Octomatics

  description the octomatics project is about a new number system which has a lot of advantages over our old decimal system. the name comes from the mixture of ‘octal’ and ‘mathematics’.

The Koch Snowflake

A fractal, also known as the Koch island, which was first described by Helge von Koch in 1904. It is built by starting with an equilateral triangle, removing the inner third of each side, building another equilateral triangle at the location where the side was removed, and then repeating the process indefinitely. The Koch snowflake…

The golden ratio manifesting in nature

The universe may be chaotic and unpredictable, but it’s also a highly organized physical realm bound by the laws of mathematics. One of the most fundamental (and strikingly beautiful) ways these laws manifest is through the golden ratio. It’s not hard to find examples of this logarithmic phenomenon in nature — whether it’s a simple…

Laplace’s Equation, Mathematical Key to … Everything

Physics has its own Rosetta Stones. They’re ciphers, used to translate seemingly disparate regimes of the universe. They tie pure math to any branch of physics your heart might desire. And this is one of them: It’s in electricity. It’s in magnetism. It’s in fluid mechanics. It’s in gravity. It’s in heat. It’s in soap films….

A peculiar pattern in prime numbers

Prime numbers, divisible only by 1 and themselves, hate to repeat themselves. They prefer not to mimic the final digit of the preceding prime, mathematicians have discovered. “It is really, really bizarre,” says Stanford University postdoctoral researcher Robert Lemke Oliver, who, with Stanford number theorist Kannan Soundararajan, discovered this unusual prime predilection. “We are still…

Ancient Babylon figured out forerunner of calculus

Tracking and recording the motion of the sun, the moon, and the planets as they paraded across the desert sky, ancient Babylonian astronomers used simple arithmetic to predict the positions of celestial bodies. Now, new evidence reveals that these astronomers, working several centuries B.C.E., also employed sophisticated geometric methods that foreshadow the development of calculus….

The Rolling Shutter Phenomenon

  I remember seeing the photo above on Flickr once, and having my brain melt slightly from trying to figure out what went wrong. The issue was the propeller was rotating as the camera detector ‘read out’, i.e. there was some motion during the exposure of the camera. This is an interesting thing to think…

Magnetic Resonance Imaging

A familiarity with basic electromagnetic properties will assist the reader of this text. A detailed introduction to electromagnetism is beyond the scope of this appendix, but a handful of basic principles and concepts pertinent to MRI are presented, prima facie, in this appendix. The electricity and magnetism sections in introductory college physics texts for engineers…

The Far Ends of a New Universal Law

Imagine an archipelago where each island hosts a single tortoise species and all the islands are connected — say by rafts of flotsam. As the tortoises interact by dipping into one another’s food supplies, their populations fluctuate. In 1972, the biologist Robert May devised a simple mathematical model that worked much like the archipelago. He…

Life Is a Braid in Spacetime

Excuse me, but what’s the time?” I’m guessing that you, like me, are guilty of having asked this question, as if it were obvious that there is such a thing as the time. Yet you’ve probably never approached a stranger and asked “Excuse me, but what’s the place?”. If you were hopelessly lost, you’d probably…

Maths whizz solves a master’s riddle

A mathematical puzzle that resisted solution for 80 years — including computerized attempts to crack it — seems to have yielded to a single mathematician. Terence Tao, a mathematician at the University of California, Los Angeles, and a winner of the Fields Medal in 2006, submitted a paper1 to the arXiv preprint server on 17…

Parallel Universes Is Not Just Math: It Can Be Tested

The existence of parallel universes may seem like something cooked up by science fiction writers, with little relevance to modern theoretical physics. But the idea that we live in a “multiverse” made up of an infinite number of parallel universes has long been considered a scientific possibility – although it is still a matter of…