Category Archives: Mathematics

Scotland’s Quiet Revolutions – One Nation with Sovereign Achievements… and a Pure Dead Brilliant Future!

A photograph of the countryside north of Glasgow - sheep grazing. Image: NaturPhilosophie

Scotland’s Quiet Revolutions

It seems quiet at first, and even dull.  Not much happening…  Dreich, as one might say!  Sad.  Grim.  Bleak.  Not much to do…  Not much to see here…  Just sheep…  But wait!!  Look closer!  Is that Dolly in this field?  Now, that’s interesting!  Oh, Aye, we’re in Scotland!  It changes EVERYTHING… 

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Friends or Fourth Cousins

A photograph of a group of friends hugging each other. Friends or Fourth Cousins.
Do your Friends have Similar Genomes?

Do you know who your fourth cousins are?  The chances are you don’t.  But do you know who your friends are?  Of course, you know that much.  But did you ever stop and think why or how your friends are your friends?  Could your friends actually share part of your DNA, to the same extent a distant family member does?

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Satellite of Love – It’s Up, Up and Away for Scotland’s UKube-1

An artist's impression of the new Scotland UKube-1 micro-satellite in orbit around Earth.
Scotland’s First Nano-Satellite

Earlier this month, UKube-1, a satellite built by Glasgow-based technology firm Clyde Space, successfully launched on a test flight from Baikonur, Kazakhstan.  It is the first ever spacecraft to be fully assembled in Scotland.

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Calculating Entropy – The Energy of Change

A drawing showing a snowflake of Ice melting into molecules of water. From order to disorder, there is only entropy.
It’s About Heat and Temperature

What is the difference between heat and temperature?  Heat is thermal energy.  Temperature is a measurement of the average kinetic energy of the particles which compose the matter being tested.  When heat flows into a material, one of two things happen: either the temperature of the material can rise, or there may be a change in its state (such as from ice to liquid, or liquid to vapour).

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Colossal Genius: Alan Turing

A black and white portrait of Alan Turing - the man behind the Enigma decryption.
60 Years Hence

Today’s the 60th Anniversary of the Death of Alan Turing – a genial mathematician, a cryptographer and one of the pioneers of computer science at Bletchley Park.  He is considered one of the greatest minds of the 20th Century.  Alan Turing‘s life was one of complexity and secret triumphs, overshadowed by a very public tragedy. 

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Up Archimedes! – The Principle of Buoyancy

A photograph showing a huge mass of helium balloons carrying their human payload up into the sunset sky. Image: Jonathan Frappe
Archimedes’ Principle and Helium Balloons

Buoyancy is the upward force exerted by a fluid that opposes the weight of an object immersed in a particular substance.  Essentially, this is what Archimedes (c.287212 BC) observed when he stated that:

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Winning at Rock-Paper-Scissors… Lizard-Spock!

A picture representing the traditional game of Rock, Paper, Scissors.
A Little Game Theory

What is the ultimate strategy for winning at rock-paper-scissors?  According to three physicists in China, the answer does not lie in having absolutely no strategy and ensure that your choice of weapon is completely random, unlike previously thought.  If that strategy seemed obvious, perhaps you haven’t played the game enough to delude yourself into thinking that this might be a winning strategy… 

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Fibonacci’s Golden Spiral – The Relationship between Maths and Nature

A close-up photograph of a cross section through a Nautilus shell showing that the Fibonacci sequence can be found everywhere in Nature.
The Language of Nature

They are found everywhere in Nature.  From the leaf arrangement in plants, to the pattern of the petals of a flower, the bracts of a pine cone, or the scales of a pineapple.  The Fibonacci numbers are applicable to the growth of every living thing: a single cell, a grain of wheat, a hive of bees, all of mankind.  From sunflowers to sea shells, the same recurrent mathematical pattern can be observed in Nature, again, and again, and again… 

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Magnetic “Monopole” Observed in Quantum System – The Lowdown on Electromagnetism

A representation of an artificial magnetic monopoles field.
On the Trail of the Elusive Magnetic Monopole

Break a magnet into two pieces, and what do you obtain?  What you get, unsurprisingly perhaps, are two new magnets – each one with two sides of opposite polarity.  You don’t get a north half and a south half.  Back to square one, it seems… 

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Euler’s Equation: A Thing of Great Beauty

A picture showing the equation for Euler's Identity: e^{i Pi} + 1 = 0.
Euler’s Identity

Please take a moment to enjoy this thing of great beauty…  Simple to look at.  Yet incredibly profound.  Does it get any better than this? 

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