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InvisibleMinstrel
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Re: is anyone really good at doing math in their head? [Re: Montgomery26]
    #8688675 - 07/27/08 03:03 PM (15 years, 9 months ago)

I can almost instantly determine the formula weight of any organic compound if the formula is written as CxNy and so forth, so long as it doesn't contain atoms other than carbon, hydrogen, oxygen, chlorine or nitrogen.


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InvisibleDieCommie


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Re: is anyone really good at doing math in their head? [Re: Minstrel]
    #8688779 - 07/27/08 03:31 PM (15 years, 9 months ago)

To how many sig figs?  :wink:    :nerd:

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Offlinekotik
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Re: is anyone really good at doing math in their head? [Re: DieCommie]
    #8700963 - 07/30/08 05:14 AM (15 years, 9 months ago)

I'm surprised I'm the first one to mention Vedic math, otherwise known as "magic" math.

Vedic math is based on 16 principles (sutras).  It still uses math, but there are lots of shortcuts.

For example, multiple any number by 9, and the digits of the solution will also add up to 9 (or a multiple of 9). 

e.g.  5x9 = 45.  4+5=9.
and:  73x9 = 657. 6+5+7 = 18.  (and 1+8=9)

So instead of actually doing the traditional concept of math in your head, it's a bit different; more like translating a language I guess.  Some people confuse it with numerology, which it is not.

There's another method for adding times very easily, not sure which sutra it is (or if it has its sutra).

basically when adding times, say 1:27 and 5:44, you have to convert the times to seconds, or at least do some mental math to deal with the 60/100 denominator difference...  however there is a "magic time" number with a constant value of 40 that takes that entire step out.  Instead of converting the time, you just bunch the numbers together, add, and then add 40.  Hard to explain, easy to illustrate:

instead of this process:
1:27 = (1x60)+27 = 60+27 = 87
5:44 = (5x60)+44 = 300+44 = 344
87 + 344 = 431
431/60 = 7 r11
7:11

you do this:
1:27 = 127
5:44 = 544
127 + 544 = 671
671 + 40 = 711
711 = 7:11

admittedly, each of those have 5 steps... but clearly the second version was much easier.  3 steps involved removing or adding a colon, with only 2 actual steps with very simple addition.  This would be at most a 2-step mental process.

The typical (western) method can be done mentally as well, but it takes a bit longer, since you have to do a variety of mental calculations.

The sutras get into complex math, such as square roots, cubic roots, long division, etc.  It's not limited to simple equations by any means.

Just some very small examples of vedic math opposed to western math.  I firmly believe that if I was taught both methods in school, I would have ended up keeping an active interest in math, instead of having it beaten out of me with long, boring equations.  I'll stop before a rant ensues.


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Offlinedelta9
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Re: is anyone really good at doing math in their head? [Re: kotik]
    #8701068 - 07/30/08 06:52 AM (15 years, 9 months ago)

Quote:

kotik said:
I'm surprised I'm the first one to mention Vedic math, otherwise known as "magic" math.

Vedic math is based on 16 principles (sutras).  It still uses math, but there are lots of shortcuts.

For example, multiple any number by 9, and the digits of the solution will also add up to 9 (or a multiple of 9). 

e.g.  5x9 = 45.  4+5=9.
and:  73x9 = 657. 6+5+7 = 18.  (and 1+8=9)



How does this help you multiply faster?

The easiest way in base 10 to multiply N by 9 more quickly is to multiply N by 10 and then subtract N.  The same goes for multiplying N by 11 only you add N at the end.


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InvisibledeCypher
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Re: is anyone really good at doing math in their head? [Re: Epigallo]
    #8703754 - 07/30/08 06:29 PM (15 years, 9 months ago)

Pssh... doing math in your head is overrated.  It's all about seeing how many digits of pi you can memorize instead. :wink:


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Re: is anyone really good at doing math in their head? [Re: deCypher]
    #8705682 - 07/31/08 01:24 AM (15 years, 9 months ago)

Quote:

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203496252451749399651431429809190659250937221696461515709858387410597885959772975498930161753928468138268683868942774155991855925245953959431049972524680845987273644695848653836736222626099124608051243884390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506016842739452267467678895252138522549954666727823986456596116354886230577456498035593634568174324112515076069479451096596094025228879710893145669136867228748940560101503308617928680920874760917824938589009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364542858444795265867821051141354735739523113427166102135969536231442952484937187110145765403590279934403742007310578539062198387447808478489683321445713868751943506430218453191048481005370614680674919278191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961567945208095146550225231603881930142093762137855956638937787083039069792077346722182562599661501421503068038447734549202605414665925201497442850732518666002132434088190710486331734649651453905796268561005508106658796998163574736384052571459102897064140110971206280439039759515677157700420337869936007230558763176359421873125147120532928191826186125867321579198414848829164470609575270695722091756711672291098169091528017350671274858322287183520935396572512108357915136988209144421006751033467110314126711136990865851639831501970165151168517143765761835155650884909989859982387345528331635507647918535893226185489632132933089857064204675259070915481416549859461637180270981994309924488957571282890592323326097299712084433573265489382391193259746366730583604142813883032038249037589852437441702913276561809377344403070746921120191302033038019762110110044929321516084244485963766983895228684783123552658213144957685726243344189303968642624341077322697802807318915441101044682325271620105265227211166039666557309254711055785376346682065310989652691862056476931257058635662018558100729360659876486117910453348850346113657686753249441668039626579787718556084552965412665408530614344431858676975145661406800700237877659134401712749470420562230538994561314071127000407854733269939081454664645880797270826683063432858785698305235808933065757406795457163775254202114955761581400250126228594130216471550979259230990796547376125517656751357517829666454779174501129961489030463994713296210734043751895735961458901938971311179042978285647503203198691514028708085990480109412147221317947647772622414254854540332157185306142288137585043063321751829798662237172159160771669254748738986654949450114654062843366393790039769265672146385306736096571209180763832716641627488880078692560290228472104031721186082041900042296617119637792133757511495950156604963186294726547364252308177036751590673502350728354056704038674351362222477158915049530984448933309634087807693259939780541934144737744184263129860809988868741326047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I could continue...

