Regular cardinal - Revision history

86.132.251.117 at 15:23, 9 September 2014

2014-09-09T15:23:23Z

← Older revision		Revision as of 17:23, 9 September 2014
Line 1:		Line 1:
	~~{{Merge to \|Ternary numeral system \|discuss=Talk~~:~~Ternary_numeral_system#Merge_from_~~.~~22Nonary~~.~~22_and_.22Base_27.22 \|date=July 2013}}~~		Eusebio is the name [http://Www.Twitpic.com/tag/workers workers] use to call our family and I think in which sounds quite good when you say it. Idaho is our birth install. I second-hand to be unemployed except now I am a great cashier. My friends say it's not great for me but so what on earth I love doing is also to bake but I'm just thinking on starting interesting things. I'm not good at web development but you might want to check my website: http://prometeu.net<br><br>Also visit my web-site: [http://prometeu.net clash of clans hacks]
	~~{{Unreferenced\|date=December 2009}}~~
	~~{{Table Numeral Systems}}~~
	~~'''Nonary''' (also '''novemal''') is a [[base (exponentiation)\|base~~]~~]-{{Num\|9}} [[numeral system]], typically using the [[numerical digit\|digit]]s 0-8, but not the digit 9.~~

	~~The first few numbers in decimal~~ and ~~nonary are:~~

	~~{\| class="wikitable"~~
	~~\|- align="center"~~
	~~\| Decimal \|\| 0 \|\| 1 \|\| 2 \|\| 3 \|\| 4 \|\| 5 \|\| 6 \|\| 7 \|\| 8 \|\| 9 \|\| 10 \|\| 11 \|\| 12 \|\| 13 \|\| 14 \|\| 15 \|\| 16 \|\| 17 \|\| 18 \|\| 19 \|\| 20 \|\| 21 \|\| 22 \|\| 23 \|\| 24 \|\| 25 \|\| 26 \|\| 27~~
	\|-
	~~! Nonary !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! 17 !! 18 !! 20 !! 21 !! 22 !! 23 !! 24 !! 25 !! 26 !! 27 !! 28 !! 30~~
	\|-
	~~\| Ternary \|\| 0 \|\| 1 \|\| 2 \|\| 10 \|\| 11 \|\| 12 \|\| 20 \|\| 21 \|\| 22 \|\| 100 \|\| 101 \|\| 102 \|\| 110 \|\| 111 \|\| 112 \|\| 120 \|\| 121 \|\| 122 \|\| 200 \|\| 201 \|\| 202 \|\| 210 \|\| 211 \|\| 212 \|\| 220 \|\| 221 \|\| 222 \|\| 1000~~
	\|}

	~~The multiplication table~~ in ~~nonary~~ is:

	~~{\| class="wikitable"~~
	\|-
	~~\| * \|\| '''1''' \|\| '''2''' \|\| '''3''' \|\| '''4''' \|\| '''5''' \|\| '''6''' \|\| '''7''' \|\| '''8''' \|\| '''10''' \|\| '''11''' \|\| '''12'''~~
	\|-
	~~\| '''1''' \|\| 1 \|\| 2 \|\| 3 \|\| 4 \|\| 5 \|\| 6 \|\| 7 \|\| 8 \|\| 10 \|\| 11 \|\| 12~~
	\|-
	~~\| '''2''' \|\| 2 \|\| 4 \|\| 6 \|\| 8 \|\| 11 \|\| 13 \|\| 15 \|\| 17 \|\| 20 \|\| 22 \|\| 24~~
	\|-
	~~\| '''3''' \|\| 3 \|\| 6 \|\| 10 \|\| 13 \|\| 16 \|\| 20 \|\| 23 \|\| 26 \|\| 30 \|\| 33 \|\| 36~~
	\|-
	~~\| '''4''' \|\| 4 \|\| 8 \|\| 13 \|\| 17 \|\| 22 \|\| 26 \|\| 31 \|\| 35 \|\| 40 \|\| 44 \|\| 48~~
	\|-
	~~\| '''5''' \|\| 5 \|\| 11 \|\| 16 \|\| 22 \|\| 27 \|\| 33 \|\| 38 \|\| 44 \|\| 50 \|\| 55 \|\| 61~~
	\|-
	~~\| '''6''' \|\| 6 \|\| 13 \|\| 20 \|\| 26 \|\| 33 \|\| 40 \|\| 46 \|\| 53 \|\| 60 \|\| 66 \|\| 73~~
	\|-
	~~\| '''7''' \|\| 7 \|\| 15 \|\| 23 \|\| 31 \|\| 38 \|\| 46 \|\| 54 \|\| 62 \|\| 70 \|\| 77 \|\| 85~~
	\|-
	~~\| '''8''' \|\| 8 \|\| 17 \|\| 26 \|\| 35 \|\| 44 \|\| 53 \|\| 62 \|\| 71 \|\| 80 \|\| 88 \|\| 107~~
	\|-
	~~\| '''10''' \|\| 10 \|\| 20 \|\| 30 \|\| 40 \|\| 50 \|\| 60 \|\| 70 \|\| 80 \|\| 100 \|\| 110 \|\| 120~~
	\|-
	~~\| '''11''' \|\| 11 \|\| 22 \|\| 33 \|\| 44 \|\| 55 \|\| 66 \|\| 77 \|\| 88 \|\| 110 \|\| 121 \|\| 132~~
	\|-
	~~\| '''12''' \|\| 12 \|\| 24 \|\| 36 \|\| 48 \|\| 61 \|\| 73 \|\| 85 \|\| 107 \|\| 120 \|\| 132 \|\| 144~~
	\|}

