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The Collatz Conjecture was named after and introduced by Lothar Collatz in 1937. The Collatz Conjecture is one of the most infamous unsolved problems in mathematics. It concerns a sequence of integers in which each term is obtained from the previous term following this process: if the previous term is
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Imagine this, a tired chemist dozes of for a few hours only to dream about a snake that is biting its own tail. This dream may sound very bizarre to us but it would later lead to one of the most renowned discoveries in the field of organic chemistry. This
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When discussing the discovery of DNA's double helix structure, James Watson and Francis Crick are two common names that pop up. These scientists received a Nobel Prize in Physiology/Medicine in 1962 for their discovery of the molecular structure of DNA. However, what many people don't
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The binomial theorem describes the algebraic expansion of powers of a binomial. But first, what is a binomial? Well, it is simply a two-term polynomial or, in other words, an algebraic expression having exactly two unlike terms, including the variables and the constant. According to the theorem, it possible to
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Many of us are familiar with the concept of prime numbers: natural numbers greater than 1 that are not a product of two smaller natural numbers. Listing out the first several prime numbers gives us: 2, 3, 5, 7, 11, 13, 17,... Though their definition is rather straight forward, prime
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The Hidden Side of Napoleon Bonaparte Upon first hearing the name Napoleon Bonaparte, one might think of the great military commander who seized the position of Emperor of France following the French Revolution in the 18th century. During his reign, he introduced numerous political and societal reforms, including reconstructing the
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Archimedean semi-regular polyhedra (ASRP) are convex, multi-faceted 3-D objects whose faces are all regular polygons that have sides of equal length and angles of equal degrees. Around every vertex, the same polygons appear in the same sequence, e.g., hexagon-hexagon-triangle in the truncated tetrahedron shown below. Archimedes' original writings
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The Fibonacci Sequence, Golden Ratio and Golden Spiral An introduction to the world of sequences and ratios Introduction to the Fibonacci Sequence The Fibonacci Sequence is a set of integers in which each number, except for the first two, is equal to the sum of the two preceding ones. Numbers
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I have always enjoyed researching and learning about mathematical paradoxes. Partly because they are interesting to think about, and partly because they make us question our already-existing knowledge about the world around us. The Infinite Hotel Paradox or Hilbert's Paradox of the Grand Hotel is one such paradox,
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Research regarding cancer treatment has gradually improved over the years, expanding the range of effective intervention methods: From tumour removal surgery and radiation therapy to targeting rapidly growing cells with chemotherapy. Now, thanks to ever-expanding research, scientists have come up with another treatment that has proven more effective than the
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An Overview Obsessive-compulsive disorder (OCD) is a long-lasting mental and behavioural disorder featuring patterns of intrusive thoughts and fears known as obsessions. Obsessions are persistent unwanted thoughts, mental images, or urges that cause feelings of anxiety, disgust or discomfort. Such obsessions may lead one to do repetitive behaviours, known as
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Introduction The ratio between a circle's circumference and diameter is a mathematical constant known as pi. (i.e. C∕D=π) It is estimated to be around π ≈ 3927⁄1250 = 3.1416 (accuracy 2·10^-6). Two of the very earliest civilizations, the Ancient Egyptians and Babylonians both