Summation chart - Revision history

ZHOUY1: fix math display

2018-01-22T21:01:38Z

fix math display

← Older revision		Revision as of 16:01, 22 January 2018
Line 81:		Line 81:
	The '''summation chart''' is used to determine the number of ranks required to attain a bonus, based on an incremental additive. It is used particularly for [[Lore]] bonuses in certain spells.		The '''summation chart''' is used to determine the number of ranks required to attain a bonus, based on an incremental additive. It is used particularly for [[Lore]] bonuses in certain spells.

	For spells that provide a summation bonus, the first step to determine the progression at which you will gain further benefits is to find the first rank at which you gain a bonus. This is commonly called the "seed" (~~<math>\mathrm{\sigma}</math>~~). Find this rank number in the red row underneath the red Seed heading. Since the seed is also the first rank at which you gain a bonus, it corresponds with '1' under the Bonus column.		For spells that provide a summation bonus, the first step to determine the progression at which you will gain further benefits is to find the first rank at which you gain a bonus. This is commonly called the "seed" (σ). Find this rank number in the red row underneath the red Seed heading. Since the seed is also the first rank at which you gain a bonus, it corresponds with '1' under the Bonus column.

	Now, reading downward from the seed will tell you the next rank at which the next bonus can be achieved. Each of these milestones corresponds to their respective numbers in the Bonus column.		Now, reading downward from the seed will tell you the next rank at which the next bonus can be achieved. Each of these milestones corresponds to their respective numbers in the Bonus column.
Line 99:		Line 99:
	{\| {{prettytable}}		{\| {{prettytable}}
	\|-		\|-
	\| align=right\| ~~<math>\mathrm{~~Bonus~~}</math>~~		\| align=right\| Bonus
	\| <math~~>\quad~~ n = ~~\left \~~lfloor 1-~~\sigma~~ + ~~\sqrt~~{(~~\sigma~~ - 1)^2 + 2r} ~~\right \~~rfloor~~\quad </math>~~		\| {{math\|n {{=}} &lfloor;1 - σ + {{sqrt\|(σ - 1)<sup>2</sup> + 2r}}&rfloor;}}
	\|-		\|-
	\| align=right\|~~<math>\mathrm{~~Skill\ Ranks\ Needed~~}</math>~~		\| align=right\|Skill Ranks Needed
	\| <math~~>\quad~~ r = ~~\frac{~~n^2 - n}{2} + ~~n\sigma</math>~~		\| {{math\|r {{=}} (n<sup>2</sup> - n)/2 + nσ}}
	\|-		\|-
	\| align=right\|~~<math>\mathrm{~~Seed~~}</math>~~		\| align=right\|Seed
	\| <math~~>\quad \sigma~~ = ~~\frac{~~1-n}{2} + ~~\frac{~~r}{n}~~</math>~~		\| {{math\|σ {{=}} (1 - n)/2 + r/n}}
	\|}		\|}
	~~<br style="~~clear~~:both;">~~		{{clear}}
	== Resources ==		== Resources ==
	* [[/saved posts\|Saved posts]]		* [[/saved posts\|Saved posts]]

VANKRASN39: math fix

2017-12-07T15:42:33Z

math fix

← Older revision		Revision as of 10:42, 7 December 2017
Line 1:		Line 1:
	{\| {{prettytable\|text-align:center;float:left;}}		{\| {{prettytable\|text-align:center;float:left;}}
	\|- bgcolor = #ddd		\|- bgcolor = #ddd
	! rowspan=2 valign=bottom \| Bonus (n)		! rowspan=2 valign=bottom \| Bonus (n)

VANKRASN39: math fix

2017-05-26T16:57:50Z

math fix

← Older revision		Revision as of 11:57, 26 May 2017
Line 1:		Line 1:
	{\| {{prettytable\|text-align:center;float:left;}}		{\| {{prettytable\|text-align:center;float:left;}}
	\|- bgcolor = #ddd		\|- bgcolor = #ddd
	! rowspan=2 valign=bottom \| Bonus (n)		! rowspan=2 valign=bottom \| Bonus (n)

VANKRASN39: /* Resources */ update link

2017-04-19T16:42:55Z

Resources: update link

← Older revision		Revision as of 11:42, 19 April 2017
Line 110:		Line 110:
	<br style="clear:both;">		<br style="clear:both;">
	== Resources ==		== Resources ==
	* [[~~Seed~~ ~~chart (saved~~ ~~post)~~]]		* [[/saved posts\|Saved posts]]

	[[category:Magic]][[category:Lores]][[category:Skills]]		[[category:Magic]][[category:Lores]][[category:Skills]]

PFLATS: unbalanced parens in n, removed unnecessary roman tags

2016-10-06T21:22:52Z

unbalanced parens in n, removed unnecessary roman tags

← Older revision		Revision as of 16:22, 6 October 2016
Line 100:		Line 100:
	\|-		\|-
	\| align=right\| <math>\mathrm{Bonus}</math>		\| align=right\| <math>\mathrm{Bonus}</math>
	\| <math>\quad ~~\mathrm{~~n = \left \lfloor 1-\sigma + \sqrt{(\sigma - 1)^2 + 2r)} \right \rfloor}\quad </math>		\| <math>\quad n = \left \lfloor 1-\sigma + \sqrt{(\sigma - 1)^2 + 2r} \right \rfloor\quad </math>
	\|-		\|-
	\| align=right\|<math>\mathrm{Skill\ Ranks\ Needed}</math>		\| align=right\|<math>\mathrm{Skill\ Ranks\ Needed}</math>
	\| <math>\quad ~~\mathrm{~~r = \frac{n^2 - n}{2} + n\sigma }</math>		\| <math>\quad r = \frac{n^2 - n}{2} + n\sigma</math>
	\|-		\|-
	\| align=right\|<math>\mathrm{Seed}</math>		\| align=right\|<math>\mathrm{Seed}</math>
	\| <math>\quad ~~\mathrm{~~\sigma = \frac{1-n}{2} + \frac{r}{n} }</math>		\| <math>\quad \sigma = \frac{1-n}{2} + \frac{r}{n}</math>
	\|}		\|}
	<br style="clear:both;">		<br style="clear:both;">

