Discussion:
Four Weird Mathematical Objects
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Vincent Granville
2017-06-09 23:19:01 UTC
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Here I discuss four interesting mathematical problems (mostly involving famous unsolved conjectures) of considerable interest, and that even high school kids can understand. For the data scientist, it gives an unique opportunity to test various techniques to either disprove or make progress on these problems. The field itself has been a source of constant innovation -- especially to develop distributed architectures, as well as HPC (high performance computing) and quantum computing to try to solve (to non avail so far) these very difficult yet basic problems.

And the data sets involved in these problems are incredibly massive and entirely free: it consists of all the integers, and real numbers! The first two problems have been addressed on Data Science Central (DSC) before, the two other ones are presented here on DSC for the first time.

http://www.datasciencecentral.com/profiles/blogs/four-weird-mathematical-objects
b***@gmail.com
2017-06-10 00:02:05 UTC
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Flint Hill series etc...

What is:

lim n->oo tan(n)/n = ?
Post by Vincent Granville
Here I discuss four interesting mathematical problems (mostly involving famous unsolved conjectures) of considerable interest, and that even high school kids can understand. For the data scientist, it gives an unique opportunity to test various techniques to either disprove or make progress on these problems. The field itself has been a source of constant innovation -- especially to develop distributed architectures, as well as HPC (high performance computing) and quantum computing to try to solve (to non avail so far) these very difficult yet basic problems.
And the data sets involved in these problems are incredibly massive and entirely free: it consists of all the integers, and real numbers! The first two problems have been addressed on Data Science Central (DSC) before, the two other ones are presented here on DSC for the first time.
http://www.datasciencecentral.com/profiles/blogs/four-weird-mathematical-objects
Markus Klyver
2017-06-15 20:11:12 UTC
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Post by b***@gmail.com
Flint Hill series etc...
lim n->oo tan(n)/n = ?
Post by Vincent Granville
Here I discuss four interesting mathematical problems (mostly involving famous unsolved conjectures) of considerable interest, and that even high school kids can understand. For the data scientist, it gives an unique opportunity to test various techniques to either disprove or make progress on these problems. The field itself has been a source of constant innovation -- especially to develop distributed architectures, as well as HPC (high performance computing) and quantum computing to try to solve (to non avail so far) these very difficult yet basic problems.
And the data sets involved in these problems are incredibly massive and entirely free: it consists of all the integers, and real numbers! The first two problems have been addressed on Data Science Central (DSC) before, the two other ones are presented here on DSC for the first time.
http://www.datasciencecentral.com/profiles/blogs/four-weird-mathematical-objects
Doesn't exist.

SteveGG
2017-06-10 12:17:37 UTC
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Why don't you post so everyone can easily read ?!
James Waldby
2017-06-15 19:56:26 UTC
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...[blog ref]
Post by Peter Percival
The decimal digits of sqrt(2)/2 algorithm -
p(0)=0, p(1)=1,e(1)=2
if 4p(n)+1 < 2e(n) then
p(n+1)=2p(n)+1
e(n+1)=4e(n)-8p(n)-2
d(n+1)=1
else
p(n+1)=2p(n)
e(n+1)=4e(n)
d(n+1)=0
is unclear to me. If n starts at 0, then the first time through
e(n) is undefined.
Note, the referenced web page says "The above ... algorithm ...
computes the digits in base 2 for SQRT(2) / 2", ie it claims to
generate bits, not decimal digits.

It works ok (for small numbers of bits -- the number of bits of p
increases by one at every step) if e(0) is initialized to one, ie
e(0)=1.

Note, Vincent Granville apparently doesn't read replies to his
posts, which usually are brief advertisements for his blog.
--
jiw
Peter Percival
2017-06-15 18:28:21 UTC
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Post by Vincent Granville
http://www.datasciencecentral.com/profiles/blogs/four-weird-mathematical-objects
The decimal digits of sqrt(2)/2 algorithm -

p(0)=0, p(1)=1,e(1)=2

if 4p(n)+1 < 2e(n) then
p(n+1)=2p(n)+1
e(n+1)=4e(n)-8p(n)-2
d(n+1)=1
else
p(n+1)=2p(n)
e(n+1)=4e(n)
d(n+1)=0

is unclear to me. If n starts at 0, then the first time through e(n) is
undefined.
--
Do, as a concession to my poor wits, Lord Darlington, just explain
to me what you really mean.
I think I had better not, Duchess. Nowadays to be intelligible is
to be found out. -- Oscar Wilde, Lady Windermere's Fan