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Post by fcg710647 on Aug 7, 2015 22:32:18 GMT -8
18>12>24>15>20>16 in general... each of those bases has its advantages. Yes, 15 is odd, but a lot of its recurring stuff has very short periods and it terminates somewhat more fractions than 16.
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Post by fcg710647 on Aug 10, 2015 20:28:16 GMT -8
Oh lol 10/8 is 1.25 on your website for cutting the lumber, 1.125 would be 9/8, although it's not a big difference. Anyway, I forgot to check the little arithmetic thingy you wrote. 1/4 and 1/3 of Od. are 4.9 and 6, the sum is A.9; multiply it by 9 (half of eighteen) and you get 54.9... translated to decimal, this would be 4.5 + 6 = 10.5, 10.5 * 9 = 94.5 A depressing thing... when multiplying two numbers that both don't end in zero, it's base six that gives the highest probability that the product ends in zero. 2*3 = 10 and 4*3 = 20 are the ones it uses, and each one appears twice on the table due to commutativity. The probability is 4 / 25 or 0.16 in decimal. Dozenal's chances are 17 / 121 (decimal), or about 0.14050. I believe the base in third place is quaternary, where 2^2 = 10 and the chance is 1/9 = 0.11111... or 0.2 in Od. and 0.14 in doz. lol
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Post by Buffoonery on Aug 15, 2015 11:22:28 GMT -8
Finally back, oooo and an interesting read. Thank you. Yeah, I'd agree with you, an odd base would be better than a bad one. But then again, since 16 is a power of 2, wouldn't it would be nicer to use for an average tradesman than any odd base.
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Post by Buffoonery on Aug 15, 2015 11:30:23 GMT -8
Ahhhh thank you so much, how could I miss that 10/8, I also spotted another mistake nearby, I'm gonna read through my article again and make sure I don't have any more obvious mistakes. - How did you get those fractions 4/25, 17/121, 1/9 for the probability of products ending in zero? I'm kind of interested to see.
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Post by Buffoonery on Aug 15, 2015 11:37:49 GMT -8
Lol, can you imagine the look on people's faces as you pull out a compass. "Stuff's going down, he's got a compass!" Bases 6 and 8 seem cool, but 6 doesn't like quarters, and base 8 doesn't like thirds. The next one up is the dozenal system, which has thirds and quarters easy. But then as you go higher, octadecimal doesn't like eighths or quarters as much as dozenal. That's at least what I see.
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Post by fcg710647 on Aug 16, 2015 17:12:56 GMT -8
Wow, this board said you made the last post, as if my previous one didn't exist. Anyway, one twelfth in base 42 is 0.3a and one eighteenth is 0.2C
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Post by Buffoonery on Sept 10, 2015 16:09:32 GMT -8
Oh no! Hopefully that was just a connection issue and not the forum on the frits. Sometimes I accidentally double post, other times it wouldn't post at all, like on G+. That was sad lol, having to retype 3 paragraphs, I learned to copy into word and then post. I wish data could be handled a little more directly, it's like giving your mail to a mailman with alzeimers.
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Post by fcg710647 on Sept 13, 2015 19:01:40 GMT -8
The total number of possible products, zero-ending or not, is (base number - 1)^2. Anyway, if the base must be a multiple of 4 and 3, I prefer 36, which has the least ugly recurring expressions by far when compared with 12 and 24. 48 doesn't help anything and 60 is hopelessly high.
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Post by Buffoonery on Sept 17, 2015 17:55:12 GMT -8
Yeah base 36 seems pretty solid, and it happens to use all the letters and digits we currently commonly use in english. Since, there are 26 letters in the alphabet and 10 digits including 0. It exactly fits for at least the English language. So you'd see weird numbers like X5, which would be 1,193. Imagine that compactness eh? It's pretty solid, but any higher bases would become a bit more of a nuisance. Base 36 would still be a bit of a nuisance, while trying to do any algebra: 3Wx(X5+6J)^Y = X Maybe you'd have to use lowercase letters and use the asterisk for multiplication? 5j+8c*h8b = X Hehe, just a funny thought. I'd rather use 2 extra unicode characters that no one uses than have 26 letters of the alphabet to use.
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Post by fcg710647 on Sept 17, 2015 20:06:06 GMT -8
My symbols are still case sensitive, and I dodge S5, O0, I1, and Il stumbling (in some sans serifs, capital Is look almost identical to lower case ls). Anyway, if you think of making a giant 36*36 chart on your website, all the relevant fractions for dozenal work, plus ninths, twelfths, and eighteenths... maybe you need more colors lmao 1/9 = 0.4, 40 / 100 1/6 = 0.6, 60 / 100 1/4 = 0.9, 90 / 100 1/3 = 0.U, U0 / 100 1/2 = 0.y, y0 / 100 2/3 = 0.E, E0 / 100 // E is 2^3 * 3 and e is 3^3 3/4 = 0.e, e0 / 100 5/6 = 0.d, d0 / 100 // d is 2*3*5 (thirty) 8/9 = 0.R, R0 / 100 // R is thirty-two (2^5) Yes, 36 is used for encoding due to stuff like 2176782336(Dec.) = 600000(alphad.) Avogadro's Number is roughly 2.?2C*10^A(alphadecimal), or 2?2C000000000000. Yes, a ? is twenty-six At least a question mark shape is the same shape as your dec symbol and fits in an SSD. Let me recode a base testing program for a bit...
