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The application of the Pythagorean theorem with water
(42) | 30/12/2012 | Translate: 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).
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How do we do that? What materials
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.
Really good presentation I really liked it. Thank you for it by the way.
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.
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.
Asto better. You're lucky that you did not because I proved one that you're not in education, but for education.
no IME tycheros, IME egkratis, prosgeiwmenos, and non-EPI South fragmitoy .
I am in training and having tithaseysei the eparsi I know it ekpaideyontas ekpaideyomai. These do not however shaping reality:
the construction of this as epoptiko boithima is just amazing.
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...
Indeed when the teacher only speak without to hear what the caller says, These are the results
That's why I said from the beginning "it's better".
and worse piasto, but the construction of this as epoptiko boithima is just amazing.
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...
not that Zadar ESI archises to synomileis Mazi MOU, for a construction that as epoptiko boithima is just amazing.
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, as long as it's Kalamon...
If you didn't have suffered shock from the fantastic this app can be in parexigoysa.
Finally!! the 1 and the recognition.
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…
Finally I say, Finally. and the report and your very outset visit ego katalava and katanoisa you :)
And I want to say "I have no doubt.
AMA thou shalt say ESI, no doubt say that thou tell
parepiptontws,the construction of this as epoptiko boithima is just amazing.
"By the way" you want to say.
chat do you two ;;
now they can be a couple after two years...
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.
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!
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.
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, to make it appear that no water is "hiding" under it.
Your last sentence is somewhat rude. Ratings may be missing.
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:
ELLINIKI MATHIMATIKI ETAIREIA
Athens, April 2, 2007
No.. Protocol: 12234/2-4-07
Mr Lambros th. Maglaras addressed in Greek
Mathematical Society submitting its claim, that the Pythagorean theorem is incorrect.
He cited these:
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, in order to be.
2. That theoretically the Pythagorean theorem:
(a). Requests and makes for the receipt, in aggregates
shapes (The sum of squares, etc.) not covered by the axiomatic system of Euclid, Neither of the later standardization by Hilbert.
(b). Is not necessary for every theorem of axiomatic
support.
The Hellenic Mathematical Society, in response to complaints of responsibility for Mr Lambrou th. Maglara, considering debt simultaneously
to clarify the issue, 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, actually
appears on supervisory nature, BC. materials and designs, as himself
notes, This weakness does not affect the correctness of Pythagorean,
as the construction supervisory and mathematics abstract work of
nature.
2. In relation to the aggregates of shapes, the highlighted, that actually is not foreseen (as you rightly argues) from the geometry, but
against interpretation, the aggregates these aggregates in areas, namely, numbers and no shapes. So, on equilateral triangle rectangle, with vertical side measure 1, the square of the hypotenuse is expressed by an integer
positive number 2, that is, from a square with area 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, After the aggregates and aggregates areas are not shapes.
ELLINIKI ETAIREIA FOR THE MATHEMATICAL
The introducer interpretation.
PRESIDENT EXECUTIVE
EUCLID HISTORY II
George Tassopoylos
NIMS PRESIDENT
Nikolaos Alexandris
Be well and if you have proof of Pythagorean in the context of set theory in which the axiom of area (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.