![]() ![]() Trigonometric functions and existence of circle ratio. Formulas and identities of trigonometric functions. Chanapat Pacharapokin, Kanchun, and Hiroshi Yamazaki. Extremal properties of vertices on special polygons. ![]() General Fashoda meet theorem for unit circle and square. Angle and triangle in Euclidean topological space. Inverse trigonometric functions arcsin and arccos. Stanisława Kanas, Adam Lecko, and Mariusz Startek. The Mathematical Association of America (Inc.), 1967. The sum and product of finite sequences of real numbers. Introduction to real linear topological spaces. Segments of natural numbers and finite sequences. Grzegorz Bancerek and Krzysztof Hryniewiecki. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.Grzegorz Bancerek. , sets furnished with various structures having no classical analogues. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. " During the seventies of the last century there occurred another scientific revolution. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. It does not really exist in the real world we live in, but we pretend it does, and we try to learn more about that perfect world. It is safe to say that it was a turning point in the history of all mathematics. In Euclidean geometry we describe a special world, a Euclidean plane. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry.
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