Thursday, May 24, 2012
Olympiad Math
1 Geometry and Trigonometry
1.1 A Property of Equilateral Triangles
1.2 Cyclic Quadrilaterals
1.3 Power of a Point
1.4 Dissections of Polygonal Surfaces
1.5 Regular Polygons
1.6 Geometric Constructions and Transformations
1.7 Problems with Physical Flavor
1.8 Tetrahedra Inscribed in Parallele pipeds
1.9 Telescopic Sums and Products in Trigonometry
1.10 Trigonometric Substitutions
2 Algebra and Analysis
2.1 NoSquare IsNegative
2.2 Look at the Endpoints
2.3 Telescopic Sums and Products in Algebra
2.4 On an Algebraic Identity
2.5 Systems of Equations
2.6 Periodicity
2.7 The Abel Summation Formula
2.8 x+1/x
2.9 Matrices
2.10 The Mean Value Theorem
3 Number Theory and Combinatorics
3.1 Arrange in Order
3.2 Squares and Cubes
3.3 Repunits
3.4 Digits ofNumbers
3.5 Residues
3.6 Diophantine Equations with the Unknowns as Exponents
3.7 Numerical Functions
3.8 Invariants
3.9 Pell Equations
3.10 Prime Numbers and Binomial Coefficients
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There are an enormous number of uses of trigonometry and trigonometric functions.Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.
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