View Full Version : the number e, all the way
Gilby
2002-01-03, 06:03 AM
e is better than pi, but pie tastes better.
e = 2.7182818284590452353602874713526624977572470936999595749669676277240766 303535475945713821785251664274274663919320030599218174135966290435729003 342952605956307381323286279434907632338298807531952510190115738341879307 021540891499348841675092447614606680822648001684774118537423454424371075 390777449920695517027618386062613313845830007520449338265602976067371132 007093287091274437470472306969772093101416928368190255151086574637721112 523897844250569536967707854499699679468644549059879316368892300987931277 361782154249992295763514822082698951936680331825288693984964651058209392 398294887933203625094431173012381970684161403970198376793206832823764648 042953118023287825098194558153017567173613320698112509961818815930416903 515988885193458072738667385894228792284998920868058257492796104841984443 634632449684875602336248270419786232090021609902353043699418491463140934 317381436405462531520961836908887070167683964243781405927145635490613031 072085103837505101157477041718986106873969655212671546889570350354021234 078498193343210681701210056278802351930332247450158539047304199577770935 036604169973297250886876966403555707162268447162560798826517871341951246 652010305921236677194325278675398558944896970964097545918569563802363701 621120477427228364896134225164450781824423529486363721417402388934412479 635743702637552944483379980161254922785092577825620926226483262779333865 664816277251640191059004916449982893150566047258027786318641551956532442 586982946959308019152987211725563475463964479101459040905862984967912874 068705048958586717479854667757573205681288459205413340539220001137863009 455606881667400169842055804033637953764520304024322566135278369511778838 638744396625322498506549958862342818997077332761717839280349465014345588 970719425863987727547109629537415211151368350627526023264847287039207643 100595841166120545297030236472549296669381151373227536450988890313602057 248176585118063036442812314965507047510254465011727211555194866850800368 532281831521960037356252794495158284188294787610852639813955990067376482 922443752871846245780361929819713991475644882626039033814418232625150974 827987779964373089970388867782271383605772978824125611907176639465070633 045279546618550966661856647097113444740160704626215680717481877844371436 988218559670959102596862002353718588748569652200050311734392073211390803 293634479727355955277349071783793421637012050054513263835440001863239914 907054797780566978533580489669062951194324730995876552368128590413832411 607226029983305353708761389396391779574540161372236187893652605381558415 871869255386061647798340254351284396129460352913325942794904337299085731 580290958631382683291477116396337092400316894586360606458459251269946557 248391865642097526850823075442545993769170419777800853627309417101634349 076964237222943523661255725088147792231519747780605696725380171807763603 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542139230617876753958711436104089409966089471418340698362993675362621545 247298464213752891079884381306095552622720837518629837066787224430195793 793786072107254277289071732854874374355781966511716618330881129120245204 048682200072344035025448202834254187884653602591506445271657700044521097 735585897622655484941621714989532383421600114062950718490427789258552743 035221396835679018076406042138307308774460170842688272261177180842664333 651780002171903449234264266292261456004337383868335555343453004264818473 989215627086095650629340405264943244261445665921291225648893569655009154 306426134252668472594914314239398845432486327461842846655985332312210466 259890141712103446084271616619001257195870793217569698544013397622096749 454185407118446433946990162698351607848924514058940946395267807354579
harper
2002-01-03, 06:31 AM
You rule. I can't get that many significant digits on my 12" slide rule.
