo, the opportunity of the trip spent more than 30 minutes is 0,0571
Then, we bring it to binomial deviation.
• The success opportunity is p = 0,0571
• The failure opportunity is q = 1 – 0,0571 = 0,9249
The opportunity when twice success from three times repetition :
b( 2 ; 3 ; 0,0571 ) = 3C2 . (0,0571)2 . (0,9429)3-2 = 3 . (0,0033) . (0,9429) = 0,0092
So, the opportunity that twice of three times next trips spent more than 30 minutes is 0,0092.

3. From the clue, we know that 1≤√(1+x4)≤1+x4. Then, integral all of them in limit [0,1] toward x, become :
∫01 1 dx ≤ ∫01 √(1+x4) dx ≤ ∫01 (1+x4) dx
 1 ≤ ∫01 √(1+x4) dx ≤ [x+(1/5) x5]01
 1 ≤ ∫01 √(1+x4) dx ≤ (1+(1/5)-0)
 1 ≤ ∫01 √(1+x4) dx ≤ 6/5 PROVED!!

4. There is a theorm in numeric theory contain :
If a|b => a|mb for every m is round number
From that theorm, we can solve it when (b4-1) is m(b-1)
• b4-1 = (b2+1)(b2-1) ; b2-1 = (b+1)(b-1)
 b4-1 = (b2+1)(b+1)(b-1)
Assume that (b2+1)(b+1) = m so
 b4-1 = m(b-1)
a|(b-1) => a|m(b-1), when m=(b2+1)(b+1) so a|(b4-1) PROVED!!

5. For example, plane-α // plane-β
The steps to find the distance between plane-α and plane-β :
1) Investigate plane-α as same as plane-β or not, if they are same, the distance is zero (0).
2) When plane-α is different with plane-β, the ways to find the distance are :
2.1 Choose a point in plane-α, for example A(xA,yA,zA)
2.2 Find the normal vectors of both planes, because they are parallel, the normal vectors are same. For example the vector is k.
2.3 Find the perpendicular plane-α passing A. For example line g.

g Ξ = + ρk ; ρ is parameter


2.4 Find the passage point of line g with plane-β by equating the right side of equation g with the right side of plane-β equation. We will get system of linear equation, solve it and get the value of parameters and then subtitude them to equation g or equation of plane-β, so we get the passage point, for example point B(xB,yB,zB).
2.5 Find the distance between A and B.
Distance(A,B) = √((xA-xB)2 + (yA-yB)2 + (zA-zB)2)
The distance between A and B is the distance of plane-α and plane-β.

Review of Book

PREFACE
In the name of Allah SWT, the authors want to say thanks to God, because only God help we can finished our review of book which have a title ”Mathematic For Junior High School VIII” on time and without matter problem.
This report made for completed the order of lecture English I in the Mathematic Department Yogyakarta State University.
In this case authors would say thanks to:
Mr.Marsigit As English I lecturer
Our mathematic friends
Our parents
This report is study about mathematic for junior high school. This report consist of side of book. They are contents, interest, technology be used, information, and quality. From its, we hope the readers interest to have the book.
Hopefully this report can be useful to whosever read this report. For sure the authors need developed critics and suggestion for the authors reports in the future.









CONTENTS
The book which be title ”Mathematic For junior High School” be arranged by Mr.Marsigit . Mathematic editor of the book are Fitri Puspitasari and Dewi Noviyanti Sari. Translator of the book is Mrs.Endah Retnowati. She is one of lecturer in Yogyakarta State university.
This book is first edition and first printing. The book be print at Safar 1430 H or February 2009.
The book which based on KTSP 2006 consist of seven chapters. They are Algebra and Its Application, Relation and Function, Straight Line Equation, Two Variable Equation System, Pythagoras Teorm, Circle, And Polyhedral.
Algebra and Its Application consist of three subchapter. They are The Meaning of Algebra, Algebra Form, factorization in Algebra Form, Fraction Operation in Algebra Form.
Relation and Function consist of three subchapter. They are relation, function, and Value of Function.
Straight Line Equation consist of three subchapter. They are Characteristic of Straight Line Equation, Gradient, and Line Equation
Two Variable Equation System consist of three subchapter. They are One Variable Linier Equation System, Two Variable Linier Equation System, and Linier Equation System.
Pythagoras theorems consist of three subchapter. They are Length of Side Right Triangle, Length of kinds Triangle, Rate of side in Right Triangle, and Pythagoras theorems in Life.
Circle consist of four subchapter. They are Be recognize with circle and Elements, Central angle and Perimeter Angle, Tangent circle and Outside Circle and Inside Circle.
Polyhedral consist of four subchapter. They are Prism, Cube, Epaulet, and Pyramid.
The book which reduction are edited by Verranita and Muchris, is close by life so the readers can understand.
The book which contents is designed by TAVIP’S, is completed by interest picture and the picture related to the subject.
The book which cover designed N.Nurhadi, is completed with example and solution, exercise in subchapter, exercise in chapter, and in the last book is completed by final evaluation.
The good book is not apart from publisher. Yudhistira make the book must be had every student in junior high school.

