Inductive reasoning, definition and induction of solid geometry

Student name: Lin

School: National Tainan No.1 Senior High School.

Instructor: Professor Ke Wenfeng

First, the purpose of learning

Laplace once said that the main tools for finding truth in mathematics are induction and analogy.

Cubes, triangular prisms, pentagonal prisms, square cones and octahedrons, Euler formula F+V = E+2 is derived, in which

The basic element of induction is to compare the geometric shapes of the top of the tower and the truncated cube. We study geometry.

The purpose of learning is essentially to study and reason about the tangible things around you.

The first layer is to promote the concept of plane space and increase the flexibility of thinking logic.

It is to visually observe the various properties of numbers known today with mathematical units such as arithmetic, geometry and set.

Most of them are discovered through observation, and strict proof takes decades or even hundreds of years to be born.

Second, learning methods.

Through the professor's explanation, peer discussion, or going to the blackboard to try to explain to the new siblings,

We can further explore the concepts of logic, geometry and solid geometry, and we can also learn from the process of inductive reasoning

Know the ins and outs of the formula, not just the Euler formula of F+V = E+2.

Participation, learning process and results

First, observation and induction are the steps for scientists to deal with experience. When using observation induction to guess, it is necessary.

We must adhere to the following three principles: First, we must be able to correct our opinions at any time. Second, if there is any problem,

If you have to change your point of view, you must make a quick decision to correct it. Third, there is no good reason not to be there.

With support, blindly change our views. Even if most people disagree, we won't rely on watermelons.

Edge.

Second, this part of the dividing elements seems to be nothing new (when the number of dividing elements is small), but

When I counted a little more, I began to use my head, but I still had no clue. Fortunately, it was finally divided.

For example, the points divided from a line are 1, 2, 3, 4,

5,6, …, push the number of planes divided by straight lines to 1, 2,4,7, 1 1, 16, …, and finally.

It can be inferred that the number of spaces in plane division is 1, 2, 4, 8, 15, 26, ...

Four. Discussions and suggestions

First, we should be patient when using observation induction, and don't jump to conclusions too quickly. For example, the French mathematician Fermat thought

The n+ 1 power of 2 is a prime number. But he only figured out that n = 1, 2, 3 and 4 are all prime numbers, so he deduced.

N = 5, 6 is true ... and so on. But Euler really substituted n = 5 and found that it could

64 1 is divisible, so it is not a prime number.

Second, we can learn a lot from implementation. In terms of speed, implementation takes time, but

Practice has the advantage of slow work and fine work. For example, carbon 60, commonly known as buckyball, is the latest.

I just found the allotrope of carbon. One day in class, Professor Ke asked me to be one with another partner.

Bucky ball, it takes a lot of effort to fold a curved ball, but with it, I get it.

It has 12 regular pentagons and 20 regular hexagons, as well as some accessories, 90 sigma bonds and.

30 pi keys.