A smart construction proving the Pythagorean theorem with water (The square of the hypotenuse of a right triangle equals the sum of the squares of the two vertical sides).

29 Comments

1. AdelIno 25 says:

   03/01/2018 at 14:53

   How do we do that? What materials

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   • Mk says:

     06/01/2021 at 20:21

     It's just smooth water. You know the Pythagorean theorem? That is the answer. (a2+b2=c2) There are 3 plexiglass cubes in the middle and one triangular in shape, he poured water into the bottom two, because, according to the consensus, it fills the c2 cube, explain this. Pythagoras was very clever he invented this item.

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2. Simster says:

   13/06/2016 at 13:37

   Really good presentation I really liked it. Thank you for it by the way.

   

   

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3. dimitris81 says:

   08/10/2013 at 20:33

   First of all, Lampros congratulations for the presentation. The colleague you just noticed it is an exquisite example of understanding and memorizing students. I would say eyfiestato .... because it is so simple and clear. Nobody talked about precision proof. And you imagine when they formed the shapes in any table is not absolute. We lost stuff. The truth is that your colleague seems to be an excellent teacher and surely you are too but you did not show that you know it.... Education is not only Encyclopedias.

   

   

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   • Andreas Horn says:

     02/07/2024 at 12:21

     Bildung hat sich in D leider zu Enzyklopädie und deren Anwendung zurückentwickelt. Normaler Weise hat jedes (Aus-) Bildungs- auch ein Erziehungsziel. Ich habe de Eindruck, heute wird man wieder auf Gehorsam und Obrigkeitshörigkeit getrimmt. Selber denken scheint unerwünscht zu sein.

     

     

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4. Asto Kalitera says:

   07/10/2013 at 15:49

   the construction of this as epoptiko boithima is just amazing. I want to gkriniaxw from my cartoon that didn't I thought first to Kano, Tosa hronia in education but Leo na min Kano.

   

   

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   • Lambros Th. Magklaras says:

     07/10/2013 at 17:41

     Asto better. You're lucky that you did not because I proved one that you're not in education, but for education.

     

     

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     • Asto Kalitera says:

       07/10/2013 at 18:48

       no IME tycheros, IME egkratis, prosgeiwmenos, και μη επι φραγμίτου του νότιου .ΕΙμαι στην εκπαιδευση και εχοντας τιθασευσει την επαρση μου γνωριζω οτι εκπαιδευοντας εκπαιδευομαι. These do not however shaping reality:the construction of this as epoptiko boithima is just amazing.

       

       

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       • Lambros Th. Magklaras says:

         07/10/2013 at 19:20

         Well, if you are indeed in education – which since you assure me I believe so – much is explained about the quality of education! When the teacher speaks only to hear what the caller says, These are the results. STOU Khufu the door. Cheers to my tamed conceit and I am sorry for the sharpness of the colloquialism I have used...

         

         

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         • Asto Kalitera says:

           07/10/2013 at 19:26

           Indeed when the teacher only speak without to hear what the caller says, These are the results

           

           

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           • Lambros Th. Magklaras says:

             07/10/2013 at 20:02

             That's why I said from the beginning 'it's better'.

             

             

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             • Asto Kalitera says:

               07/10/2013 at 21:59

               and worse piasto, but the construction of this as epoptiko boithima is just amazing.

               

               
             • Lambros Th. Magklaras says:

               07/10/2013 at 22:36

               A little longer and will you be amazed (for song) with the gargling. Did you see that your finally made good the conversation with me; So educate me. With tangible results. Even the engineer make awkward. I don't hide that you started to please me...

               

               
             • Asto Kalitera says:

               07/10/2013 at 22:44

               not that Zadar ESI archises to synomileis Mazi MOU, for a construction that as epoptiko boithima is just amazing.

               

               
             • Lambros Th. Magklaras says:

               07/10/2013 at 23:41

               Remembering me now! But all remember; Rather do it deliberately to dyskolepseis; For your own sake I did because I realized instantly that you're in education, because of the conclusion on the hint of peripeplegmenis and amazing this nomination of supervisory device. You know the honey with the amazing application, and with olive oil, αρκεί να είναι Καλαμών… Αν δεν είχες πάθει καταπληξία από την καταπληκτική αυτή εφαρμογή μπορεί να σε παρεξηγούσα.

               

               
             • Asto Kalitera says:

               08/10/2013 at 10:55

               Finally!! the 1 and the recognition.

               

               
             • Lambros Th. Magklaras says:

               08/10/2013 at 11:23

               You want to say from the outset. From the outset, in dikaiwsa and in recognized, except I made it a bit complicated and you didn't get it…

               

               
             • Asto Kalitera says:

               08/10/2013 at 11:46

               Finally I say, Finally. and the report and your very outset visit ego katalava and katanoisa you :)

               

               
             • Lambros Th. Magklaras says:

               08/10/2013 at 12:43

               And I want to say 'I have no doubt.

               

               
             • Asto Kalitera says:

               08/10/2013 at 15:53

               AMA thou shalt say ESI, no doubt say that thou tell

               

               
         • Asto Kalitera says:

           07/10/2013 at 19:27

           parepiptontws,the construction of this as epoptiko boithima is just amazing.

           

           

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           • Lambros Th. Magklaras says:

             07/10/2013 at 20:01

             'By the way' you want to say.

             

             

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             • GEORGIOS KOUTSOGIANNIS says:

               31/10/2015 at 09:06

               chat do you two ;;

               

               
             • trapkoulas says:

               02/11/2015 at 13:56

               now they can be a couple after two years...