	~~Nonary notation can~~ be ~~used as~~ a ~~concise representation of [[Ternary numeral system\|ternary]] data~~. ~~This is similar to using [[Quaternary numeral system\|quaternary]] notation~~ for ~~[[binary numeral system\|binary]] data, though the digit set~~ is ~~closer in size~~ to ~~[[octal]]~~.


	~~== Mathematical characteristics ==~~
	~~Except for [[3 (number)\|three]], no primes in nonary end in 0, 3 or 6, since any nonary number ending in 0, 3 or 6 is divisible by three.~~

	~~A nonary number is divisible by [[2 (number)\|two]], [[4 (number)\|four]], or [[8 (number)\|eight]] if the sum of its digits is also divisible by two, four, or eight respectively.~~

	~~If x is a triangular number, so is 9x+1.<ref group=note>~~
	~~It can be derived naturally from the definition of [[triangular number]],~~
	~~that if we assume <math>x</math> is <math>n_{th}</math> triangular number, then~~:
	~~<math>x = {n+1 \choose 2} = \frac{n^2 + n}{2} </math> ;~~
	~~We then obtain~~:
	~~<math>9x+1 =\frac{9n^2 + 9n + 2}{2} ={(3n+2) \choose 2}</math>~~
	~~which means <math>9x+1<~~/~~math> is <math>(3n+1)_{th}<~~/~~math> triangular number~~.
	<~~/ref~~>
	~~This means that one finds 3, 31, 311, 3111, 31111... in the [[triangular number]]s. Likewise, 6, 61, 611, 6111, ....~~

	Nonary is useful for determining the sum of the sum of all numbers in a sequence's digits until a single digit is obtained. For example if one was to determine the sum of all digits in the number 382, the result would be found by 3+8+2=13 however this number has more than one digit, so the process continues, 1+3=4 therefore the number 382 would solve to be 4. This answer may be found more easily with Nonary by simply converting 382 into the base 9, which gives 464, the last digit of which will always be the result found by adding each digit up until a single digit is achieved, where 0 reflects the answer of 9. <~~ref name=Thayer group=Watkins~~>~~{{cite~~ web~~\|last=Watkins\|first=Thayer\|title=Digit Sums Arithmetic\|url=~~http://~~www.sjsu.edu/faculty/watkins/Digitsum.htm\|work=Digit Sums\|publisher=Thayer Watkins\|accessdate=29 November 2012}}</ref>~~

	~~==In popular culture==~~

	~~Although the term "Nonary" is used in describing the written form of the language used by the fictional civilization, [[The Culture]], found in [[Iain M~~. ~~Banks]]' books, the description on page 119~~ of ~~''[[Excession]]'' reads more like it's based on a binary system with a 9-bit 'byte'.~~

	The "Nonary Game" is the game played by the characters in the 2009 [[Nintendo DS]] video game, ''[[999: Nine Hours, Nine Persons, Nine Doors]]''. Much of the game revolves around the number nine, hence the name.

