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Calculation of Values of Trigonometric Functions
Uhlířová, Iva ; Halas, Zdeněk (advisor) ; Štěpánová, Martina (referee)
Title: Calculation of Values of Trigonometric Functions Author: Iva Uhlířová Department: Department of Mathematics Education Supervisor: Mgr. Zdeněk Halas, DiS., Ph.D. Abstract: This bachelor thesis deals with various calculation methods of how to calculate values of trigonometric functions (sine and tangent chiefly). These methods either were used in the past times or are still used nowadays. However, in this thesis, these methods are explained in a modern way in order to be easily understandable by such readers who have basic knowledge of calculus. In each chapter, there is only one method discussed. At first, lengths of chords are calculated and a table of them is constructed, based on Ptolemy's and Copernicus' methods. Then, al-Kashi's approximation method is interpreted elaborately. Furthermore, Newton's method of development of Taylor series for the sine function is explained in detail. Last but not least the CORDIC algorithm is discussed. In order to provide a better understanding, there are particular values calculated in each chapter. Keywords: Almagest, CORDIC, Taylor series
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Goniometry in Ptolemy's Almagest
Kušnír, Martin ; Halas, Zdeněk (advisor) ; Bečvář, Jindřich (referee)
The main focus of this bachelor thesis are the beginnings of goniometry in ancient Greece, mainly in the book Almagest from Claudius Ptolemy. We describe a predecessor of modern goniometric function - the length of a chord in a circle and it's similarity to the modern goniometric function sine. In the first part we focus on computing the table of chords. In the thesis the process of computing the table of chords is unchanged from the original in Almagest, it is only translated into a modern mathematical language. We present description of the Heron's algorithm for computing square roots and discuss the accuracy of the table of chords. In the second part we show the usage of the table of chords in astronomical calculations. Our work is based on how Ptolemy viewed the solar system and the movements of heavenly bodies. Keywords: goniometry, Ptolemy, Almagest, chord, sine
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