Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 89
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There's a conspiracy again...
I think I've got it. It's all about progessors and mathematicians.
and "bodies falling at different speeds" generates a lot of interest, discussion with intuition, attempts at verbal explanations.
Why doesn't anyone answer questions with calculations and formulas? that would remove 99% of the differences in concepts and show the model the other is presenting.
and so it stretches out trying to prove it for several pages.
and it's just mechanics... and what happens next.
I think I've got it. It's all about progessors and mathematicians.
and "bodies falling at different speeds" is a lot of interest, discussion with intuition, attempts at verbal explanations.
Why doesn't anyone answer questions with calculations and formulas? It would eliminate 99% of the differences in concepts and show the model that the other presents.
but it takes a few pages to prove it.
and that's just mechanics... what's next.
formulas alone do not mean anything, first you must understand the process and then you may or may not describe it
why does papa need a formula from a school textbook? v^ 2=2gh He sees the process differently.
Why does Daddy need a formula from a school textbook? v2=2gh He sees the process differently.
so it's from the maths that you can see the process.
understand what data the left-hand side of the equation depends on the right-hand side.
and then you can see that we have different models of the process!
and everyone will add the one they have and give the specific factors that describe the model.
so it's from the maths that you can see the process.
understand what data the left-hand side of the equation depends on the right-hand side.
and it becomes clear that we have different models of the process!
and everyone will add the one they have and give the specific factors that describe the model.
(5) The cake is shaped like an arbitrary triangle. Two megabrains divide it in the following way: the first points a point on the cake, the second makes a rectilinear cut through this point and takes most of it. How much of the cake can the first megabrain get for himself? It is assumed that the cake has the same thickness everywhere.
Let us prove that the required point is the intersection point of the medians of the triangle.
Consider tr. ABC, denote by M the intersection point of its medians (centroid). As we know, all three medians of triangle are divided by centroid in the ratio 2:1, counting from the vertex. This means (Fig. a) that the line DE passing through the centroid parallel to one of its sides cuts off a smaller triangle with area 2/3*2/3=4/9. That is, if the first brain points to point M and the second brain makes a cut parallel to one of the sides, it will capture 5/9 of the cake. Let's check if he can still increase his share. Draw through point M the line FG intersecting the same sides of the triangle as DE. In triangles DMF and GME DM=ME, and the angles at vertex M are equal. Then, since obviously MF>MG, the area of triangle DMF is larger than that of triangle GME. Hence, in turn, the area of triangle AFG is larger than the area of triangle ADE, but it is also smaller than half the area of triangle ABC, since the halving is achieved only when FG coincides with CM.
Thus, in the case where the first megamosk has pointed to point M, then the second megamosk should make a cut parallel to one of the sides to obtain at most 5/9 of the cake.
Suppose now that the first megamosk has pointed a point K different from M (Fig. b). The second musk can proceed as follows: he draws through point M three lines parallel to each side of the triangle, and chooses from them the cutting triangle, inside which point K lies (or one of those on the boundary of which it lies, if the point is on the boundary). Let it be the line DE. Now the second bridge draws a line parallel to DE through point K. The median of BM is cut by this line in the ratio smaller than 2:1, hence the area of the cut trapezium is greater than 5/9. Thus, the first mosk is less than 4/9, so it is unprofitable for him to specify a point other than M.
Answer: The first brain should point to the centroid of the triangle (the point of intersection of its medians). Then he is guaranteed to get 4/9 of the cake.
To be fair, M is indeed the centre of mass of the cake)) but that is a different problem!
I think I've got it. It's all about the progessors and the mathematicians.
Formulas don't mean anything on their own, you need to understand the process first, and then you can describe it or not.
Why does the class need a formula from a school textbook? v^ 2=2gh He sees the process differently.
Misha, I respect you.
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