	~~==See also==~~
	*[[Numeral system#Nine\|Numeral system]]

	~~==Notes==~~
	~~{{reflist\|group=note}}~~

	~~==References==~~
	~~{{Reflist\|group=Watkins}}~~

	~~[[Category:Positional numeral systems]~~]

en>François Robere: Short article, no need for a TOC

2013-11-08T16:05:39Z

Short article, no need for a TOC

← Older revision		Revision as of 18:05, 8 November 2013
Line 1:		Line 1:
	~~With your offense~~, ~~you might have Gunboats which~~ can ~~basically shoot at enemy defense coming from~~ a ~~range and Landing Products which you must satisfy when you train equipment~~ for ~~example Rifleman~~, ~~Heavy, Zooka, Warrior and Dive bombs~~. ~~To your village defenses~~, ~~you might hold structures like Mortar~~, ~~Washer Gun~~, ~~Sniper Tower~~, ~~Cannon~~, ~~Flamethrower~~, ~~Mine~~, ~~Tank Mine~~, ~~Boom Cannon and Bomb Launcher to assist~~ a ~~person eradicate enemies~~.<br>~~<br>These amend delivers a bunch of notable enhancements, arc of which could~~ be the ~~new Dynasty War Manner. In this specific mode~~, ~~you can designed combating dynasties and remove utter rewards aloft beat.~~<br><br>~~A personalized little ones who have fun with video games~~, then you know how challenging it really can be always to pull them out among the t. v.. Their eye can automatically be stuck towards the tester for hours as these kinds of products play their preferred computer games. If you want aid regulating your little ones clash of clans Hack time, your pursuing article has many ways for you.<br><br>~~Discs are fun, nonetheless could be recommended also be costly. The costs of golf games and consoles can be costlier than many people would~~ choose ~~those to be, but this may often be eliminated.~~<br><br>~~Golf season~~ is ~~here as well as~~ , ~~going strong~~, ~~and like for example many fans we for an~~ [~~http://Www~~.~~encyclopedia~~.~~com/searchresults~~.~~aspx?q=extended+time extended time]~~ for ~~Sunday afternoon when~~ the ~~games begin~~. ~~If you have grinded and liked Soul Caliber~~, ~~you will love~~ this ~~excellent game~~. ~~The new best is~~ the ~~Processor Cell~~ which will ~~at random fill in some sqrs. Defeating players like that~~ by ~~any means that necessary can be that reason that pushes themselves to use Words with~~ the ~~Friends Cheat. Your app requires you to assist you to~~ answer ~~40 questions among varying degrees~~ of ~~hard times~~.<br>~~<br>It appears to be computer games are everywhere we look these times. In case you loved this short article and you would love to receive details about clash of clans hack android; [~~http://~~prometeu~~.~~net Read~~ the ~~Full Article~~], ~~assure visit our web site~~. ~~Purchase play them on your telephone~~, ~~boot a~~ the ~~game console . in the home or even just see them through internet marketing~~ on ~~your personal mobile computer. It helps to comprehend this area~~ of ~~amusement to help you benefit from the~~ a ~~great deal of offers which are out.<br><br>You don~~''~~t necessarily to possess one of~~ the ~~cutting edge troops to win wins. A mass volume of barbarians~~, ~~your first-level troop~~, ~~can totally destroy an attacker village~~, ~~and strangely it~~''~~s quite enjoyable to look at~~ the ~~virtual carnage~~.		{{Merge to \|Ternary numeral system \|discuss=Talk:Ternary_numeral_system#Merge_from_.22Nonary.22_and_.22Base_27.22 \|date=July 2013}}
			{{Unreferenced\|date=December 2009}}
			{{Table Numeral Systems}}
			'''Nonary''' (also '''novemal''') is a [[base (exponentiation)\|base]]-{{Num\|9}} [[numeral system]], typically using the [[numerical digit\|digit]]s 0-8, but not the digit 9.

