mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Closed Thread
 
Thread Tools
Old 2020-08-13, 13:56   #89
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

5,923 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
Except the multiplication tables will be too much for the elementary school students to memorize. Hex multiplication tables are not as easy as the Dozenal versions.
You only have to go as far as you want, of course. If you want to go up to A * A, fine. If you want to go to C * C, great. There's no reason to go to precisely 10 * 10 in the given base.
CRGreathouse is offline  
Old 2020-08-13, 13:58   #90
tuckerkao
 
Jan 2020

2·29 Posts
Default

Quote:
Originally Posted by CRGreathouse View Post
You only have to go as far as you want, of course. If you want to go up to A * A, fine. If you want to go to C * C, great. There's no reason to go to precisely 10 * 10 in the given base.
Then it's like teaching only up to 7 * 7 in decimal.

Quote:
Originally Posted by Uncwilly View Post
"A Zero" and "Eight Zero" You say the characters.
This might have been the reason why hex wasn't popular outside the computerized professions. Some Spanish speaking natives will likely mix the 2 up.

Last fiddled with by tuckerkao on 2020-08-13 at 14:14
tuckerkao is online now  
Old 2020-08-13, 14:17   #91
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

25·179 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
Except the multiplication tables will be too much for the elementary school students to memorize.
Why are you deciding for them? Perhaps this is the real problem then. Let's dumb everything down so that even the dullards don't feel left out because, OMG, we can't make anyone feel left behind no matter how much they don't wish to learn things.

Hey tweedle-dee, how much is 6*4?
I dunno tweedle-dumb, how much is 6*4?
No, it is a real question, how much is 6*4?
Are you kidding me? That is for those advance nerd-brains to know, not normal in-group people like us. So moving on, what's been trending in the last 5 seconds?
retina is online now  
Old 2020-08-13, 14:20   #92
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

134438 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
Then it's like teaching only up to 7 * 7 in decimal.
Fortunately, the mathematics doesn't care one whit what you think it's like. If you decide to work in ternary you're not restricted to teaching the times tables up to 3, and if you work in sexigesimal you don't need to memorize times tables up to 60. There are lots of ways to do things.

Of course if you wanted to teach a full times table, you could use octal just as easily, but that's beside the point.

Last fiddled with by CRGreathouse on 2020-08-13 at 14:21
CRGreathouse is offline  
Old 2020-08-13, 14:24   #93
tuckerkao
 
Jan 2020

728 Posts
Default

Quote:
Originally Posted by CRGreathouse View Post
Fortunately, the mathematics doesn't care one whit what you think it's like. If you decide to work in ternary you're not restricted to teaching the times tables up to 3, and if you work in sexigesimal you don't need to memorize times tables up to 60. There are lots of ways to do things.

Of course if you wanted to teach a full times table, you could use octal just as easily, but that's beside the point.
The main reason it's because hex is not the default math base that everyone has to use on the daily routines. Of course, Sexigesimal won't be an ideal default base anyway. Let the numbers speak for themselves, people will eventually realize decimal isn't the best base for the default.

For Dozenal multiplication tables: 2, 3, 4, 6 are easy. 8, 9, Ɛ are medium, only 5, 7 and Ӿ are hard. Dozenal 7 times table is actually easier than Decimal 6 times(on the odds) table if you know both bases equally well.

Like what retina said, Dozenal as the default math base won't leave behind the kids behind.
Attached Thumbnails
Click image for larger version

Name:	Dozenal Multiplications of 7 - Shiny Color Ball Towers.png
Views:	6
Size:	112.4 KB
ID:	23065  

Last fiddled with by tuckerkao on 2020-08-13 at 14:56
tuckerkao is online now  
Old 2020-08-13, 15:09   #94
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

2·13·331 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
This might have been the reason why hex wasn't popular outside the computerized professions. Some Spanish speaking natives will likely mix the 2 up.
So, by your logic English letters B, C, D, E, G, P, T, and Z should have different names because people can mis-hear them.
Uncwilly is online now  
Old 2020-08-13, 15:43   #95
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

