Recent content by haruspex

No, it does not make that assumption. I am defining H to be the height of the water above the base B of the ball. The top of the ball is higher yet.

Read post #15 carefully. The argument goes like this: With a ball floating inside its hexagonal prism, there are three regions of interest above the level of the bottom of the ball, B: The volume of water, ##V_w## The volume of ball in the water, ##V_i## The volume of ball above the water...

It is not an approximation. Archimedes' Principle is exact and depends only on the volume, not details of the shape.

Have we? How does the algorithm generate the list, to the required length, as needed?

Except when the object is, instantaneously, at the rotation axis?

Apologies - I misread your method. It’s fine, and it is the same as in post #1.

https://en.wikipedia.org/wiki/Coriolis_force lays it all out very clearly. Correctly describing the motion in a rotating reference frame needs three virtual forces, known as the Euler force (involving the angular acceleration and object location), the centrifugal force (involving the angular...

Not so fast. Consider e.g. if instead they were almost the same density as the water, also hexagonal in section and 1m tall. (Btw, not all cells would be hexagonal. What other shape is likely to arise, and how many of those would there be?) Edit: I misread post #1. Your method works fine for...

Which means it is not a solution to the problem. Each player can anticipate the other’s strategy. If player 2 calculates player 1's best strategy then player 2 can reconsider her own strategy. But player 1 can anticipate that, and so on. Please read posts #17 and #20, and see...

Well, I have a result, but hard to be sure how accurate it is. R has probability of about 0.625 of winning. The strategy distributions are both, graphically, and with some smoothing The peak is at distance 0.56. Note the slight asymmetry. Some notes on my method: I divided the 1m distance...

Working on it, but I don’t see an analytic way and I can’t get an accurate numerical result before the program exceeds its execution time.

That does not define a stable solution. Exactly how long does L wait to decide R has failed to fire? If L waits for ##\Delta t## then R will delay ##\Delta t##, so L waits ##2\Delta t##… The problem is to find a pair of strategies, each a fixed probability distribution known to the other, such...

We have to make an assumption about realism. Can each duellist observe the other pulling the trigger and respond rapidly enough to achieve a dead heat (in terms of moment of firing) deliberately? If not, we can consider a dead heat effectively impossible. Either way, in general, we may need to...

The original text does not say "once". You added that in your instruction. But what does cutting once mean? It suggests a single straight cut, but that appears impossible. Do you mean one continuous line, but not necessarily straight? I can do that, but it seems too easy.

Bingo. As should have been obvious, it would not have been possible to time an individual transit since that is defined as the period Io is invisible in consequence of Jupiter's shadow. From Earth, that can be observed at one end of the transit only; at the other, it will be hidden from Earth...