VANKRASN39 at 20:18, 6 October 2016

2016-10-06T20:18:15Z

← Older revision		Revision as of 15:18, 6 October 2016
Line 108:		Line 108:
	\| <math>\quad \mathrm{\sigma = \frac{1-n}{2} + \frac{r}{n} }</math>		\| <math>\quad \mathrm{\sigma = \frac{1-n}{2} + \frac{r}{n} }</math>
	\|}		\|}
			<br style="clear:both;">

	== Resources ==		== Resources ==
	* [[Seed chart (saved post)]]		* [[Seed chart (saved post)]]

DAID: quick aside noting that the pattern is similar to triangular numbers

2016-10-06T14:07:03Z

quick aside noting that the pattern is similar to triangular numbers

← Older revision		Revision as of 09:07, 6 October 2016
Line 79:		Line 79:
	\|}		\|}

	The '''summation chart''' is used to determine the number of ranks required to attain a bonus, based on an incremental additive ~~scale~~. It is used particularly for [[Lore]] bonuses in certain spells.		The '''summation chart''' is used to determine the number of ranks required to attain a bonus, based on an incremental additive. It is used particularly for [[Lore]] bonuses in certain spells.

	For spells that provide a summation bonus, the first step to determine the progression at which you will gain further benefits is to find the first rank at which you gain a bonus. This is commonly called the "seed" (<math>\mathrm{\sigma}</math>). Find this rank number in the red row underneath the red Seed heading. Since the seed is also the first rank at which you gain a bonus, it corresponds with '1' under the Bonus column.		For spells that provide a summation bonus, the first step to determine the progression at which you will gain further benefits is to find the first rank at which you gain a bonus. This is commonly called the "seed" (<math>\mathrm{\sigma}</math>). Find this rank number in the red row underneath the red Seed heading. Since the seed is also the first rank at which you gain a bonus, it corresponds with '1' under the Bonus column.

	Now, reading downward from the seed will tell you the next rank at which the next bonus can be achieved. Each of these milestones corresponds to their respective numbers in the Bonus column.		Now, reading downward from the seed will tell you the next rank at which the next bonus can be achieved. Each of these milestones corresponds to their respective numbers in the Bonus column.

			The method is based on [https://en.wikipedia.org/wiki/Triangular_number triangular numbers] and allows for a relatively straight forward manner to set the skill required corresponding to a given bonus threshold simultaneously to the degree with which the returns diminish.
	__NOTOC__		__NOTOC__
	===Example===		===Example===

VANKRASN39: radical format idea. move text from play.net and adapt example for Wiki

2016-10-06T13:33:06Z

radical format idea. move text from play.net and adapt example for Wiki

@@ Line 1: / Line 1: @@
 ! colspan=10 style="color:#ff0000" | Seed (σ)
 |-
@@ Line 78: / Line 58: @@
 |-
 ! 18
-|171 ||189 ||207 ||225 ||243 ||261 ||279 ||297 || colspan="2" |
+|171 ||189 ||207 ||225 ||243 ||261 ||279 ||297 || colspan=2 |
 |-
 ! 19
-|190 ||209 ||228 ||247 ||266 ||285 || colspan="4" |
+|190 ||209 ||228 ||247 ||266 ||285 || colspan=4 |
 |-
 ! 20
-|210 ||230 ||250 ||270 ||290 || colspan="5" |
+|210 ||230 ||250 ||270 ||290 || colspan=5 |
 |-
 ! 21
-|231 ||252 ||273 ||294 || colspan="6" |
+|231 ||252 ||273 ||294 || colspan=6 |
 |-
 ! 22
-|253 ||275 ||297 || colspan="7" |
+|253 ||275 ||297 || colspan=7 |
 |-
 ! 23
-|276 ||299 || colspan="8" |
+|276 ||299 || colspan=8 |
 |-
 ! 24
-|300 || colspan="9" |
+|300 || colspan=9 |
 |}
 == Resources ==
 * [[Seed chart (saved post)]]
 [[category:Magic]][[category:Lores]][[category:Skills]]

VANKRASN39: remove from advanced mechanics

2016-10-06T03:56:30Z

remove from advanced mechanics

← Older revision		Revision as of 22:56, 5 October 2016
Line 103:		Line 103:
	* http://www.play.net/gs4/info/spells/lores.asp#Summation - The summation chart		* http://www.play.net/gs4/info/spells/lores.asp#Summation - The summation chart

	[[category:Magic]][[category:Lores]][[category:Skills~~]][[category:Advanced Mechanics~~]]		[[category:Magic]][[category:Lores]][[category:Skills]]

VANKRASN39 at 16:23, 16 October 2015

2015-10-16T16:23:52Z

← Older revision		Revision as of 11:23, 16 October 2015
Line 98:		Line 98:
	\|300 \|\| colspan="9" \|		\|300 \|\| colspan="9" \|
	\|}		\|}

	== See Also ==
⚫	* [[Seed chart (saved post)]]

	== Resources ==		== Resources ==
		⚫	* [[Seed chart (saved post)]]
	* http://www.play.net/gs4/info/spells/lores.asp#Summation - The summation chart		* http://www.play.net/gs4/info/spells/lores.asp#Summation - The summation chart