Wikipedia:Reference desk/Archives/Mathematics/2023 December 29

= December 29 =

a mathematical formula that is useful in error correction
why isnt anyone using this formula?

Pr = sigma n = 0 until ceil(log2(Pe)): C(Pr * Pd, n)

Pr = possblities of redundant data. Pe = possblities of maximum error. Pd = possblities of actual data. here is another way of writing this:

d <= floor(log2((2^a)/(sigma n= 0 until E: C(a, n))))

d = length of data in bits. a = all bits, a = d + r, r = length of redundant data in bits. E = maximum error bits, i didnt use e to dont get wrong with euler's constant netrual expantion number.

the way it works is sigma ...: C(t,n) gives number of possble errors and dividing all possblities for a by error possblities results in number of possble data values and getting its log2 results in length of data in bits Mahdoosh1 (talk) 09:03, 29 December 2023 (UTC)


 * I haven't the foggiest idea what you're trying to say above and would need a better explanation and an example of use. Even not having the foggiest though having Pr on both sides of the first equation looks funny to me. Wikipedia has lots of articles on various types of error correction in communication, possibly the top one would be Information theory, perhaps you could identify a relevant field?. NadVolum (talk) 10:56, 29 December 2023 (UTC)

second formula may make better sense, here is an example:

to encode 2 bits in a way that can correct 1 bit error we need 3 redundant data at least, this means a=5,E=1,d=2,r=3:

d <= floor(log2(2^(a)÷sigma n=0 until E:C(a,n))) 2 <= floor(log2(2^(2+3)÷sigma n=0 until 1:C(2+3,n)))

2 <= flog2(2^5 ÷ (1+5)) 2 <= flog2(32 ÷ 6) 2 <= flog2(5.33...) 2 <= 2

if this is hard, here will be a desmos link for this formula:
 * https://www.desmos.com/calculator/cywvtoi0w8

— Preceding unsigned comment added by Mahdoosh1 (talk • contribs) 11:09, 29 December 2023 (UTC)
 * You might be interested in Hamming code which deals with correcting errors in small amounts of data like this. The Hamming bound deals with theoretical limits for error correcting fixed length data with no feedback and lists some other bounds. NadVolum (talk) 16:31, 29 December 2023 (UTC)

Tetrahedral assembly
A regular tetrahedron of twice the edge length of another has eight times the volume. Could eight of the smaller ones be assembled into one of the larger?2A00:23C6:AA0D:F501:D9BD:B595:E656:54D3 (talk) 22:53, 29 December 2023 (UTC)
 * No. If you start by filling the corners of the 2x tetrahedron with four or the 1x tetrahedrons, the remaining space is an octahedron (with four outer and four inner faces) that cannot be filled with the remaining four 1x tetrahedrons - the face-to-face angles of the octahedron are not compatible with the tetrahedrons. See also tetrahedron packing, which states "Tetrahedra do not tile space". -- Tom N talk/contrib 23:27, 29 December 2023 (UTC)
 * This Stack Exchange question also has a discussion that includes the rationale "a tetrahedron is not a space-filling solid, since neither the angle between faces nor the solid angle in a vertex are rational multiples of a radian/steradian." -- Tom N talk/contrib 23:49, 29 December 2023 (UTC)
 * Obligatory link to Tetrahedral-octahedral honeycomb. That works because the dihedral angles of the tetrahedron and octahedron add up to $\pi$, though neither by itself is a rational multiple of π. Double sharp (talk) 04:30, 30 December 2023 (UTC)
 * (OP) Thanks.2A00:23C6:AA0D:F501:D82A:F6B2:DF1A:5A6D (talk) 16:23, 30 December 2023 (UTC)