Category Archives: mathematics

Richard Feynman: A Life Of Curiosity And Science

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It was World War II and scientists belonging to the Manhattan Project worked on calculations for the atomic bomb. Meanwhile, in one of the buildings, future Nobel Prize winning theoretical physicist Richard Feynman was cracking the combination lock on a safe because doing so intrigued him. That’s as good a broad summary of Feynman as any: scientific integrity with curiosity driving both his work and his fun.

If you’ve heard of him in passing it may be because of his involvement on the Space Shuttle Challenger disaster commission or maybe you’ve learned something from one of his many lectures preserved …read more

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Solve 2D Math Equations Colorfully

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Electronics can be seen as really just an application of physics, and you could in turn argue that physics is the application of math to the real world. Unfortunately, the way most of us were taught math was far from intuitive. Luckily, the Internet is full of amazing texts and videos that can help you get a better understanding for the “why” behind complex math topics. Case in point? [3Blue1Brown] has a video showing how to solve 2D equations using colors. If you watch enough, you’ll realize that the colors are just a clever way to represent vectors and, in …read more

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Katherine Johnson: Computer To The Stars

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In 1962, John Glenn sat in his capsule waiting for his rocket engines to light-up and lift him to space. But first, he insisted that Katherine Johnson double-check the electronic computer’s trajectory calculations. While that’s the dramatic version of events given in the recent movie, Hidden Figures, the reality isn’t very far off. Glenn wasn’t sitting on the launchpad at the time, but during the weeks prior to launch, he did insist that Johnson double-check the computer’s calculations.

So who is this woman who played an important but largely unknown part of such a well-known historical event? During her long …read more

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Bob and Alice Meet The Ultimate Firewall

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Not the Alice and Bob we know running and frolicking along and about various and sundry paths to Security Nirvana, oh no me prtetties, but the Alice and Bob of mathematics, blackholes, paradoxes and whatnot… Examine – if you will – what happens when… Continue reading Bob and Alice Meet The Ultimate Firewall→

All The Stuff You Wished You Knew About Fourier Transforms But Were Afraid To Ask

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The Fourier transform underpins so much of our technological lives, in most cases probably without our realising it. The ability to mathematically split a waveform into its frequency components and vice versa underpins much of the field of digital signal processing, and DSP has become an essential part of many electronic devices we take for granted.

But while most of us will know what a Fourier transform is, fewer of us will know anything of how one works. They are a function called from a library rather than performed in themselves. Even when they are taught in schools or university …read more

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Building a Working Game of Tetris in Conway’s Game of Life

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If you haven’t been following along with Conway’s Game of Life, it’s come a long way from the mathematical puzzle published in Scientific American in 1970. Over the years, mathematicians have discovered a wide array of constructs that operate within Life’s rules, including many that can be leveraged to perform programming functions — logic gates, latches, multiplexers, and so on. Some of these creations have gotten rather huge and complicated, at least in terms of Life cells. For instance, the OTCA metapixel is comprised of 64,691 cells and has the ability to mimic any cellular automata found in Life.

A …read more

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Symmetry for Dummies: Noether’s Theorem

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Einstein referred to her as the most important woman in the history of mathematics. Her theorem has been recognized as “one of the most important mathematical theorems ever proved in guiding the development of modern physics.” Yet many people haven’t the slightest clue of who this woman was, or what she did that was so significant to our understanding of how our world works. If you count yourself as one of those who have never heard of Emmy Noether and wish to enlighten yourself, please read on. I can only hope I do her memory justice. Not just by telling …read more

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