unique math

Helo kawan semuaaa

Sebenernya nih saya lagi pingin nulis artikel tentang sequences and series (yang ga bisa basing, baca: baris dan deret :p ). Soalnya kan baru aja diajarin sama sang guru matem, jadi masih fresh di otak. Hoho

Tapi si Naomi udah nulis artikel tentang barisan bilangan asli berurutan. Jadi nanti dikhawatirkan kalian bosen sama yang namanya kata ‘baris’, terus langsung ninggalin blog ini. Hahaha *alasan mekso (banget)*

Yaah alasan lebih jujurnya sih, karna saya lagi males ngetik sambil mikir. Hihi

Jadi kali ini saya mau nampilin sesuatu yang unik tentang matematika. Langsung deh. Cekidooot

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=123456789 87654321

Nah, unik kan? Unik kan? Luar biasa! *haha alay

Barisan Bilangan Asli Berurutan

Yuk... Waktunya main-main dengan barisan. Kita coba, yuk! Salah satu topiknya adalah Barisan Bilangan Asli Berurutan.

Rumus:
Untuk 1+2+3+4+5+ ... + n = n(n+1)
                                                 2
Pembuktian
1. Kasus: n = 1
maka             1 = 1(1+1)
                                2
                        = 1
OKE!

2. Anggap : n = k
maka 1+2+3+ ... + k = k(k+1)  BENAR, KAN?!
                                         2
OKE!

3. Maka untuk n = (k+1)  JUGA BENAR!
1+2+3+ ... + k + (k+1) = (k+1)(k+1+1)
                                                  2
k(k+1) + (k+1)             = (k+1)(k+2)
    2                                        2
                                                                 kedua sisi dikalikan dengan 2
k(k+1) + 2(k+1)           = (k+1)(k+2)
(k+1)(k+2)                   = (k+1)(k+2)      BENAR!

Jadi, 1+2+3+ ... + n = n(n+1) terbukti benar, ∀n∈A
                                       2

GOOD LUCK! :)

sirkel.. sirkel.. sirkel..

Sebelum nulis artikel tentang lingkaran ini, izinkanlah saya untuk sumbang suara saya yang nggak sumbang ini (nah lho, bingung nggak ama kata" gua ) Hahay  :p
Mari nyanyi : "Lingkaran kecil.. lingkaran kecil.. lingkaran besar.. Diberi pisang.. diberi pisang.. nggak mau makan.. Enam.. enam.. 36. Enam.. enam.. diberi sudut"
Gila gokil banget kan lagunya
Masa habis ngomongin lingkaran, nyambung ke pisang, nyambung ke angka 6 sama 36, trus sudut. Imajinatif banget ya tu manusia yang nyiptain lagu

Imut kan? Imut kan? *Cuih

Yasudah, daripada diterusin ocehan saya yang gaje ini.. Langsung aja ngebahas materi. Yuk mariii..

A circle is a simple shape consisting of points in a plane which are equidistant from given point called centre. It’s a simple closed curve which divide the plane into two regions, interior and exterior.

Below are some definition which related to a circle:

Arc                             : A curved line that is part of the circumference of a circle.

Chord                         : A line segment within a circle that touches 2 points on the circle.

Circumference         : The distance around the circle.

Diameter                   : The longest distance from one end of a circle to the other.

Phi (µ)                         : A number, 3.141592..., equal to the circumference / the diameter of any circle.

Radius                         : The distance from center of circle to any point on it.

Sector                         : A circle wedge.

Tangent of circle     : A line which perpendicular to the radius that touches only one point on the circle.

 

Formulae

Circumference   = 2µr

Because 2r             = d, so Circumference = µd

 Area    = µr²

*µ         =  22/7 or 3.14

  r         = radius

 d         = diameter 

 

Tangent line

• The line drawn perpendicular to a radius through the end point of the radius is a tangent to the circle.

• A line drawn perpendicular to a tangent through the point of contact with a circle passes through the centre of the circle. 

• Two tangents can always be drawn to a circle from any point outside the circle, and these tangents are equal in length.

I²          = d² – (R-r)²

O²           = d² + (R-r)²

* I        = Inner tangent line

  O       = Outer tangent line

  d        = Diameter between two center points

  R        = First radius,   r   = Second radius

math = favorite! :)

Some people say that math drives us crazy! Sometimes it can make our headache appear, right? *be honest :p* But if you try to consider it as a game, it's really amazing. What people assume sometimes could be wrong. Numbers mean a lot in life and that's amazing. How can millions of people count?! Because the fact is, numbers are not real. Illusion, and abstract. Fantastic, right? And do you know? They (numbers) keep extraordinary secret!