               

               
5. Lambros Th. Magklaras says:

   16/09/2013 at 10:58

   Mathematics is not juggle. To the naked eye it is found that the square of the hypotenuse is not produced by the hypotenuse of the right triangle. The rectangular triangle (Yellow) It has smaller side, After the sides there are gaps to passing water, of the other three sides of the square in which the hypotenuse of the triangle participates as one of the sides of. The square has four equal sides, rather than 3 and a lower. The precision is supposed to be the pride of mathematics and is chopped error.

   

   

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   • Sideboard Pa says:

     06/10/2013 at 22:14

     I disagree with you. In construction it is not necessary that there are gaps caused by unequal sides (Anyway it didn't seem anything like). The vacuum seems to be below, i.e. at depth. Anyway, If the construction were not accurate, This would result, According to the Pythagorean theorem!

     

     

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     • Lambros Th. Magklaras says:

       07/10/2013 at 09:41

       In manufacturing it is necessary to have the empty because no spaces can not pass water! However that is not the issue. The Pythagorean like any katskeyi in geometry is done exclusively with compass and Straightedge. With this method (fluids) the squaring of the circle is 'constructively' proved and the stupid problem of doubling the cube is also solved. Non so you disagree. Is a farcical notion (not to say perception adaoys) around Pythagorio and geometry in General.

       

       

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       • Sideboard Pa says:

         07/10/2013 at 11:07

         And again: the gaps appear to be underneath, It is not some little side. At least so it seems, If tapping and flow of water. The only criticism I could make of this as 'evidence' (comment I did the same) is that the triangle should be transparent, για να φαίνεται ότι δεν “κρύβεται” νερό από κάτω του.Η τελευταία σου πρόταση είναι κάπως αγενής. Ratings may be missing.

         

         

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         • Lambros Th. Magklaras says:

           07/10/2013 at 15:12

           I didn't mean to offend you and if so have although not true, I regret and apologies. On the merits: Doesn't look and so much attention (This offended me chat with you completely well-intentioned) in my remarks that the Pythagorean (as any construction) belongs in mathematics only if proven with compass and Straightedge. Beyond that the Pythagorean theorem is wrong through construction even with compass and Straightedge. You're justified to do not know why you hide and what I say is not generic and vague. However we gladly help you if desired: ΕΛΛΗΝΙΚΗ ΜΑΘΗΜΑΤΙΚΗ ΕΤΑΙΡΕΙΑΑθήνα 2 Απριλίου 2007 Αρ. Protocol: 12234/2-4-07 Ο κύριος Λάμπρος Θ. Μαγκλάρας απευθύνθηκε στην ΕλληνικήΜαθηματική Εταιρεία καταθέτοντας τον ισχυρισμό, ότι το πυθαγόρειο θεώρημα είναι εσφαλμένο.Επικαλέστηκε τα εξής:1. That construction cannot prove the theorem, because during transformations 2 pairs of vertical angles are impossible – e.g. 2 pairs of equal right-angled isosceles triangles – touching at the same time at the 'center' of the square being composed, ώστε να το αποτελέσουν.2. That theoretically the Pythagorean theorem:(a). Requests and makes for the receipt, σε αθροίσειςσχημάτων (The sum of squares, etc.) not covered by the axiomatic system of Euclid, Neither of the later standardization by Hilbert. (b). Δεν έχει την αναγκαία για κάθε θεώρημα αξιωματικήστήριξη. The Hellenic Mathematical Society, in response to complaints of responsibility for Mr Lambrou th. Maglara, θεωρώντας ταυτόχρονα χρέος τηςνα διαλευκάνει το ζήτημα, invited him in Committee II and crowd presence EUCLID fellow mathematics teachers, the provided the following clarifications about the Pythagorean theorem. 1. Compared with the manufacturing weakness, που όντωςεμφανίζεται επί εποπτικής φύσεως, BC. materials and designs, όπως ορθά και ο ίδιοςεπισημαίνει, This weakness does not affect the correctness of Pythagorean,καθώς η κατασκευή είναι εποπτική και τα μαθηματικά λειτουργούν αφαιρετικά τηςφύσης.2. In relation to the aggregates of shapes, the highlighted, that actually is not foreseen (as you rightly argues) from the geometry, αλλάκατά ερμηνεία, the aggregates these aggregates in areas, namely, numbers and no shapes. So, on equilateral triangle rectangle, with vertical side measure 1, το τετράγωνο της υποτείνουσας εκφράζεται από τον ακέραιοθετικό αριθμό 2, δηλαδή από τετράγωνο με εμβαδόν 2.3. In comparison with the authoritative support of pythagorion, This indicated to Mr Lambros th. Maglara, that is in the Office of the area, αφού οι αθροίσεις είναι αθροίσεις εμβαδών και όχι σχημάτων.ΓΙΑ ΤΗΝ ΕΛΛΗΝΙΚΗ ΜΑΘΗΜΑΤΙΚΗ ΕΤΑΙΡΕΙΑ Ο εισάγων την ερμηνεία. ΠΡΟΕΔΡΟΣ ΕΚΤΕΛΕΣΤΙΚΗΣΓΡΑΜΜΑΤΕΙΑΣ ΕΥΚΛΕΙΔΗΣ Β΄Γιώργος ΤασσόπουλοςΠΡΟΕΔΡΟΣ ΕΜΕΝικόλαος Αλεξανδρής Να είσαστε καλά και αν έχετε απόδειξη του πυθαγόρειου στο πλαίσιο της θεωρίας συνόλων στην οποία ανήκει το αξίωμα του εμβαδού (since any other – like construction – is not accepted by EME as you can see) gladly you overthrow Similarly, that is easily. Thank you for the interesting conversation.

           

           

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