In 1826, Lobachevsky published the theory that parallel lines can intersect. Once this theory was published, it surprised many people, but it was more mocking and puzzled. They all think that Lobachevsky's theory is wrong and absurd. Some people even think that Lobachevsky is 80% crazy in theoretical research!
Until 1868, the Italian mathematician Bellamy proved Lobachevsky's theory that parallel lines can intersect. This just let the world know that Lobachevsky's theory is scientific and correct, not his whimsy.
Later, Kazan University in Russia erected a monument and a statue in memory of Lobachevsky. But by this time, Lobachevsky had died 12 years ago, and everything was meaningless!
If only Lobachevsky's theory could be verified while he was alive. At this time, he should finally be relieved. Finally, someone can recognize and understand his theory. He is not alone. He's not fighting alone. But all this came too late. He had already left.
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Definition of parallel lines:
Two straight lines that never intersect in the same plane are called parallel lines. Parallel lines must be defined on the same plane, which does not apply to solid geometry, such as straight lines on different planes, which are neither intersecting nor parallel.
In advanced mathematics, the definition of parallel lines is that two lines intersecting at infinity are parallel lines, because there is no absolute parallelism in theory.
Basic characteristics of parallel lines:
The definition of parallel lines includes three basic characteristics: one is in the same plane, the other is two straight lines, and the third is non-intersection.
In the same plane, there are only two positional relationships between two straight lines: parallel and intersecting.
Properties and judgement of parallel lines in Euclidean geometry;
Properties of parallel lines:
The nature of parallel lines is different from the judgment of parallel lines. The judgment of parallel lines is based on the quantitative relationship of angles, and the nature of parallel lines is based on the quantitative relationship of angles. The nature and judgment of parallel lines are two propositions of causal inversion. For the judgment of parallel lines, it is a conclusion that two lines are parallel, but for the nature of parallel lines, it is a condition that two lines are parallel.
It is known that two straight lines are parallel. The relationship between angles obtained from parallel lines is the nature of parallel lines, including: two straight lines are parallel and the same angle is equal; The two straight lines are parallel and the internal dislocation angles are equal; These two lines are parallel and complementary.