Pure maths, physics, logic (braingames.ru): non-trade-related brain games - page 99

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Mathemat:

The beginning of the solution has been stated for the case without friction. But when friction starts, everything changes.

I remember I wanted to solve the diphurk... I was too lazy to do it.
 
MetaDriver:

No, no. My imagination is running out today. How to find this mythical geometric centre? And does it coincide with the point obtained by averaging the coordinates?

Preferably with a proof or very obvious explanations.

// I'm particularly interested in this subject. You may consider it a separate task.

Well, let me try to explain it, bluntly. )

Take a ball. Its centre of gravity coincides with the centre of the ball. If we project this ball to a plane, then we see a circle in the centre of which the projection of the centre of gravity is located.

This example can also be given for flags. That is, for them (flags) placed on this circle, the 'centre of gravity' will be the centre of the circle or the centre of the sphere.

For an example not related to a circle (sphere) one must imagine a body, the projection of which on a plane will be a closed Bezier curve.

I do not know how to describe it mathematically, but I have an idea. It goes something like this.

 
Forever Friday branch)))
 
fyords:

Well let me try to explain, bluntly. )

We take a balloon. Its centre of gravity coincides with the centre of the ball. Now if we project this ball onto a plane, we see a circle in the centre of which is the projection of the centre of gravity.

This example can also be given for flags. That is, for them (flags) placed on this circle, the centre of the circle or the centre of the sphere will be the 'centre of gravity'.

For an example not related to a circle (sphere) one must imagine a body, the projection of which on a plane will be a closed Bezier curve.

I do not know how to describe it mathematically, but I have an idea. It goes something like this.

Is there such a thing as a closedBézier curve?))
 
Mathemat:

Well, it is the average of all coordinates, there is no need to prove anything.

And the centre of gravity is the same average, but weighted by masses.

He didn't explain anything, he didn't prove anything. It's like "for lack of need". Fucking hell. We don't do that in a vacuum! You have to prove every perpendicular here! Oh...

--

I had to weigh it myself. The answer matched, but generally speaking, it's not that trivial at this point.

--

Here's an example question: 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, do the centre and the TMR not have to coincide? And, by the way, how to find the TMR (if they do not coincide) ?

 
alsu:
Is there such a thing as a closed Bézier curve?))

Why not?

Google's first answer: a closed Bezier curve

Figure 8.7 shows that a closed Bézier curve was created by placing seven guide points ...

 
fyords:

I don't know how to describe it mathematically, but I have an idea. It's like this.

That's not interesting at all. I'm just here to formalise my not overly exuberant ideas into [correct] formulas.
 
MetaDriver:
That's not interesting at all. I'm just here to formalize my overly exuberant notions into [proper] formulas.
Understood, I do not interfere in the assault of mega-brains ))
 
fyords:
Got it, don't interfere in the mega-brainstorming))
No, no. You interfere, but have a mathematical conscience. (ц)
 
fyords:

Why not?

I hadn't thought of them before for some reason)

nevertheless, what do they have to do with projections and centres of gravity?

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