Wikipedia links of interest

1. Precipitation.

2. Prime number theorem.

“In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers. The prime number theorem gives a rough description of how the primes are distributed.

Roughly speaking, the prime number theorem states that if a random number nearby some large number N is selected, the chance of it being prime is about 1 / ln(N), where ln(N) denotes the natural logarithm of N. For example, near N = 10,000, about one in nine numbers is prime, whereas near N = 1,000,000,000, only one in every 21 numbers is prime. In other words, the average gap between prime numbers near N is roughly ln(N).”

‘Roughly’ because we’re dealing with asymptotics. For n=10, the true likelihood is 40%, the approximative result is 43,43 percent [10/ln(10)], for n=100 the true likelihood is 20%, the approximative result is 21,71% [100/ln(100)]. There’s more stuff along the same lines here. x/ln(x) is not the best estimator of pi(x), but it works.

3) Hadrian’s Wall.

The right hand side of the article has a lot of great links to articles belonging to the article series on ‘Military of ancient Rome’. If you find this subject interesting, there’s probably a lot of stuff waiting for you there.

4) Hayashi limit (the maximum radius of a star for a given mass).

5) Placoderms. They died out 360 million years ago, yet we still know that they existed and even a bit more than that. “A 380-million-year-old fossil of one species represents the oldest-known example of live birth.” The fact that we even know something like that – how cool is that? Very cool! Here’s a picture:

October 17, 2010 - Posted by | Astronomy, History, Mathematics, Paleontology, Physics, Wikipedia

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