Swimming about in mathematics
Looking around the BBC website today I came across a piece by James Gallagher on the beauty that mathematicians routinely see in some of the more famous mathematical equations. Euler’s identity equation has been voted by many of them to be the most beautiful because it is simple to look at yet incredibly profound. It comprises the five most important mathematical constants (meaning they do not change) and it also comprises the three most basic arithmetic operations: addition, multiplication and exponentiation.
iπ
e + 1 = 0
e (a transcendental number)
i (fundamental imaginary number)
π (another
transcendental number)
1 (multiplicative identity)
0 (additive identity)
Here is a fun version of what the symbols denote when someone is learning to swim
e (the
aquatic learning potential we are born with)
i
(the focus of our
imagination)
π (the
focus of our aquatic learning circle)
1 (the
nature and focus of our aquatic guardianship)
0 (Our
openness to aquatic experiences)
I enjoyed Prof David Percy waxing lyrical about Euler’s equation when he said “Given that e and i are incredibly complicated and seemingly unrelated numbers it is amazing that they are linked by this concise formula. At first you don’t realise the implications. It’s a gradual impact, perhaps as you would feel with a piece of music and then suddenly it becomes amazing as you realise its full potential”
He said beauty was a source of “inspiration and gives you the enthusiasm to find out about things”
Although I cannot pretend to understand complex mathematical formulae I do like to try and I like finding out about things, drinking in any beauty and taxing my brain with difficult ideas because they may bring me new understanding.
What else does the hidden beauty in mathematics have to say about learning to swim?
He said beauty was a source of “inspiration and gives you the enthusiasm to find out about things”
Although I cannot pretend to understand complex mathematical formulae I do like to try and I like finding out about things, drinking in any beauty and taxing my brain with difficult ideas because they may bring me new understanding.
What else does the hidden beauty in mathematics have to say about learning to swim?
Marcus Du Sautoy mathematician and Prof for the public understanding of science sees beauty where Fermat proved a relationship exists between prime numbers and square numbers.
Any prime number that can be divided by 4 with a remainder of 1 is also the sum of two square numbers. eg 41 divided by 4 is 10 remainder 1 and is also the sum of 25 and 16 which are both square numbers.
“So if it has remainder 1 it can always be written as two square numbers and there is something beautiful about that.”
“It’s unexpected! Why should the two things (primes and squares) have anything to do with each other, but as the proof develops you start to see the two ideas become interwoven like two threads in a piece of music and you start to see them come together”
He said it was the journey not the final proof that was exciting “Like in a piece of music it is not enough to play the final chord”
Parallel thoughts ripple across the surface of my mind as I ponder how to explain to people that it is the journey that matters and it is not enough to mirror the stroke patterns of accomplished swimmers. Also beautiful truths hide in unexpected places and in the pool I glimpse this as a child takes itself aside to follow its own learning thread between group activities. This little piece of stolen time annoys many teachers but not me because it is often where that child finds some gold they need.
e “we can learn to swim now because water shaped us in our ancestral past”
i ”it matters where our focus of attention is when we are learning to swim”
π “it matters what our kith and kin feel about being in water as it influences us”
1 ”we need to feel safe and be safe in water to say we can swim”
0 “Our perceptions about water can change”
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