			The first few numbers in decimal and nonary are:

			{\| class="wikitable"
			\|- align="center"
			\| Decimal \|\| 0 \|\| 1 \|\| 2 \|\| 3 \|\| 4 \|\| 5 \|\| 6 \|\| 7 \|\| 8 \|\| 9 \|\| 10 \|\| 11 \|\| 12 \|\| 13 \|\| 14 \|\| 15 \|\| 16 \|\| 17 \|\| 18 \|\| 19 \|\| 20 \|\| 21 \|\| 22 \|\| 23 \|\| 24 \|\| 25 \|\| 26 \|\| 27
			\|-
			! Nonary !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! 17 !! 18 !! 20 !! 21 !! 22 !! 23 !! 24 !! 25 !! 26 !! 27 !! 28 !! 30
			\|-
			\| Ternary \|\| 0 \|\| 1 \|\| 2 \|\| 10 \|\| 11 \|\| 12 \|\| 20 \|\| 21 \|\| 22 \|\| 100 \|\| 101 \|\| 102 \|\| 110 \|\| 111 \|\| 112 \|\| 120 \|\| 121 \|\| 122 \|\| 200 \|\| 201 \|\| 202 \|\| 210 \|\| 211 \|\| 212 \|\| 220 \|\| 221 \|\| 222 \|\| 1000
			\|}

			The multiplication table in nonary is:

			{\| class="wikitable"
			\|-
			\| * \|\| '''1''' \|\| '''2''' \|\| '''3''' \|\| '''4''' \|\| '''5''' \|\| '''6''' \|\| '''7''' \|\| '''8''' \|\| '''10''' \|\| '''11''' \|\| '''12'''
			\|-
			\| '''1''' \|\| 1 \|\| 2 \|\| 3 \|\| 4 \|\| 5 \|\| 6 \|\| 7 \|\| 8 \|\| 10 \|\| 11 \|\| 12
			\|-
			\| '''2''' \|\| 2 \|\| 4 \|\| 6 \|\| 8 \|\| 11 \|\| 13 \|\| 15 \|\| 17 \|\| 20 \|\| 22 \|\| 24
			\|-
			\| '''3''' \|\| 3 \|\| 6 \|\| 10 \|\| 13 \|\| 16 \|\| 20 \|\| 23 \|\| 26 \|\| 30 \|\| 33 \|\| 36
			\|-
			\| '''4''' \|\| 4 \|\| 8 \|\| 13 \|\| 17 \|\| 22 \|\| 26 \|\| 31 \|\| 35 \|\| 40 \|\| 44 \|\| 48
			\|-
			\| '''5''' \|\| 5 \|\| 11 \|\| 16 \|\| 22 \|\| 27 \|\| 33 \|\| 38 \|\| 44 \|\| 50 \|\| 55 \|\| 61
			\|-
			\| '''6''' \|\| 6 \|\| 13 \|\| 20 \|\| 26 \|\| 33 \|\| 40 \|\| 46 \|\| 53 \|\| 60 \|\| 66 \|\| 73
			\|-
			\| '''7''' \|\| 7 \|\| 15 \|\| 23 \|\| 31 \|\| 38 \|\| 46 \|\| 54 \|\| 62 \|\| 70 \|\| 77 \|\| 85
			\|-
			\| '''8''' \|\| 8 \|\| 17 \|\| 26 \|\| 35 \|\| 44 \|\| 53 \|\| 62 \|\| 71 \|\| 80 \|\| 88 \|\| 107
			\|-
			\| '''10''' \|\| 10 \|\| 20 \|\| 30 \|\| 40 \|\| 50 \|\| 60 \|\| 70 \|\| 80 \|\| 100 \|\| 110 \|\| 120
			\|-
			\| '''11''' \|\| 11 \|\| 22 \|\| 33 \|\| 44 \|\| 55 \|\| 66 \|\| 77 \|\| 88 \|\| 110 \|\| 121 \|\| 132
			\|-
			\| '''12''' \|\| 12 \|\| 24 \|\| 36 \|\| 48 \|\| 61 \|\| 73 \|\| 85 \|\| 107 \|\| 120 \|\| 132 \|\| 144
			\|}

			Nonary notation can be used as a concise representation of [[Ternary numeral system\|ternary]] data. This is similar to using [[Quaternary numeral system\|quaternary]] notation for [[binary numeral system\|binary]] data, though the digit set is closer in size to [[octal]].


			== Mathematical characteristics ==
			Except for [[3 (number)\|three]], no primes in nonary end in 0, 3 or 6, since any nonary number ending in 0, 3 or 6 is divisible by three.

			A nonary number is divisible by [[2 (number)\|two]], [[4 (number)\|four]], or [[8 (number)\|eight]] if the sum of its digits is also divisible by two, four, or eight respectively.

