Number of law

Mathematics during which to live is important enough to be required in all areas.
You can, depending on their profession, have a impact small or greatly.

In particular, during the development of the game, mathematics is that it is very important.
There is no part that does not require a mathematics across game design, program, and graphics, in all areas of game development.

I think When all the work, have know-how or not, there is a big difference.
If repeat doing work, even if you don't have know-how, finally you will be person what have know-how.

But it will be very slow than people what have know-how.


So, for those of you who want to develop the game, try to write a sentence re-organize the basic theory of mathematics.

Even if you are not a game developer. I think that knowledge necessary for the game development can help you in design sense, psychology, communication skills and logical thinking.

Actually, even if make simple game, requires a lot of knowledge than above.

So, let's look back about a few fundamental laws first.

All math and science are starting from the doubt that is something all take for granted, and will re-generalize it. 

Let's consider briefly. Is '2 + 2' and '3 + 2' same?? 

Course. 
When add, order is not important. We called it the 'commutative law'.

Write some of the laws of natural mathematics in this way following. 

Even + even = even 
Odd + odd = even 
Even + odd = odd 
Odd + even = odd 

It is like following.
When Add the same numeral, unconditionally Even is comes out. When adds different numeral, unconditionally odd comes out. 
We will prove this later.

Let's look case of multiplication. 

5 + 5 + 5 = 15

I have three times add 5. Let write by using the multiplication formula.

5 X 3 = 15

It can be used in this way.
It means that three times add 5.
The results will be different, depending on whether how many add 5.


If so, what happens when I write it with the character without numeral?

5 X A =?

The result '?' is same that and add 'A' time 5.

This concept, because used in mathematics of all, you must understand certainly.

You may use other character instead of 'A', However, there are characters that are most commonly used. It is like a kind of promise. 

t (Time), r (Radius), w (Width), h (Height), n and (Number) etc. 

We called it "Algebra".

Let look at the numbers we use in real life. 

1, 2, 3, 4 ......(can continue.) 

This is called the "countable number" or "natural number". 


If write by using the "Algebra". 

N = N +1 

Can write like this.

Number N of any, means that N plus 1. The number N, it means the number one greater than themselves always. 

Nature of the natural number is as follow.

1. A natural number of all, 'A' have 'A'+1 at next.
2. A natural number of all, 'A' have 'A'-1 at previous. (Except when A is 1, it will be in this case 0)
3. A natural number of all, the order exists. Natural number A and B can be one of the following three cases. A is greater than B. A and B are the same. A is less than B. 
4. A natural number of all, does not matter the order of addition. (Commutative law)
5. A natural number of all, does not matter the order in which to multiply. (Commutative law)
6. In the calculation of all natural numbers. When plus is, no matter the position of the round bracket. (Associative law) 
7. In the calculation of all natural numbers. When multiplication is, no matter the position of the round bracket. (Associative law)
8. It is to be natural number whenever you add a natural number of both. (The nature of the closed state) 
9. It is to be natural number whenever you multiply a natural number of both. (The nature of the closed state)

And, We must need order, Because case of add and multiplication comes out together in the formula. Is as follows. I was allowed to write to a high precedence.

1. I calculate first the numeral of unconditional parentheses.
2. If there are indices, calculate first index, is calculated in the order of the rest.
3. Even in the absence of parentheses, I calculate multiplication and division than addition and subtraction.
4. If the same number of priority, calculate from left to right.

Let solve one simple problem.

When hourly wage is $5,000, was for 20 hours work in the first week. And was for 24 hours work in the second week. Let calculate the money I get.

5000 X 20 + 5000 X 24 = 220000

It will now earn 220,000 won. If you look at this formula, it has in common. It is part of hourly pay are common. Calculated total working hours, and thereafter it is preferable to apply the hourly rate.

5000 X (20 + 24) = 220000

You can write like this. We called it 'distributive law'. It is possible to be used in reverse.

A X (B + C) = (A X B) + (A X C) = A X B + A X C

So, The above equation is satisfied.

Then, by using the "Algebra", let's prove the nature of addition of even and odd.

The N is the natural number, and S defined as the value of the result.

All Even,

S = 2 X N

You can write like above.

All Odd,

S = (2 X N) +1

I have a be written as above.

Let adding even and odd. Even of both is different. So, one even number is called 'M'.

S = (2 X N) + (2 X M)

S = 2 X (N + M)

Here, according to the nature of the closed state, (M + N) is also nature number. Then, S will be a natural number too.

Please make sure these methods about other natural numeral.

If you are not a mathematician, have not need like this. But logical thinking like this is important in game development. It will be repeat during develop.
In the game world, make a character and make to walk, that is the process going to solve logical problems like this.