The number π and continued fractions

This bachelor thesis deals with one of the well-known mathematical constants, the number π. The form is understandable to higher-year students of secondary schools interested in mathematics. At first, it presents the best known ways people in history tried to approximate the number π. It includes the methods of Egyptians, the people of ancient Mesopotamia and the method of Archimedes. It also presents expressing π in the form of infinite product according to F. Viète and J. Wallis. The second part of the thesis focuses on expressing the number π by continued fractions, which are at first generally defined. We introduce essential relations among them. Then the thesis presents expressing the number π in the form of continued fractions according to J. H. Lambert, L. Euler and W. Brouncker. Finally, proofs of the irrationality of π using continued fractions are presented together with a simple proof of its transcendence. The aim of the thesis is to extend information about π stated in popular books, to explain and clarify basic ideas leading to these claims