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You can get those neat looking formulas using LaTeX.
To use it, you need the math tags:
You can click any formula to see how it was written. Also, there are a lot of them here
But, if we are looking at 3D space, spherical geometry wouldn't be placed on the surface of a sphere, but rather on the surface of a hypersphere.
Also, after your post I realised that I wanted to say "in polar coordinates". But this way it's more interesting.
How do you define a plane in spherical geometry?
Now you're copying me? You are stone dead to me.
Here's mud in your eye!
If I cannot think of another pun, my name will be in mud.
Sticks and stones may break my bones, but jokes will never harm me.
No problem. No member here has a heart of stone.
It's a pun on the word "deep". It can be used to mean that it's very philosophical, but also to refer to "deep" as in "deep under the earth".
You can see the rest of us followed by even more puns with words related to dirt and mud.
Will do. Thank you for posting it!
I hope for more of these in the near future.
Ah, okay. I will try getting something out of the chain.
Hm, so you did it the same way I did?
It seems right for infinite throws. I think it's different for finite.
Hm, is expected time calculated as P(I-P)^(-2)?
So, you cannot do it by Markov chain?
Fixed my matrix above, forgot that 654321 is not an absorbing state.
Okay. Then what?
Hm, let's try the second option. I put my hands together and say the magic words.
And that is?
Yes, but I do not know how.
I wanted to do it with a Markov chain, but I couldn't find the formula for the expected number of visits to a state.
I used the independence of expectation trick.
Anyway, this wasn't as hard as you said it would be.
How did you do it?
Thanks. I have miscounted something, that's why I got the first answer.
I wouldn't have been so sure of either answer if it wasn't for the simulation.
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