It's About Mathematics

Diposkan oleh Rerir RAi Minggu, 2009 April 12 di 10:28

ABC Formula
ABC formula used to know solution about linear equation system. If there are a (ei) cross x (eks) square plus b (bi) cross x (eks) plus c (si) equal of zero, so ABC formula founded from negatif b (bi) plus or minus square root of b (bi) square minus four cross a (ei) cross c (si) defind two cross a (ei).

Area of a Range
If we want to know area from y (way) equal x (eks) square and y (way) equal x (ex) plus two, we must take the equation to x (eks) square equal x (ex) plus two, if we do that, so we can know coordinates from the graph to x (eks) equator and we can know the limit of area. Take the equation into the graph and search the area with integral formula. We know that the limit is negatif one to two, so the area is integral of negatif one to two from x (eks) plus two minus x (eks) square.

Volume of Cone
If we want to know volume of cone, we must know about its tall and diameter of cone for used to search base area of cone. So we can use the formula, one defind three cross base area from cone cross its tall for know its volume.

The Sum of Anggle From Any Triangle
The sum of angle from any triangle is one hundred eighty degree. One of many proof from this statement is, we can cut all of its angle, then take them beside other foot of angel. We can see that them form a straight line. Angle of straight line is one hundred eighty degree. So we know that the sum of angle from any triangle is one hundred eighty degree.

The Proof of Pythagoras Formula
The picture in the left is one of many proof about Pythagoras formula. They are tell to us that c (si) square equal to a (ei) square plus b (bi) square. The proof is, we can see that apotema in the raight triangle equal to line of big square. There is a small square in the center of picture, and its line equal to b (bi) minus a (ei). Then we know that area of big square is c (si) square equal to the sum of four cross area of right triangle and area of small square. So we can make a equation below :

Equation of Line Which Touch The Circle
Example, we know that line throught point at A (ei), ten point zero (10, 0), and he touch the circle. Equation of circle is x (ex) square plus y (way) square equal to nine. Equation of circle like this tell to us that its center at point O (ow), zero point zero (0, 0) and its diameter is six. For example point which through circle and line is B (bi), p point q (p,q). They can illustrated into the graph.
We can see that triangle of ABO is the right triangle, so size line of AB is root of ten square minus three square equal to nine point five. After that search area of ABO triangle equal to half cross three cross nine point five equal to fourteen point twenty five equal to half cross ten cross BB1, so BB1 equal to fourteen point twenty five defind five equal to two point eighty five. This is ordinate of B.
Search size line of OB1 equal to root of three square minus two point eighty five square equal to root of one equal to one. This is absis of B. So, coordinates of B is one, point two point five.
Search gradient line of OB equal to two point eighty five, so gradient line of BA equal to negative one defind two point eighty five. So equation of line is :
y – q = m(x – p)
y – 0 = -1/2.85 x + 10/2.85
y = -1/2.85 x + 10/2.85
So, equation of line is y (way) equal to negative one defind two point eighty five cross x (eks) plus ten defind two point eighty five.

How To Know The Sum Of First Two Hundred Odd Number
We can take a sample. For example for first four odd number are 1, 3, 5, 7 …. We can see that they form arithmetic line, so we can make a formula about member of n from the arithmetic line. The first odd number is 1 (one), distance between two member of arithmetic line is 2 (two). If Un is a nth member, a (ei) is the first member, n (en) is a number of nth member and b (bi) is distance between two member of arithmetic line, so with the formula, we can know that the two hundredth member is
Un equal to a (ei) plus paren thesis of n (en) minus 1 (one), cross b (bi) equal to 1 (one) plus paren thesis of two minus 1 (one), cross two equal to one hundred ninty nine.
Un = a + (n – 1)b
Un = 1 + (2 – 1)2 = 199
After that we can take a sample, if Sn is the sum of first nth odd number, so we can search sum of first two hundred odd number with the formula Sn equal to half of n cross paren thesis of a (ei) plus Un equal to half of two hundred cross two hundred equal to twenty thousand.
Sn = ½ n(a + Un)
S200 = ½ (200) (1 + 199)
S200 = 100(200)
S200 = 20000

How to Draw a Cube
If we know elements of cube, so we can draw the cube. For example, we know the field image of cube, frontal area of cube, base of cube, frontal line, orthogonal line, angle of cube in image, and comparison of projections, so we can draw a cube with perspective of way.
The first, draw a frontal area on the paper, after that make a inclination angle with point of angle is one of two angle at base of frontal area with size between zero degree and fourty five degree. From foot of inclination angle we can draw a line with size in comparison of projection, then draw parallel line with that line with base of line is points of frontal area, after that connect all end of line. We have one cube now.

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Natural Mathematics

Diposkan oleh yunian tri rusandi Rabu, 2009 Maret 25 di 14:26

In the article about history of mathematics write down that mathematics is the king because development of mathematics is not depent on other sciences.

But in fact, study of mathematics in general felt difficult to be done especially among students. It is different about the fact. Something in the world relates to mathematics since long time up to now. Elements of mathematics always there is on problem solving.

Example about application of mathematics in human life that is, like a child of newspaper seller, he doesn’t pass elementary school but he must know basic operation of mathematics, so he knows value about the price of his newspaper, how much his profit and how much money can be kept. Other example is about someone who is using mathematics to build a house, and it can completed powerfully.

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