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Topic: Plotting axes and the dimensions using tiles in 2D space
Replies: 27   Last Post: Mar 12, 2014 1:25 PM

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 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Plotting axes and the dimensions using tiles in 2D space
Posted: Mar 11, 2014 11:59 PM

On 3/11/2014 8:41 PM, Hlauk wrote:
> On Tuesday, March 11, 2014 6:50:09 PM UTC-8, Ross A. Finlayson wrote:
>> On 3/10/2014 10:55 PM, Hlauk wrote: > On Monday, March 10, 2014 11:53:15 PM UTC-4, Hlauk wrote: >> On Monday, March 10, 2014 8:40:16 PM UTC-4, James Waldby wrote: >> >>> On Mon, 10 Mar 2014 15:35:36 -0700, Hlauk wrote: >> >>> >> >>> ... >> >>> >> >>>> On a 3d grid x,y,z,-x-y-z,x,y,z... >> >>> >> >>>> Where each consecutive prime has the values -- >> >>> >> >>>> x=2,y=3,z=5,x=-7,y=-11,z=-13,x=17,y=19,z=23,x=-29,y=-31 >> >>> >> >>>> z=-37 and so-on... >> >>> >> >>>> Drawing a line in these coordinates using the primes then >> >>> >> >>>> at the end point prime y = 101 then at that point the >> >>> >> >>>> straight line distance back to the origin of >> >>> >> >>>> (x=0,y=0,z=0) = 93 >> >>> >> >>>> >> >>> >> >>>> Is this correct? >> >>> >> >>>> If not, what is the distance? >> >>> >> >>> >> >>> >> >>> If I understand correctly, you are taking triplets of consecutive >> >>> >> >>> primes from the sequence of prime numbers. You treat each >> >>> >> >>> triplet as (x,y,z) coordinates o
f a point and find the triplet's >> >>> >> >>> distance from (0,0,0). Perhaps you have the wrong distance >> >>> >> >>> formula? Using dist((0,0,0),(x,y,z)) = sqrt(x^2+y^2+z^2), >> >>> >> >>> triplet 97 101 103 is about 145.1 units from the origin. >> >>> >> >>> >> >>> >> >>> Formula aside, dist((0,0,0),(x,y,z)) is at least as large as >> >>> >> >>> max(x,y,z), so how could (97, 101, 103) possibly be as close >> >>> >> >>> to the origin as 93 units ? >> >>> >> >>> >> >>> >> >>> Among triplets of consecutive primes less than 100000 I don't >> >>> >> >>> find any that are located an integer distance from the origin. >> >>> >> >>> This is considering all triplets [ie, like (2,3,5), (3,5,7), >> >>> >> >>> (5,7,11), etc] rather than just aligned triplets [ie, like >> >>> >> >>> (2,3,5), (7,11,13), (17,19,23), etc]. >> >>> >> >>> >> >>> >> >>> -- >> >>> >> >>> jiw >> >> >> >> James, >> >> >> >> What triangulation distance back to the origin do you get from y = 101? >> >> >> >> My formula m
ay be wrong? >> >> >> >> These are the next coordinates --- >> >> >> >> z=103, x=-107 , y = -109 , z = -113 ,... >> >> >> >> Cheers, >> >> >> >> Dan > > Here is the actual plot for the sequential primes starting with (2) > and going to 101 for a total of 26 primes. > > 2 3 5 -5 -8 -8 12 11 15 -17 -20 -22 24 23 25 -29 -36 > -36 38 35 37 -41 -48 -52 56 53 > > Beginning with (5) the triangulation back to the origin of x=0,y=0,z=0 > Starting @ prime point 5 and continuing 7,11,13.. gives each triangulation > back to the origin. So skipping (2) and (3) because they are trivial we > have --- > > (5) = 6.164413928985596.. > (7) = 7.681145668029785.. > (11) = 10.67707824707031.. > (13) = 12.36931705474854.. > (17) = 16.49242210388184.. > (19) = 18.13835716247559.. > (23) = 22.13594436645508.. > (29) = 25.19920539855957.. > (31) = 30.2324333190918.. > (37) = 34.24908828735352.. > (41) = 38.20994567871094.. > (43) = 39.86226272583008.. > (47) = 41.59326934814453.. > (53) = 44.66542434692383..
> (59) = 52.55473327636719.. > (61) = 58.5918083190918.. > (67) = 63.52952194213867.. > (71) = 62.96824645996094.. > (73) = 63.54525756835938.. > (79) = 65.38348388671875.. > (83) = 73.17103576660156.. > (89) = 81.78630828857422.. > (97) = 90.24411010742188.. > (101)= 93 > > Could someone verify or discount these values for > each position on the 3d grid back to the origin? > > If these values are wrong, please give the correct values > of the triangulation for each prime starting with (5) > > TIA > > Dan > I hadn't heard of his new one but "Cheers Dan" I believe from his writings. But, Dan, how can (101) be 93 even?
>
> The infinte wrap of each rectangle that is connected by esch of
> it's inner diagonal's too the origin of (x=0,y=0,z=0).
> The actual distance for each prime gets chopped by the negative side
> of -x,-y,-z.
>
> So Ross can you give me the coordinates of each prime as I show them
> so I can compare because I could be wrong.
>
> Thanks
>
> Dan
>

No, not without quite the time. I don't see and wouldn't expect
anything wrong with it?

Really what would be interesting is to how in more details of
examples, here besides the main development, then that it could just
be an early initial sequence of zeros as 0s are dense as 1s in
expansions, and they're normal.

Do you have this formulaically? Then it should simply reduce that,
here to show and prove the congruence, that it is even.

As even as it could be, for that much precision less, then it is a
value for that, in those terms.

Date Subject Author
3/9/14 JT
3/9/14 JT
3/9/14 JT
3/10/14 Robin Chapman
3/10/14 JT
3/10/14 drhuang57@gmail.com
3/10/14 Daniel Joyce
3/12/14 quasi
3/12/14 Daniel Joyce
3/10/14 James Waldby
3/10/14 Daniel Joyce
3/11/14 James Waldby
3/11/14 Daniel Joyce
3/11/14 Daniel Joyce
3/11/14 Daniel Joyce
3/11/14 Daniel Joyce
3/11/14 Leon Aigret
3/11/14 Daniel Joyce
3/11/14 ross.finlayson@gmail.com
3/11/14 Daniel Joyce
3/11/14 ross.finlayson@gmail.com
3/12/14 Daniel Joyce
3/12/14 James Waldby
3/12/14 Daniel Joyce
3/12/14 James Waldby
3/12/14 Daniel Joyce