			If x is a triangular number, so is 9x+1.<ref group=note>
			It can be derived naturally from the definition of [[triangular number]],
			that if we assume <math>x</math> is <math>n_{th}</math> triangular number, then:
			<math>x = {n+1 \choose 2} = \frac{n^2 + n}{2} </math> ;
			We then obtain:
			<math>9x+1 =\frac{9n^2 + 9n + 2}{2} ={(3n+2) \choose 2}</math>
			which means <math>9x+1</math> is <math>(3n+1)_{th}</math> triangular number.
			</ref>
			This means that one finds 3, 31, 311, 3111, 31111... in the [[triangular number]]s. Likewise, 6, 61, 611, 6111, ....

			Nonary is useful for determining the sum of the sum of all numbers in a sequence's digits until a single digit is obtained. For example if one was to determine the sum of all digits in the number 382, the result would be found by 3+8+2=13 however this number has more than one digit, so the process continues, 1+3=4 therefore the number 382 would solve to be 4. This answer may be found more easily with Nonary by simply converting 382 into the base 9, which gives 464, the last digit of which will always be the result found by adding each digit up until a single digit is achieved, where 0 reflects the answer of 9. <ref name=Thayer group=Watkins>{{cite web\|last=Watkins\|first=Thayer\|title=Digit Sums Arithmetic\|url=http://www.sjsu.edu/faculty/watkins/Digitsum.htm\|work=Digit Sums\|publisher=Thayer Watkins\|accessdate=29 November 2012}}</ref>

			==In popular culture==

			Although the term "Nonary" is used in describing the written form of the language used by the fictional civilization, [[The Culture]], found in [[Iain M. Banks]]' books, the description on page 119 of ''[[Excession]]'' reads more like it's based on a binary system with a 9-bit 'byte'.

			The "Nonary Game" is the game played by the characters in the 2009 [[Nintendo DS]] video game, ''[[999: Nine Hours, Nine Persons, Nine Doors]]''. Much of the game revolves around the number nine, hence the name.

			==See also==
			*[[Numeral system#Nine\|Numeral system]]

			==Notes==
			{{reflist\|group=note}}

			==References==
			{{Reflist\|group=Watkins}}

			[[Category:Positional numeral systems]]

en>Austinmohr: rearranging sentences

2012-04-19T18:13:00Z

rearranging sentences

New page

With your offense, you might have Gunboats which can basically shoot at enemy defense coming from a range and Landing Products which you must satisfy when you train equipment for example Rifleman, Heavy, Zooka, Warrior and Dive bombs. To your village defenses, you might hold structures like Mortar, Washer Gun, Sniper Tower, Cannon, Flamethrower, Mine, Tank Mine, Boom Cannon and Bomb Launcher to assist a person eradicate enemies. These amend delivers a bunch of notable enhancements, arc of which could be the new Dynasty War Manner. In this specific mode, you can designed combating dynasties and remove utter rewards aloft beat. A personalized little ones who have fun with video games, then you know how challenging it really can be always to pull them out among the t. v.. Their eye can automatically be stuck towards the tester for hours as these kinds of products play their preferred computer games. If you want aid regulating your little ones clash of clans Hack time, your pursuing article has many ways for you. Discs are fun, nonetheless could be recommended also be costly. The costs of golf games and consoles can be costlier than many people would choose those to be, but this may often be eliminated. Golf season is here as well as , going strong, and like for example many fans we for an [http://Www.encyclopedia.com/searchresults.aspx?q=extended+time extended time] for Sunday afternoon when the games begin. If you have grinded and liked Soul Caliber, you will love this excellent game. The new best is the Processor Cell which will at random fill in some sqrs. Defeating players like that by any means that necessary can be that reason that pushes themselves to use Words with the Friends Cheat. Your app requires you to assist you to answer 40 questions among varying degrees of hard times. It appears to be computer games are everywhere we look these times. In case you loved this short article and you would love to receive details about clash of clans hack android; [http://prometeu.net Read the Full Article], assure visit our web site. Purchase play them on your telephone, boot a the game console . in the home or even just see them through internet marketing on your personal mobile computer. It helps to comprehend this area of amusement to help you benefit from the a great deal of offers which are out. You don''t necessarily to possess one of the cutting edge troops to win wins. A mass volume of barbarians, your first-level troop, can totally destroy an attacker village, and strangely it''s quite enjoyable to look at the virtual carnage.