Patterns are everywhere in the world around you – in the distribution of petals on a flower, the position of cracks in dried mud, or the wind-shaped crests of sand on the beach. Patterns are powerful because they allow for prediction and are visually beautiful.
A sequence is a list of numbers that follows a pattern. It may be as simple as a list of positive integers
1,2,3,4,5,… or more complex such as 0,1,1,2,3,5,8,13,21,34,…
The second sequence is a well-known sequence called the Fibonacci sequence, which is related to the Golden Ratio and models the patterns of the spirals in the nautilus shells.
2020.09.30 Arithmetic Sequences
TOK Connection
As seen in the magnificent video by ViHart, the Fibonacci sequence is frequently occurring in nature. Observations like this have led to the knowledge question, ‘Does mathematics exist independent of human construction?’
In short, is mathematics ‘out there’ serving as the foundational fabric holding together our very elegant universe? Or alternatively, is mathematics created by humans in the same way that we have created language?
These two competing views are referred to as, Platonism – the belief that mathematics exists independent of humanity and Formalism – the belief that mathematics is created by humanity.
Discuss arguments in favor of both Formalism and Platonism.
Exit Ticket
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