Zeno’s Paradox – Achilles and the Tortoise This is a very famous paradox from the Greek philosopher Zeno – who argued that a runner (Achilles) who constantly halved the distance between himself and a tortoise would never actually catch the tortoise. The video above explains the concept. There are two slightly different versions to this […]

Fourier Transform The Fourier Transform and the associated Fourier series is one of the most important mathematical tools in physics. Physicist Lord Kelvin remarked in 1867: “Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly […]

Non Euclidean Geometry – An Introduction It wouldn’t be an exaggeration to describe the development of non-Euclidean geometry in the 19th Century as one of the most profound mathematical achievements of the last 2000 years. Ever since Euclid (c. 330-275BC) included in his geometrical proofs an assumption (postulate) about parallel lines, mathematicians had been trying […]

The Telephone Numbers – Graph Theory The telephone numbers are the following sequence: 1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496… (where we start from n=0). This pattern describes the total number of ways which a telephone exchange with n telephones can place a connection between pairs of people. To illustrate this […]

Happy Numbers Happy numbers are defined by the rule that you start with any positive integer, square each of the digits then add them together. Now do the same with the new number. Happy numbers will eventually spiral down to a number of 1. Numbers that don’t eventually reach 1 are called unhappy numbers. As […]

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