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Post by fcg710647 on Sept 18, 2015 17:40:15 GMT -8
Dozenal ones are already written, but vigesimal hasn't been put up before, although it terminates the same stuff that decimal does.
Frac._____Vigesimal____Dozenal______Sievenal 1/2_________0.t__________0.6_________0.a 1/3_________0.6H6H6H6H...0.4_________0.C 1/4_________0.5__________0.3_________0.ta 1/5_________0.4__________0.24972497..0.8JnT8JnT8.... 1/6_________0.36H6H6H6...0.2_________0.7 1/7_________0.2N2N2N2N...0.186X3518..0.6 1/8_________0.2t_________0.16________0.5ta 1/9_________0.248NAr24...0.14________0.4Z 1/10________0.2__________0.1249724...0.48JnT8JnT8... 1/11________0.1J7591J7...0.1111111...0.3hArG3hArG... 1/12________0.1H6H6H6H...0.1_________0.3a 1/13________0.1tA7HJy9...0.0E0E0E0...0.39m39m39m39... 1/14________0.18r8r8r8...0.0X35186...0.3 1/15________0.16H6H6H6...0.0972497...0.2nT8JnT8Jn... 1/16________0.15_________0.09________0.2?ta 1/17________0.13trA5NU...0.0857921...0.2GR4Y]9L2GR... 1/18________0.1248NAr2...0.08________0.2C
Terminators? Vigesimal: 6 Dozenal: 9 Sievenal: 11 (eleven) // None of its recurring periods for those fractions were too long to illustrate in ten or eleven characters, either.
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Post by Buffoonery on Oct 2, 2015 1:36:21 GMT -8
If we have 26 letters with uppercase and lower case, we have 52 symbols. Unfortunately, we have to take away the conflicting letters as you stated above. AaBbCcDdEeFfGgHh_iJjK_L_MmNn__PpQqRr__TtUuVvWw__YyZz That leaves out I,k,l,O,o,S,s,Xx. We have 43/52. 43 symbols that we could use.
further refinement would be removing: b: looks like 6 c: looks like C
I think that could work for base 36. I would do: 1,2,3,4,5,6, 7,8,9,a,A,B, c,C,d,D,e,E f,F,g,G,h,H j,J,K,L,m,M n,N,p,P,q,10
but man, I wish there was a prettier way of doing this.
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Post by fcg710647 on Oct 2, 2015 11:02:51 GMT -8
That's your strategy? You have 41 symbols, but that's only counting letters You really have 51 when you include 0-9, so bases 42 and 48 are possible... 48 doesn't bring anything to the table, does it? Except sixteenths using one significant digit lol
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Post by Buffoonery on Oct 11, 2015 8:42:07 GMT -8
Yeah, I can see a possible representation with these letters, although it's a tough balance. On one hand you're thinking, "I want to be legible, each symbol should be unique," On the other, you're thinking, "But it gets confusing when you skip letters like 'I' and 'c'. "
I think I'm tending to lean towards the latter now. Well, I guess it would be smarter to add a different symbol before my letters too. This would allow the letter A to start on 11 instead of 10. I think this would be helpful since "A" is usually thought of as "1". Here's a visual for 36: 1 2 3 4 5 6 7 8 9 t A B // 12 C D E F G H // 18 I J K L M N // 24 O P Q R S T // 30 U V W X Y 10 // 36
What do you think? I think it makes more sense to imagine J as 20 since [10th number + 10th letter = 20]
You could even do this for base 42, lets see this:
1 2 3 4 5 6 7 8 9 t A B // 12 C D E F G H // 18 I J K L M N // 24 O P Q R S T // 30 U V W X Y Z // 36 s a b c d 10 //42
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Post by fcg710647 on Oct 11, 2015 15:27:33 GMT -8
It's interesting that you keep track of which letter you're using from the alphabet (10th, 12th, etc.) while mine appear to be chosen in a random order because I initially based them on letters from the English words (t and E for ten and eleven), w for twelve (second letter because t was used), H for thirteen (again a t was used), but after I did that I ran into 7-segment conformation issues and changed some of them with other letters that fit. I got that to work up through base 24.... Then, to create symbols for up to 42, I took the 0-20 symbols and decided to reflect them top to bottom to generate 7-segment shapes for 21-41; this reflection left a few symbols the same so I had to change things again. Lol.
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