Last class, we talked about the "whole addition and subtraction" in the "whole idea of mathematics". Its core idea is to make a whole "add and subtract" to achieve the desired "effect", and then use the "result after addition and subtraction" to solve the problem, and the problem will be solved.

At the same time, we also talked about the difference between "integral addition and subtraction" and "integral substitution" For the "whole substitution method", as long as a condition or a relationship in the topic is regarded as a "whole", a wonderful "problem-solving effect" can be achieved, and the problem can be solved by direct substitution.

As for "whole addition and subtraction", although a condition or a relationship is regarded as a whole, it is far from enough to achieve the effect of solving problems. It is necessary to carry out "addition and subtraction" between multiple whole bodies to achieve the effect of solving problems.

I won't go into details about "integral addition and subtraction". Interested friends can pay attention to me first and go to my homepage to see the complete course!

Integral transformation method

So what is the whole transformation method?

In fact, it is very simple, that is, treating a condition in a math problem as a whole and then transforming it into a condition with "problem-solving effect" is equivalent to turning the condition into a "little magic" and changing the face of the condition, and the problem will be solved.

We once talked about "mathematical transformation thought", that is, transforming "this" into "that" and solving problems with the attribute of "that" have the same meaning. The difference is that the "integral transformation method" here is based on "whole". To put it bluntly, "integral transformation method" is a branch of "mathematical transformation thought" and an application of "mathematical transformation thought".

Interested friends can pay attention to me and go to my home page to see the whole course about "Mathematics Transforming Thought".

explain

It is known that a-b= 100 and a+b= 10, and A and B are obtained respectively.

Obviously, it is difficult to solve this problem without transformation.

We take "a-b" as a whole, and then transform it into "(a+b)(a-b)", then the problem will be solved.

After the transformation, it is

(a+b)(a-b)= 100, and we substitute "a+b= 10".

10(a-b)= 100

a-b= 10

therefore

(a+b)+(a-b)=20

2a= 10

Get a= 10 and b=0.

Course summary

Up to now, we have talked about three lessons on "the whole idea of mathematics", one is "the whole method of substitution", the other is "the whole addition and subtraction" and the other is "the whole transformation method". Through the study of these three classes, I believe everyone has a deeper understanding of "the whole idea of mathematics"

It is not difficult to find that the application of "the whole idea of mathematics" in the field of mathematics mainly falls into two categories. One is that "as a whole" has the effect of "solving problems" and can be directly used instead; The other is that the expected problem-solving effect cannot be achieved after "taking the whole", and the expected effect can only be achieved through some "movements", such as "addition and subtraction movements", and then substituted into the problem-solving.

Obviously, "whole replacement method" belongs to the first category of "mathematical whole thought", which is the basis of "mathematical whole thought". The "integral addition and subtraction" to be discussed today, the "integral transformation method" to be discussed today and other "integral methods" to be discussed later all belong to the second category of "mathematical integral thought"!

Some people still don't understand this, so let's just say it. That is:

The whole idea of mathematics does not mean that everything will be fine if the conditions or relations in the problem are regarded as a whole. It's not that simple. Some problems can be easily solved by taking a condition as a whole and directly substituting it into the problem. However, some problems, even if a condition is regarded as a whole, cannot be directly used, because this "whole" has no role in solving problems, and it takes "exercise" to achieve amazing results, and finally it can be substituted into solving problems.

So, what is "sports" in mathematics?

Quite simply, the mathematical expression of "movement" is "addition, subtraction, multiplication, division, combination, distribution, sorting, transformation, etc." Through these "actions", we just want to rub out the desired "effect"

Ok, that's all for today. The next class will talk about "overall design method". See you then!