Definitions,,examples,explanation,etc

These are the definitions, examples, explanation, understanding or other explanation of the terms made by Salindri M. I write in the English language as a result of a dictionary, a thesaurus, learn the English language, internet download, open a Mr.Marsigit blog , and join Mr.Marsigit lesson.

1. BUSUR

a. archer’s bow
b. arch,arc
c. bow
d. cotton gin
e. arc
f. arch
busur derajat: protactor
Definition:curve both open, and closed that coincide with the circle.(http://en.wikipedia.org/)

Example:
AC long rope bow that is 3 cm

2. JURING

a.Section
b.Segment

Definition:is a circle in the area limited by the bow and two fingers that are on both ends.(http://en.wikipedia.org/)

Example:
broad segment AOB is 31.5 cm square

3. APOTEMA

Apotema:apotema

Definition:
bisector crossing from one side of a polygon to another side (http://www.babylon.com/definition/apotema/English)

Example:
Apotema the triangle ABC is the line AD

4. PEMBUKTIAN

Bukti: proof,evidence
Membuktikan: prove,demonstrate,establish,show
Terbukti: proven
Pembuktian:authentication,verification

Example:
mathematical induction is one of the methods of verification

5. DIKETAHUI

Tahu:know
Mengetahui:know, understand
Mempertahukan:announce
Ketahuan:be found out, detected
Pengetahuan:knowledge
Berpengetahuan: knowledgeable
Diketahui:given

Example:
Given length of the side-side triangle ABC is 5 cm, 4 cm, 3 cm

6. MENGHITUNG

Hitung : arithmatic
berhitung: count
menghitung:count, do sums, calculate
memperhitungkan:calculate,estimate
menghitungi:count repeatedly
Hitungan:count
Hitungan angka:numerical count
penghitung:counter
perhitungan:calculation,computation

Example:
Calculate how wide is the triangle that is 1 / 2 X pad X high

7. MERUMUSKAN

Rumus: formula,abbreviation
Merumuskan: formulate
Rumusan:formulation
Perumus: formulator
Perumussan: formulation

Example:
Before making the paper, first we formulate the problem

8. PEMBELAJARAN

Ajar: study
Belajar: study,learn
Mengajar:teach
Belajaran:teaching
Pengajar:teacher,instructor
Pembelajaran:learning

Example:
Learning at this time have indonesian modern

9. BERHITUNG
Berhitunmg:count

Example:
Children are counting from 1 to 10

10. PENALARAN

Nalar:logical reasoning
Bernalar:think logically,reason
Nalar sangat penting dalam pendidikan:reasoning is important in education
Menalarkan: reason or think
Penalaran: reasoningintellectual activity

Example:
Reasoning that is needed to correct problems

11. SINAR GARIS

Sinar:ray
Garis :line
Sinar garis:rayline

Definition:
A ray is part of a line which is finite in one direction, but infinite in the other.(http://en.wikipedia.org/)

Example:
Each line has a 2-ray lines of opposite

12. PEMBAGIAN

Bagi:devide
Bagi dua:divided in two
Bagi rasio: equally
Membagi: divide
Ia membagi tiga puluh denagn lima:she divided 30 by five
Membagi dua:bisect
Membagi tiga:trisect
Membagi-bagikan:share,distribute
Ia membagi-bagikan bukunya kepada teman-temannya:she distributed her book among his friends
Terbagi:divisible,divided,split up
Bagian:part,share
Pembagi:divider
Pembagian:distribution,division
Perbagian:quotient

Definition:
Division is an arithmetic operation which is the inverse of multiplication.( http://en.wikipedia.org/)

Example:
Students are learning division


13. PERKALIAN

Kali:times
Dua kali tiga menjadi enam:two times three is six
Sepuluh kali:ten times
Sekali:once,at the same time,as soon as
Kita bisa membayar sekali uang masuk:we can pay as soon as some money comes in
Mengalikan,memperkalikan;multiply
Mengalikan angka:multiply figures
Kali-kalian:multiplication
Pengali:multipier
Perkalian: multiplication,product

Definition:
Multiplication is the mathematical operation of scaling one number by another.( http://en.wikipedia.org/)

