The wrong angle on Pythagoras’s theorem

‘In using a theorem to prove something else, you need to look at its origins to ensure that it doesn’t depend on the result you are trying to prove.’ Photograph: Igor Stevanovic/Alamy

While it is heartening to see enthusiastic mathematical inquiry in young people and the academic community encourage teenagers, it is not possible to prove Pythagoras’s theorem using angle trigonometry (US teens say they have new proof for 2,000-year-old mathematical theorem, 24 March). That is because the basic definitions of sines and cosines are derived from Pythagoras’s theorem, so using them in any way to derive the theorem is therefore using circular reasoning.

In using a theorem to prove something else, you need to look at its origins to ensure that it doesn’t depend on the result you are trying to prove. We should be doing everything possible to encourage young people to explore maths, but it’s also essential to ensure that they understand the origins of theorems and definitions, and how they are linked. It seems cruel to build them up when it is impossible that they could be correct. That said, I look forward to seeing the work that they have done.
Catherine Scarlett
Driffield, East Yorkshire

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