Wikipedia:Reference desk/Archives/Mathematics/2007 November 25

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November 25

Millisecond

Why do times shorter than a millisecond feel exactly the same as a millisecond? 124.176.190.64 (talk) 09:22, 25 November 2007 (UTC)

This is essentially due to your reaction time. In order to be aware of the length of an interval of time, you need to be aware of its beginning and end, but the process of being aware of each of those is longer than a millisecond (I haven't looked up precise reaction times, so I may be off here, but the basic idea is right), so there's a shortest time scale humans can be aware of.

We can build instruments with reaction times that are much shorter and get these to measure time intervals, but this isn't really "feeling" or "experiencing" the time interval. kfgauss (talk) 11:13, 25 November 2007 (UTC)

Monsterpyramid

If I want to build a pyramid made of 2,4 billion blocks, starting with 1 block at the toplayer, 2x2=4 at the second, 3x3=9 at the third, 4x4=16 at fourth and so on. How many blocks will the bottomlayer have, and how many layers vill the pyramid be in total? Strange question perhaps, but I really have to know! —Preceding unsigned comment added by 81.94.65.50 (talk) 16:20, 25 November 2007 (UTC)

If this pyramid has n layers, it will have a total of ${\frac {2n^{3}+3n^{2}+n}{6}}$, or roughly ${\frac {n^{3}}{3}}$, blocks. I'll leave the rest to you. -- Meni Rosenfeld (talk) 16:25, 25 November 2007 (UTC)

See also Square pyramidal number. PrimeHunter (talk) 16:53, 25 November 2007 (UTC)

Thank you! The problem is that I don`t know how to solve the problem even with the equation in hand, because I don´´t know how to solwe equations at all. Please just give me the number of blocks in the bottom layer and how many layers the pyramid will have in all. In return I will give you a hard, (I suppose) problem in a few days, when I have all the numbers and fakts for the problem. —Preceding unsigned comment added by 81.94.65.50 (talk) 17:12, 25 November 2007 (UTC)

In that case, for 1930 layers you have 2398215105 blocks, and for 1931 layers you have 2401943866 blocks. Pick whichever is better for you. The number of blocks in the bottom layer is 3724900 or 3728761, respectively. -- Meni Rosenfeld (talk) 17:16, 25 November 2007 (UTC)