346310 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
Except the multiplication tables will be too much for the elementary school students to memorize. Hex multiplication tables are not as easy as the Dozenal versions.
I'm not smart enough to know that memorizing the multiplication table to sixteen times sixteen is "too much" for students to memorize. It is more of a task than memorizing up to twelve times twelve. Memorizing the multiplication table to twelve times twelve is, by the same token, more of a task than memorizing up to ten times ten -- all the more so with trying to remember cockamamie symbols for ten and eleven.
Quote:
I play triplets on 1 hand and 8th notes on the other hand all the time. There are also triplets vs 16th notes in several Chopin compositions.
Triplets aren't denoted numerically. So your statement has nothing to do with number bases or notations.
Dr Sardonicus is offline  
Old 2020-08-13, 15:55   #96
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

3,463 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
Let the numbers speak for themselves, people will eventually realize decimal isn't the best base for the default.
People were using numbers before the concept of a base (radix) was even invented. And the idea that numbers can "speak for themselves" was not unknown to them.
Dr Sardonicus is offline  
Old 2020-08-13, 16:02   #97
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

2×13×331 Posts
Default

Quote:
Originally Posted by Dr Sardonicus View Post
It is more of a task than memorizing up to twelve times twelve. Memorizing the multiplication table to twelve times twelve is, by the same token, more of a task than memorizing up to ten times ten -- all the more so with trying to remember cockamamie symbols for ten and eleven.
Historically 12x12 multiplication had to do with stores and pricing etc. Common practice was to take the cost of a dozen of an item and shift the decimal for the sale price to the customer. Dozens fit a 3x4 box nicely. But now prices are not done that way and box sizes and what is a 'case' can vary widely. So teaching future storekeepers and general office staff is no longer a thing is schools.

Any user of a base needs to know the multiplication table for all units. Anything less and you can't do the math. Base 60 systems are generally a compound base of 12 and 5.
Uncwilly is online now  
Old 2020-08-13, 18:35   #98
xilman
Bamboozled!
 
xilman's Avatar
 
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

240038 Posts
Default

Quote:
Originally Posted by Uncwilly View Post
Base 60 systems are generally a compound base of 12 and 5.
Except when they are not.

I gave a specific example which was in widespread use for well over two thousand years.

Remnants of it are still in widespread use well after four thousand years.

It is a combination of base 6 and base 10.


I type this from 28°38'30" N 17°52'04" W.

Last fiddled with by xilman on 2020-08-13 at 18:39 Reason: s/write/type/
xilman is offline  
Old 2020-08-13, 20:49   #99
sweety439
 
sweety439's Avatar
 
Nov 2016

26×5×7 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
The main reason it's because hex is not the default math base that everyone has to use on the daily routines. Of course, Sexigesimal won't be an ideal default base anyway. Let the numbers speak for themselves, people will eventually realize decimal isn't the best base for the default.

For Dozenal multiplication tables: 2, 3, 4, 6 are easy. 8, 9, Ɛ are medium, only 5, 7 and Ӿ are hard. Dozenal 7 times table is actually easier than Decimal 6 times(on the odds) table if you know both bases equally well.

Like what retina said, Dozenal as the default math base won't leave behind the kids behind.
https://dozenal.fandom.com/wiki/Properties_of_dozenal many properties of dozenal, e.g. all squares end with square digits, all primes end with prime digits or 1, all even perfect numbers except 6, 24 and 354 end with either 054 or 854
sweety439 is offline  
Closed Thread

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Dozenal near- and quasi- repunit primes sweety439 And now for something completely different 22 2020-07-21 14:49
Smallest multiple of n satisfying given condition in dozenal sweety439 sweety439 0 2020-06-11 06:36
Mersenne numbers in Dozenal base tuckerkao Lounge 7 2020-02-11 04:44
Jason's sieved ranges(for the prp and llr addicts with Intels) jasong Sierpinski/Riesel Base 5 8 2005-04-29 05:13

All times are UTC. The time now is 22:55.

Wed Sep 23 22:55:09 UTC 2020 up 13 days, 20:06, 0 users, load averages: 1.71, 1.53, 1.64

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.