A poem about the three-line octagon in mathematics 1. Math diary, my views on the three-line octagon.

The eight angles obtained by the intersection of two straight lines on the plane are called "three-line octagon".

The eight corners have different names according to their relative positions (as shown in the figure): ∠ 1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8. The relative position is the same, which is called "congruence angle". The isosceles angle is shaped like the letter F.

Two straight lines with the same angle are parallel (it can be regarded as a theorem), and the angles are staggered in the same direction: ∠ 1 and ∠8, ∠4 and ∠5, ∠3 and ∠6, ∠2 and ∠7 are in the same direction as the cut straight line, but they are cut. Internal dislocation angles: ∠ 2 and ∠ 8, ∠ 3 and ∠ 5, all of which are internal, are called "internal dislocation angles".

The internal angles are shaped like the letter Z, and the internal dislocation angles are equal. Two straight lines are parallel (as a theorem). External dislocation angles: ∠ 1 and ∠7, ∠4 and ∠6, which are all outside, are called "external dislocation angles".

The ipsilateral internal angles: ∠ 2 and ∠ 5, ∠ 3 and ∠ 8 are on the same side of the section line and are all inside, which are called "ipsilateral internal angles". The inner corner on the same side is shaped like a letter u or a door frame.

Two straight lines that are parallel to each other (can be used as theorems) and have the same external angles: ∠10 and ∠ 6, ∠ 4 and ∠ 7 are on the same side of the section line and both are outside, which is called "the external angles are the same". The shape of the same outer corner is similar to the Greek letter π.

(It can only be used after theoretical verification) Note: The congruent angle and the internal angle appear in pairs, and it cannot be said that "∠ 5 is the internal angle" or "∠ 6 is the external angle on the same side". Things like Jordan's theorem can be directly used as conditions for geometric reasoning, and others can only be verified by reasoning.

2. Three-line octagon

three lines and eight angles

Open classification: mathematics, geometry, congruent angle, internal angle, internal angle of the same side.

The eight obtained by the intersection of a straight line and two straight lines on the plane is called "three-line octagon" Eight corners have different names according to their relative positions (as shown in the figure).

Isomorphism angles: ∠ 1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 have the same relative positions, which are called "isomorphism angles".

Co-directional dislocation: ∠ 1 and ∠8, ∠4 and ∠5, ∠3 and ∠6, ∠2 and ∠7 are in the same direction, but the cut-off lines are staggered, which is called "dislocation".

Internal angles: ∠2 and ∠8, ∠3 and ∠5 cross each other and are all included, which is called "internal angle".

External dislocation angles: ∠ 1 and ∠7, ∠4 and ∠6, which are all outside, are called "external dislocation angles".

Internal angles on the same side: ∠ 2 and ∠ 5, ∠ 3 and ∠ 8 are on the same side of the section line, and they are all on the inside, which is called "internal angles on the same side".

External angles of the same side: ∠ 1 and ∠6, ∠4 and ∠7 are on the same side of the section line and are all on the outside, which is called "external angles of the same side".

3. The definition of three-line octagon

The eight angles obtained by the intersection of two straight lines on the defined plane are called "three-line octagon". Edit this paragraph to return the relative positions of the last eight corners. The eight corners have different names according to their relative positions (as shown in the figure).

Isomorphism angles: ∠ 1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8 have the same relative positions, which are called "isomorphism angles". The isosceles angle is shaped like the letter F, the same angle is equal, and two straight lines are parallel (which can be used as a theorem).

Co-directional dislocation: ∠ 1 and ∠8, ∠4 and ∠5, ∠3 and ∠6, ∠2 and ∠7 are in the same direction, but the cut-off lines are staggered, which is called "dislocation". (It can only be used after theoretical verification)

Internal angles: ∠2 and ∠8, ∠3 and ∠5 cross each other and are all included, which is called "internal angle". The internal angle is shaped like the letter Z. The internal dislocation angle is equal and two straight lines are parallel (which can be used as a theorem).

External dislocation angles: ∠ 1 and ∠7, ∠4 and ∠6, which are all outside, are called "external dislocation angles". (It can only be used after theoretical verification)

Internal angles on the same side: ∠ 2 and ∠ 5, ∠ 3 and ∠ 8 are on the same side of the section line, and they are all on the inside, which is called "internal angles on the same side". The shape of the inner corner on the same side is like the letter U or C, and the two complementary lines of the inner corner on the same side are parallel (which can be used as a theorem).

External angles of the same side: ∠ 1 and ∠6, ∠4 and ∠7 are on the same side of the section line and are all on the outside, which is called "external angles of the same side". The shape of the same outer corner is similar to the Greek letter π. (It can only be used after theoretical verification)

Note: Coincidence angle and internal dislocation angle appear in pairs, and it cannot be said that "∠ 5 is internal dislocation angle" or "∠ 6 is ipsilateral external angle". Things like Jordan's theorem can be directly used as conditions for geometric reasoning, and others can only be verified by reasoning. Support our team. Thank you!

4. Poetry praising mathematics

1. Mathematics becomes poetry

Once you walk two or three miles, there are four or five smoke villages.

There are six or seven pavilions and eighty or ninety flowers.

This is a poem written by Shao Yong in the Song Dynasty describing the scenery all the way, with 20 words and 10 numbers. This poem reflects the distance, villages, pavilions, flowers and plants with numbers, which is popular and natural.

One, two, three or four, five, six, seven or eight.

Nine pieces, ten pieces, countless pieces, all disappeared when flying into the plum blossom.

This is a poem about Xue Mei written by Lin Hejing in Ming Dynasty. The whole poem uses quantifiers to indicate the number of snowflakes. After reading it, it's like being in the snow. When snowflakes fly into Meilin, it is difficult to tell whether they are snowflakes or plum blossoms.

One nest, two nests, three or four nests, five nests, six nests, seven or eight nests,

Eat all the royal millet, and there will be no more phoenix.

This is a poem "Sparrow" by Wang Anshi, a statesman, writer and thinker in the Song Dynasty. Seeing that many officials in the Northern Song Dynasty were full of food, corrupt and opposed to political reform, he compared them to sparrows and satirized them.

A pole, an oar, a fishing boat, a fisherman and a hook,

Bend down and laugh, one person monopolizes the autumn scenery of a river.

These are ten "One" poems written by Ji Xiaolan in Qing Dynasty. It is said that Emperor Qianlong saw a fishing boat paddling in the river one day, so he asked Ji Xiaolan to write a poem about fishing and asked him to use ten "ones" in the poem. Ji Xiaolan soon sang a poem, writing about scenery and modality, which was natural and appropriate and full of charm. No wonder Gan Long even said, "What a genius!"