Actually, there is an interesting case of this guy they thought was a genius with a superb memory - turns how he was just really good at doing math in his head so when they asked him to recite digits of pi or e he could just calculate each digit fast enough to appear to be reciting from memory.


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delta9

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InvisibledeCypher
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Re: is anyone really good at doing math in their head? [Re: delta9]
    #8706547 - 07/31/08 09:29 AM (15 years, 9 months ago)

UR DOIN IT WRONG.

Quote:

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999... and so on ad infinitum. :wink:




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Offlinedelta9
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Re: is anyone really good at doing math in their head? [Re: deCypher]
    #8707166 - 07/31/08 12:42 PM (15 years, 9 months ago)

Quote:

The Cypher said:
UR DOIN IT WRONG.

Quote:

3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196442881097566593344612847564823378678316527120190914564856692346034861045432664821339360726024914127372458700660631558817488152092096282925409171536436789259036001133053054882046652138414695194151160943305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912983367336244065664308602139494639522473719070217986094370277053921717629317675238467481846766940513200056812714526356082778577134275778960917363717872146844090122495343014654958537105079227968925892354201995611212902196086403441815981362977477130996051870721134999999... and so on ad infinitum. :wink:






Actually, you're doing it wrong.  Your post suggests it reaches 9 and then continues with 9s for infinity or that the pattern preceding the nines repeats for infinity. WRONG


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InvisibleDieCommie


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Re: is anyone really good at doing math in their head? [Re: delta9]
    #8707198 - 07/31/08 12:46 PM (15 years, 9 months ago)

pfft..Only engineers care about decimal approximations.  Formula: 0 is exact.

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Offlinedelta9
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Re: is anyone really good at doing math in their head? [Re: DieCommie]
    #8707405 - 07/31/08 01:19 PM (15 years, 9 months ago)

Agreed, which is somewhat my point...  It is an exact number and therefore cannot be approximated by simply truncating and suggesting "ad infinitum" it must ACTUALLY continue forever (as far as we know).  Same goes for most any ratio, really, which is why I like systems like Lisp that allow you to work directly with ratios (therefore your results are more likely to be exact, until you ASK for an approximation).


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InvisibledeCypher
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Re: is anyone really good at doing math in their head? [Re: delta9]
    #8707675 - 07/31/08 02:05 PM (15 years, 9 months ago)

Quote:

delta9 said:
Actually, you're doing it wrong.  Your post suggests it reaches 9 and then continues with 9s for infinity or that the pattern preceding the nines repeats for infinity. WRONG




:rofl2: 'tis called sarcasm, my friend.  Feynman pulled this trick a few times to his friends, actually.


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Invisiblejohnm214
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Re: is anyone really good at doing math in their head? [Re: DieCommie]
    #8707952 - 07/31/08 03:03 PM (15 years, 9 months ago)

Quote:

DieCommie said:
pfft..Only engineers care about decimal approximations.  Formula: 0 is exact.





pfft.. Only physicists care about exact numbers...


Organic chemists say:  ehh... about 2 moles... about 60% yield... close enough

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Offlineisaacein
exp(ix) = cosx + isinx


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Re: is anyone really good at doing math in their head? [Re: johnm214]
    #8709356 - 07/31/08 08:36 PM (15 years, 9 months ago)

I'm not bad at this.
I average 9 seconds for multiplying two two-digit numbers together, and about 70 seconds for two three-digit numbers.
I can extract cube roots of perfect cubes up to 27 000 000.

http://www.jimmyr.com/blog/speed_math.html is a nice little web program to practice mental calculation.

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Mental_arithmetic.html "Memory, mental arithmetic and mathematics", an article about the greatest mental calculators in history, most of which were kids. The article is very well written and has good sources. A ten year old american kid is reported to have done the following...

Quote:


    Multiply in your head 365,365,365,365,365,365 and 365,365,365,365,365,365. He flew around the room like a top, pulled his pantaloons over the tops of his boots, bit his hands, rolled his eyes in their sockets, sometimes smiling and talking, and then seeming to be in agony, until, in not more than one minute, said he 133,491,850,208,566,925,016,658,299,941,583,225!





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Formula: 0

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Offlinedelta9
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Re: is anyone really good at doing math in their head? [Re: isaacein]
    #8709392 - 07/31/08 08:43 PM (15 years, 9 months ago)

Quote:

isaacein said:
I'm not bad at this.
I average 9 seconds for multiplying two two-digit numbers together, and about 70 seconds for two three-digit numbers.



That's not that fast...
Quote:

I can extract cube roots of perfect cubes up to 27 000 000.



This is pretty good though :yesnod:

Good resources :thumbup:


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Offlineisaacein
exp(ix) = cosx + isinx


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Re: is anyone really good at doing math in their head? [Re: delta9]
    #8709418 - 07/31/08 08:48 PM (15 years, 9 months ago)

I know it's not that fast. I said I wasn't bad, not that I was good :wink:
Extracting cubes is easy. Easier than 873*978, that's for sure.


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