Example:
Students are learning basic multiplication

14. HIMPUNAN SOLUSI

Himpunan:set,association,club
Himpunan solusi:set of solution

Example:
Set of solutions of x + 5 = 7 is 2

15. JARI-JARI

Jari-jari:radius

Definition:
a radius (plural: radii) of a circle or sphere is any line segment from its center to its perimeter.( http://en.wikipedia.org/)

Example:
Radius of A circle is 7 cm

16. SUDUT DALAM SEPIHAK

Sudut dalam sepihak:angle in the unilateral

Example:
Large angle is the same in unilateral
17. SUDUT DALAM BERSEBERANGAN
Sudut dalam bersebrangan:angle in the opposed

Example:
Large number of corners opposite each other in a 180 degree

18. SEGI BANYAK

Segi banyak:Terms of many

Example:
One of many examples of terms of the square

19. SEBARANG

Sebarang:Any

Example:
Take any 2 elements of matrix A

20. PERBANDINGAN

Banding:equivalent,equal
Memperbandingkan:compare
Terbandingkan:comparable
Bandingan:comparison
Pembanding: standard of comparison
Pembandingan:process of comparing
Perbandingan:comparison

Example:
Comparison of the triangle on the carpenter's square is 3:4:5

21. SEJAJAR

Jajar:row,line
Sejajar:parallel
Dua jalan ini sejajar:these two roads are parallel

Example:
That parallel lines have the same gradient

22. TEGAK LURUS

Tegak lurus:perpendicular
Garis Tegak lurus:perpendicular

Example:
Line perpendicular to each other has a 90 degrees difference

23. RADIAN

Radian:radian
Definition:a unit of plane angle, equal to 180/π degrees, or about 57.2958 degrees, or about 57°17′45″. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level.( http://en.wikipedia.org/)

24. BERLAWANAN

Lawan:opponent,adversary,rival
Berlawanan:disagree with,be contrary,compete,contradictory
Berlawanan denagn kenyataan:contrary to the fact

Example:
A corner to the opposite corner of B

25. JAJARANGENJANG

Jajaran genjang:parallelogram

Definition:
parallelogram is a quadrilateral with two sets of parallel sides.(http://en.wikipedia.org/)

Example:
Wide range formula parallelogram is base X high
26. BELAH KETUPAT
Belah ketupat:rhombus

Definition:
a rhombus (from Ancient Greek ῥόμβος - rhombos, “rhombus, spinning top”), (plural rhombi or rhombuses) or rhomb (plural rhombs) is an equilateral parallelogram. In other words, it is a four-sided polygon in which every side has the same length. .( http://en.wikipedia.org/)

Example:
Wide range formula rhombus is ½ X diagonal X diagonal

27. LIMAS

Limas:pyramid
definition:a building where the outer surfaces are triangular and converge at a point. The base of pyramids are usually quadrilateral or trilateral (but may be of any polygon shape), meaning that a pyramid usually has four or five faces.(http://en.wikipedia.org/)
Example:
Pyramid volume formula is 1 / 3 wide base X high

28. PRISMA

Prisma: Prism
Definition:a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids.( http://en.wikipedia.org/)

Example:
Prism volume formula that is wide base Xhigh

29. PERPOTONGAN

Potong:piece

Example:
A piece between the lines g and h is the point A

30. IRISAN

Irisan:slice,section, rasher,shred,snag,incision
Example:
Incision area that is rhomboid
31. GARIS TINGGI
Garis tinggi:high line

Example:
Line high triangle can define a broad triangle

32. GARIS BERAT

Garis berat:line weight

Example:
Line weight on the triangle ABC is the line AD

Introduction In english 1

hello everybody, my name is Anis Septiana Sari. I am student inUNY. I an proud be student in there. I think enough to introduce my self.
This is my second blog. And for my first posting I want to tell about y first english lesson in UNY. my english teacher is Mr. Marsigit. In my first a meeting with my teacher just introduce each body.

In first, Mr Marsigit introduced his self. Then he talk about his experience in foreighn countries. For example Japan, France, Thailand,etc. He once went to Frace. He lost way there.

And the second,my friends and I introduced each self. we are consist of several city. There are central Java, West Java, NTB,Jambi,lampung,jogja,etc.

In the third Mr. Marsigit advised about how to learn something.In first we must have motivation. motivation to learned mathematics was Praying to God. We must had spirit and good perseption too. Then Mr. Marsigit talked that we must have good behavior. There are good daily activity and my be have.Then we must have knowledge. we can got it from book,,internet,teacher,ect. And the last we mus thad skill. There are speaking,reading,experience math,ect.
Mr. Marsigit talked to Me to Communicate math in english. In the first we must be an adult. then we must had responsibility,independent learn, cooperater,and looking rof source from book, internet,etc.
I think enough to posting my first posting. I think my experience can give information for the readers.