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《生活与哲学》在分析“真理是具体的有条件的”(教材47页)知识点时引用了以下文字:三角形内角之和等于180。,这是古希腊数学家欧几里得提出的定理。在此之后的两千多年里,人们一直把它当作任何条件下都适用的真理。随着航海事业的发展和人们对于球面认识的不断深入,这一定理的局限性逐渐暴露出来。19世纪初,俄国数学家罗巴切夫斯基提出:在凹曲面上,三角形内角之和小于180°。随后,德国数学家黎曼提出:在球形凸面上,三角形内角之和大于180°。由此,人们关于空间的观念发生了革命性的
Life and Philosophy quotes the following words in the analysis of Knowledge Points: Truth is Concrete Conditional (Textbook, p. 47): The sum of the interior angles of the triangles equals 180. , Which is the theorem proposed by the ancient Greek mathematician Euclid. Over the two thousand years that follow, people have always regarded it as a truth that applies under all conditions. With the development of navigation and people’s continuous understanding of the sphere, the limitation of this theorem gradually exposed. At the beginning of the nineteenth century, Russian mathematician Robakowski proposed that the sum of the internal angles of the triangles be less than 180 ° on a concave curved surface. Later, German mathematician Riemann proposed that the sum of the interior angles of the triangles is greater than 180 ° on the spherical convex surface. As a result, people’s ideas about space have taken a revolutionary turn