3,4,5 triangle).ġ1) Mersenne primes: These are primes that can be written as 2^n -1.ġ2) Magic squares and cubes: Investigate magic tricks that use mathematics. There is a $1 million prize for solving the Riemann Hypothesis and $250,000 available for anyone who discovers a new, really big prime number.ġ0) Pythagorean triples: A great introduction into number theory – investigating the solutions of Pythagoras’ Theorem which are integers (eg. The great Indian mathematician Ramanujan discovered some amazing examples of these.ħ) Patterns in Pascal’s triangle: There are a large number of patterns to discover – including the Fibonacci sequence.Ĩ) Finding prime numbers: The search for prime numbers and the twin prime conjecture are some of the most important problems in mathematics. Fermat’s Last Theorem is one of the most famous such equations.Ħ) Continued fractions: These are fractions which continue to infinity. For example, Mod 3 means the remainder when dividing by 3.Ģ) Goldbach’s conjecture: “Every even number greater than 2 can be expressed as the sum of two primes.” One of the great unsolved problems in mathematics.Ĥ) Applications of complex numbers: The stunning graphics of Mandelbrot and Julia Sets are generated by complex numbers.ĥ) Diophantine equations: These are polynomials which have integer solutions. Suitable for Applications and Interpretations students (SL and HL) and also Analysis and Approaches students (SL and HL).ġ) Modular arithmetic – This technique is used throughout Number Theory. ![]()
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