Mathematics come from Greek 'μάθημα (máthēma)' which means learning, study, and science. Here is some of what the scientists said about math:
1. Benjamin Peirce, "the science that draws necessary conclusions"
2. Albert Einstein, "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality"
3. Carl Friedrich Gauss, "mathematics as the Queen of the Sciences"

B. Pierce

Einstein

And some people think that when you're good at math, so you are able to learn all things easily. Why? Because math is around logical. It helps you to be logic in solving complicated problems.

Gosh! Math also really helpful in our daily life. Not only in mathematical study and science, but also the other fields. Check this out:
1. Structure
* all about structural. Hey, don't kidding! It comes from mathematical theory :)
2. Music
* how come?! Okay, let me tell you about notation. In music, you have to count how long you should play the notation and how many times you should clap your hands and taping. Count it by mathematics! Remember 3/4, 5/4, 4/4, 6/8?
3. Financial
*don't ask why... :p
4. Playing games
* don't believe it? Just play 'ular tangga', then you need to count the sum of the dice out.

Don't consider math as your favorite? Now it's your time! TIPS to learn math fun:
1. See math like seeing your favorite. i.e, game online. Try to see math as a problem in a game you need to solve. And don't be satisfied first before you succeed the game.
2. Flirt your tutor a.k.a 'pedekate'. By doing this, your tutor wont mind trying to help you understand until you REALLY understand.
3. Find the easiest way to make math fun. i.e, THE EASY WAY TO COUNT FAST THE SQUARED NUMBER ENDED WITH 6 :
- 16 x 16
* Square the number before 16 = 15 ^ 2 = 225
* Plus 15 and 16 with the former step = 225 + 15 + 16 = 256 
4. Don't hate yourself when you're not talented in math. Everybody was born with each special talents. And when you don't get math, you can get the effort, right? It's just about training and more training.
SO, LET'S HAVE FUN WITH IT! GBU :)

Sin.. Cos.. Tan.. TRIGONOMETRY !

The trigonometric functions of angles are the ratios of the various sides of a triangle. Consider a right-angled triangle ABC as shown in the figure below.

The following terminology is useful.

Hypotenuse: The side opposite to the right angle in a triangle is called the hypotenuse. Here the side AB is the hypotenuse.

 

Opposite Side: The side opposite to the angle in consideration is called the opposite side. So, if we are considering angle A, then the opposite side is BC.

 

Base or Adjacent: The third side of the triangle, which is one of the arms of the angle under consideration, is called the base. If A is the angle under consideration, then the side AC is the base.

For angle A, the following fundamental trigonometric functions can be defined.

Sin A = Opposite side / Hypotenuse (alias: demi; depan/miring)

Cos A = Base / Hypotenuse (alias sami; samping/miring)

Tan A = Opposite side / Base (alias desa; depan/samping)

From the definitions, it can be seen that Tan A = Sin A / Cos A.

Tessellation

What is tessellation??

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps.                   

The word "tessellate" is derived from the Greek word "tesseres". In English, it means "four". Because, the first tesselations were made from square tiles.

A regular tessellation is a tessellation which made of congruent regular polygons. Regular means that all the sides and angles of the polygon are equivalent or proportional.

Here are the examples of regular tessellation :

a tessellation of triangles
a tessellation of squares
a tessellation of hexagons

We can also use a variety of regular polygons to make semi-regular tessellations. The properties of semi-regular tessellations are:

1.      Formed by regular polygons.

2.     The arrangement of polygons at every vertex point is identical.

First of all.. let me introduce our self ^^

Hai hai.. haloha ^^

Welcome to our blog!

Perkenalkan.. kita (baca: Naomi & Alya) adalah dua orang anak remaja putri *ceilah* yang tengah menempuh pendidikan di kelas 9A alias Nastula atau singkatnya Nst (sambil berseru: Nastula Keren! Bung bung bung bung!) di SMP 1 Kudus, sekolah bertaraf internasional yang paling fantastis, bombastis, spektakuler.. di Kudus. Hehe

Tau nggak *pasti nggak tau* kenapa kita bikin ini blog? Ini semua berawal karena kita berdua  anak Nst dapet mandat alias amanat alias perintah (baca aja: tugas) dari sang guru matematika tercinta. Yap yap.. sapa lagi kalau bukan Ibu Ida Achyani , S.Pd., yang asli canggih (terbukti, kita dikasih tugas kaya begini) dan of course cantiiiiik sakdonya (ngomong gini sambil berharap nilai dinaikin  :p)

Karna yang nyuruh guru matem, so pasti blog ini isinya tentang matematika, dan pake bahasa Inggris loh :D Zzz :cd

Tentunya berguna dan menarik untuk dibaca *bo’ong* wkwk

Tapi nggak cuma itu kok.. kita juga bakal nulis artikel” lain yang oke punya, dan nggak pake bahasa Inggris :D So, keep reading on this blog ya kawan” :mantap

Cukup sekian.. *pegel gua, ni keyboard warnet keras banget sumpah ==a*

Selamat membaca dan melihat-lihat :) Bubye

  

culipid