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.9) Random numbers 10) Pythagorean triples: A great introduction into number theory – investigating the solutions of Pythagoras’ Theorem which are integers (eg. 11) Mersenne primes: These are primes that can be written as 2^n -1.
Be aware that this page gets a large amount of traffic from IB students – do not simply copy articles – it may well be spotted by the moderators.12) Magic squares and cubes: Investigate magic tricks that use mathematics. 13) Loci and complex numbers 14) Egyptian fractions: Egyptian fractions can only have a numerator of 1 – which leads to some interesting patterns. Can all fractions with a numerator of 2 be written as 2 Egyptian fractions?15) Complex numbers and transformations 16) Euler’s identity: An equation that has been voted the most beautiful equation of all time, Euler’s identity links together 5 of the most important numbers in mathematics. This is a puzzle that was posed over 1500 years ago by a Chinese mathematician. 18) Fermat’s last theorem: A problem that puzzled mathematicians for centuries – and one that has only recently been solved.Use this resource as a starting point and inspiration for your own personal investigation.Before choosing a topic you also need to read this page which gives very important guidance from the IB. IB Revision I’d strongly recommend starting your revision of topics from Y12 – certainly if you want to target a top grade in Y13.27) Prime number sieves 28) Recurrence expressions for phi (golden ratio): Phi appears with remarkable consistency in nature and appears to shape our understanding of beauty and symmetry.
29) The Riemann Hypothesis – one of the greatest unsolved problems in mathematics – worth $1million to anyone who solves it (not for the faint hearted!
6) Continued fractions: These are fractions which continue to infinity.
The great Indian mathematician Ramanujan discovered some amazing examples of these.
5) Diophantine equations: These are polynomials which have integer solutions.
Fermat’s Last Theorem is one of the most famous such equations.
How all our digital communications are kept safe through the properties of primes. A post which looks at the maths behind this particularly troublesome series. How strange things happen when we start to manipulate divergent series.