Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 100
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I didn't think of them before for some reason)
nevertheless, what do they have to do with projections and centres of gravity?
OK, I'll try a second run.
Imagine a piece of ..... loaf of bread on the table )
It (the loaf) has a centre of gravity - right? And now imagine the projection of this loaf on the table. And this curve is the Bezier curve. The same table has the projection of the centre of gravity. Well, I've described the rest before.
For example: Does the point obtained by averaging the coordinates (centre of gravity, CG) coincide with the point at which the sum of the distances to the flags is minimum (point of minimum distance, TMR)?
Or in general case DT and TMR do not have to coincide? And by the way, how to find TMR (if they do not coincide) ?
These are different things. In one case you take coordinates and average them, and in the other you take distances that are stupidly not coordinates.
I think so too. How do you find such a point (TMR)? Any thoughts?
I don't have any so far.
It is not necessary to solve this problem. Simple considerations will suffice.
I'll bring them up when everyone is exhausted.
OK, trying a second run.
Imagine a piece of ..... loaf of bread on the table )
It (the loaf) has a centre of gravity - right? And now imagine the projection of this loaf on the table. And this curve is the Bezier curve. The same table has the projection of the centre of gravity. Well, I've described the rest before.
And why is it Bezier, Bezier curves are polynomial curves, in the most common case cubic... Why is the loaf projection suddenly described by a polynomial of degree 3?(Or do you mean approximation?)
(4) A tributary forms a sharp corner as it flows into the river. On land, inside the corner, is Megamozg's shack. Every day, Megamozg leaves it, walks to the tributary, meets the sunrise, then goes to the river, meets the sunset and returns to the shack. How does Megamozg need to plot a route so that the distance he walks each day is minimal? Consider the banks of the river and the tributary as straight lines.
Let MM live at point A, let's call the dawn meeting point B and the sunset meeting point C. Our problem is to minimize the perimeter of triangle ABC. Let's make the megamosk sing symmetrically twice: first with respect to the tributary bank, and then with respect to the obtained image of the river bank. The path A->B->C->A will be mapped into an equivalent-length polyline A->B->C'->A'. Obviously, the length of this polyline is always greater than the length of the segment AA'.
Hence the way of construction of the minimal route follows: the megamancer should perform twice the symmetry transformation, find the crossing points B'' and C'' of the line AA' with the tributary bank and the first image of the river bank, and then transfer by inverse symmetry transformation the point C'' to the "real" river bank. The perimeter of the resulting triangle is equal to the length of segment AA', hence it has minimal length.
TheXpert, +10 for intuition!
TheExpert, +10 for intuition!
It's not intuition. If you need to find the best path, the path of the beam of light is often the right one.
+10 for the construction, I didn't get it.
Most of the time - but not always. Here, say, it doesn't work with the state border.
P.S. My solution is very similar, differing in minor details.
P.P.S. (1), made it up myself:
A respected company's forum has come up with an original way of stimulating forum member activity. Each post in a thread, in addition to the top starter's own posts, adds an extra point to his rating - regardless of who wrote in that thread. His own posts thus gain two points.
Can the cumulative rating of forum members be odd?
I came up with it myself:
A respected company's forum has come up with an ingenious way of stimulating forum activity. Each post in a thread, in addition to the topic's own posts, adds an extra point to his rating - regardless of who wrote in the thread. His own posts thus gain two points.
Can the total rating of forum members be odd?