Genady

Turns out that the sum of squares of the three distances, a2 + b2 + c2, is the same for all points on the circle. It appears as an algebraic "accident." What could be a geometric reason for this fact?

I don't know. But this factor is so obvious that I doubt it was not addressed. How do you know that it was not addressed?

All these factors go under the "tired light" hypotheses. They were investigated quite thoroughly, and the general conclusion is that they don't fit observations. There are many articles about them, their predictions and tests. Perhaps other members here will give you more specific answers.

I've found some information on it here: quote source - Who said "Poetry is the art of giving different names to the same thing"? - Literature Stack Exchange

Does it mean abstraction? For the context, nawinterviewP.pdf (uu.nl):

In what reference frame?

Yes. Gravitational waves.

He asked about (my emphasis) Edit: x-posted

I understand that they ask about, in this case, P(y(x) < 0), which is in [0,1]. Example: y(x) = x2, on [0, 10]. What is probability of y to be within [36, 64]? For x2 < b, x < sqrt(b). So, P(36<y<64) = (8 - 6)/10 = .2

If you can solve inequality y(x)<b, then the range of x in this solution over x1-x0 gives you probability P(y<b). The probability P(a<y<b)=P(y<b)-P(y<a).

Because they hit you sometimes, or something else?

Thank you. Yes, this is new to me, although it is not surprising as my course of set theory was quite basic. But why did you call these solutions "not altogether satisfactory"?

Thank you. Here I've sketched it. The four shapes are 1-0, 2-0, 3-0, and 4-0, where I've numbered the opposite vertices of each:

ChatGPT asked me to tell you this: Just passing the message 😉

In addition to very good questions above, what does it mean to prove a theory? Is there a proof of any theory in physics that you can point to?

Two triangular pyramids, not necessarily equilateral, attached at a base make a shape with triangular faces and nine edges. Trying to imagine how to put four of these shapes together.

What are you talking about?

I do. One. I saw how a person was misdiagnosed with bipolar disorder. (Unfortunately, it turned out to be something much worse.)

Yes, this is right. One syntax might be preferred over another, depending on a context. For example, to the question, what bites the man? the preferred answer would be, cheloveka bites dog. Exactly.

I think that I've answered what @TheVat was referring to, judging by his following up.

Almost. What is modified in Russian in this case is the object noun. 'Man' = 'chelovek'. But 'dog bites man' = 'dog bites cheloveka'. All six permutations are grammatically correct and mean the same, with a different emphasis: 'dog bites cheloveka' 'dog cheloveka bites' 'bites dog cheloveka' 'cheloveka dog bites' 'bites cheloveka dog' 'cheloveka bites dog'

A seasonal sport, watching developing storms. This one, the #1 in the image, is quite close to the equator, but I bet it will miss us anyway.

I know many people who don't suffer from the bipolar disorder but are as well capable of generating a new speculation every 10 minutes. They just don't get excited by this activity.

Kay Redfield Jamison - Wikipedia has written about her own bipolar disorder as a professional psychologist working on this illness.