Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 94
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.......... and prove that running to the points is at least as close as the geo-centre.
The sum of the cathetuses is always greater than the hypotenuse.
Um, elaborate :) it's a bit more complicated than that.
This is your revenge for this:
A triangle cannot have more than one centre of circumcircle.
This is your revenge for this:
Okay, I'll explain.
More precisely, there always exists a point whose N distances are equal to the sum of the distances to the given N points. This point is defined by a simple procedure of averaging all the checkbox coordinates, and it is invariant with respect to the choice of origin. Consequently, 30 round trips are equivalent to 30 round trips to the geometric centre of the formation. Whichever point of this centre is located, we can always choose a point on the circle more than a radius away from it (100m), hence the total length of runs would be more than 100*30*2 = 6000m, which is needed to prove.
There's an inaccurate 'insufficiency' in this 'proof'.
No, that's not all. You still have to prove that (1) is also true for the geometric centre of the circle, and you have to prove that it is at least as close to the geometric centre as it is to the points.
Let us try to repair. Let us start with the same - find a point in the plane being the average of all checkbox coordinates in an arbitrary coordinate system. Let's call it a "characteristic point"(XT). The megamizm's solution is to find the point on a circle as far away from XT as possible (let's call it a "decision point"(TP)). As we can easily see, the most difficult position for a megamizm in the case of XT coincides with the circle centre. In this case for guaranteed survival it must also take into account the correction(P), which we will find out in the course of the proof. And we will prove the fact that there is always a point on the circle which guarantees that the sum of distances to flags is strictly greater (not equal!) than 30 distances to HT.
Proof:
To simplify the proof, we transform the coordinate system in this way: we place 0 in TP and the X axis in the direction of XT. Then we drop a perpendicular from each flag to the X axis. Now it is easy to see that the sum of coordinates along the X axis of the flags is equal to thirty times the distance to XT.The sum of the distances to the flags themselves will always be greater than or equal to this value, and strict equality will hold only if all the flags are strictly on the X-axis.
// Hence, correction(P): if flags are equidistant from the circle centre and lined, the megabrain should not select intersection points
// circle with this line. All other points are at its disposal.
Comrades, can this really work? There is no violation of the laws of physics here (second law of thermodynamics)?
PS: Judging by the comments, there's a battery hidden in there. But the trick is cool )
Comrades, can this really work? There is no violation of the laws of physics here (second law of thermodynamics)?
Of course, this is a trick.
Comrade says that he just replaced the electromagnets with permanent ones and everything started working. That's where the dog is in the hole. In a DC motor, the magnetic field of the electromagnets is not actually constant. The four-tooth rotor shown here (the one with the wound coils) has several commutation zones (3, I think) on its contact surface, so at least one coil is short-circuited at any given time. This is what makes the motor self-starting - the constant alternation of solenoid connection/closure - possible: if we applied current to all four coils, they would enter a stable equilibrium position in the stator's magnetic field and not move.
All right. I'll explain.
wah shaitan.
Score!
Score!
Yes, it's beautiful.
______________
Yes, by the way -- the problem about the boxes on the spring when the vector changes almost loses its meaning -- with the greater frictional force of the small box, any energy can be stored.
Of course, this is a trick.
A friend says that he simply replaced the solenoids with permanent solenoids and everything started working. That's where the dog's mouth is at work. In a DC motor, the magnetic field of the electromagnets is not actually constant. The four-tooth rotor shown here (the one with the wound coils) has several commutation zones (3, I think) on its contact surface, so at least one coil is short-circuited at any given time. It is this - the constant alternating connection/short-circuit of the solenoids - that ensures the motor starts itself: if we applied current to all four coils, they would enter a position of stable equilibrium in the stator magnetic field, and would not move.