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Maths Visualized. Geometry. Pythagoras theorem. ►
Tarannum Sehgal's profile photoArturo Gutierrez's profile photoCati Vawda's profile photoAndrzej Solecki's profile photo
Rena H.
Learning this is easy.
Remembering it after three months of no practice is froggin' hard.
What a great way to learn for the visually oriented.
Maths are amusing !! A great thank to pioneer Greek Mathematician Πυθαγόρας (Pythagoras) !
Before I say what I have to say, caveat : I am not a dinosaur. How can I prove it? Well, since I bought my first computer I use Linux. It was 17 years ago. And as soon as 1997 I was communicating with my students taking multiple advantages of the Internet.

And I am a mathematician. And although I like this proof of the Pythagorean theorem more than many others, I do not like it in this version of a colourful, tidy applet.

The simple reason is: one of the essential elements of the proof is showing that once you fix four "equal" triangles in the corners, you are left with a square in the center. It is simple - oh, is it? Fine, convince me that it is. Show why ! You will call some theorems to help you - and this is mathematical reasoning, this is the kernel of mathematics.

But in the description of the animated gif there appears the affirmation The inner square created by the triangles ... wait a moment, what is it? A class of religion? A military drill? Thou shalt not smuggle thy statements! Prove it - or you are doing mumbo-jumbo instead of maths.
+Andrzej Solecki As a high school Geometry teacher, I agree. Even within a course, whose sole purpose in the curriculum IMHO is to teach logical reasoning skills, the aspect of this proof you speak of is often glossed over. Frustrating.
Would this be more acceptable if instead of the flashy applet this exercise was done with paper and scissors, after which students were asked to show why with logical reasoning (theorems)?
+Cati Vawda: sure, let us stay with this Chinese idea and argue why two ways of measuring the figure prove something. This is maths. By the way, it brings a natural question why Greeks had not invented it but used a reasoning that seems much more cumbersome - it will lead to reflections on different attitudes when dealing with geometric problems.

+Teo Nikolaides: maybe calling him a philosopher would be better - and hail him for bringing to Greece the Egyptian maths which he had learnt in his travels...
+Andrzej Solecki: Thank you for exploring this idea further. Perhaps the experience of different attitudes and approaches to dealing with problems in other areas of life (without marginalising geometry, of course).
+Cati Vawda: that's that. There attitude (in some periods, at least; after all, Greek maths is the sum of results of many, many centuries) has been much more concrete; if two figures  have the same measure then let us cut the first in pieces and form the other. Comparing some areas attributed to both of them would seem to them really weird. 
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