pi=3.1415926535897932384626433832795028841971693993751058209749445923078 164062862089986280348253421170679821480865132823066470938446095505822317 253594081284811174502841027019385211055596446229489549303819644288109756 659334461284756482337867831652712019091456485669234603486104543266482133 936072602491412737245870066063155881748815209209628292540917153643678925 903600113305305488204665213841469519415116094330572703657595919530921861 173819326117931051185480744623799627495673518857527248912279381830119491 298336733624406566430860213949463952247371907021798609437027705392171762 931767523846748184676694051320005681271452635608277857713427577896091736 371787214684409012249534301465495853710507922796892589235420199561121290 219608640344181598136297747713099605187072113499999983729780499510597317 328160963185950244594553469083026425223082533446850352619311881710100031 378387528865875332083814206171776691473035982534904287554687311595628638 823537875937519577818577805321712268066130019278766111959092164201989380 952572010654858632788659361533818279682303019520353018529689957736225994 138912497217752834791315155748572424541506959508295331168617278558890750 983817546374649393192550604009277016711390098488240128583616035637076601 047101819429555961989467678374494482553797747268471040475346462080466842 590694912933136770289891521047521620569660240580381501935112533824300355 876402474964732639141992726042699227967823547816360093417216412199245863 150302861829745557067498385054945885869269956909272107975093029553211653 449872027559602364806654991198818347977535663698074265425278625518184175 746728909777727938000816470600161452491921732172147723501414419735685481 613611573525521334757418494684385233239073941433345477624168625189835694 855620992192221842725502542568876717904946016534668049886272327917860857 843838279679766814541009538837863609506800642251252051173929848960841284 886269456042419652850222106611863067442786220391949450471237137869609563 643719172874677646575739624138908658326459958133904780275900994657640789 512694683983525957098258226205224894077267194782684826014769909026401363 944374553050682034962524517493996514314298091906592509372216964615157098 583874105978859597729754989301617539284681382686838689427741559918559252 459539594310499725246808459872736446958486538367362226260991246080512438 843904512441365497627807977156914359977001296160894416948685558484063534 220722258284886481584560285060168427394522674676788952521385225499546667 278239864565961163548862305774564980355936345681743241125150760694794510 965960940252288797108931456691368672287489405601015033086179286809208747 609178249385890097149096759852613655497818931297848216829989487226588048 575640142704775551323796414515237462343645428584447952658678210511413547 357395231134271661021359695362314429524849371871101457654035902799344037 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harper
2002-01-04, 05:46 PM
Where do you find these sources of e, pi, etc. to so many significant digits? I knew them both to about 10 but that's not even the first line of your printouts. Here's another one. Are you still able to derive the solution to the general quadratic equation? This was probably 2nd year HS algebra. I make myself do that occassionally.
Gilby
2002-01-04, 06:23 PM
Originally posted by harper
Where do you find these sources of e, pi, etc. to so many significant digits? I knew them both to about 10 but that's not even the first line of your printouts.
I memorized them. :)
Actually, the internet is a great resource to quickly find stuff like this.
Here's another one. Are you still able to derive the solution to the general quadratic equation? This was probably 2nd year HS algebra. I make myself do that occassionally.
Sure, it's not that hard, but right now, I am on winter break mode. :)
harper
2002-01-04, 06:40 PM
Kevin-
Check out these gears and bearings I received that I'll be using for the epicyclic unicycle hub.
http://www.harper.unicyclist.com/gears.jpg
http://www.harper.unicyclist.com/g-and-b.jpg
Pretty, eh? The gears and the 6 bearings required weigh a ton. This thing is going to be like a lump of steel but I don't think it will break.
Gilby
2002-01-04, 07:59 PM
I sure hope that is not actual size. :)
Yeah, it does look over designed.
rebecca
2002-01-20, 02:28 AM
Best equation ever:
1+e^(i*pi)=0
Gilby
2002-01-20, 02:50 AM
Originally posted by rebecca
Best equation ever:
1+e^(i*pi)=0
And why is that?
harper
2002-01-20, 05:24 AM
If the question is why is it the best equation ever it's because it includes the irrational numbers pi and e and the two real constants zero, the additive identity element, and one, the multiplicative identity element, and the imaginary unit i all in one equality.
Gilby
2002-01-20, 05:47 AM
Originally posted by harper
If the question is why is it the best equation ever it's because it includes the irrational numbers pi and e and the two real constants zero, the additive identity element, and one, the multiplicative identity element, and the imaginary unit i all in one equality.
Yeah, that's what I was asking... Now how can I use it?
- Gilby
former math competitor
dangerdale
2002-01-20, 12:29 PM
1+e^(i*pi)=0
(i*pi)e^+1
i*want (1 pi)e
i want one pie
ЪñGé®Ðã£ë + pie = mmmm
rebecca
2002-01-20, 04:56 PM
it has a lot of applications in electrical engineering and stuff (i don't know much abt this) and the compounded interest equation comes from that, it's also used for falling body problems when air resistance is not negligible, and for spring problems...and if you ever find a corpse, you can use it to find out how long it's been dead (my personal favorite)!
it's also really useful if you wake up one morning and say to yourself, "self, there is reallly nothing i would love more this morning than to solve some differential equations!" yeah, i say that every day....NOT AT ALL
but it is used in diff eq. like if you have y'' + y' +4y = 0, the solution is y=C1*e^2t + C2*te^(2t)...you really don't need to know euler's equation to solve this, but whoever proved WHY this is the solution needed it...i'd really like to understand teh mathematics behind it, but i don't.
and harper's right abt why it's the best equation ever.
gilby, which math competitions did you do?
Gilby
2002-01-20, 06:23 PM
Well, I was more of wondering what that specific equation is used for, not similar ones.
Originally posted by rebecca
gilby, which math competitions did you do?
Ummm... I did a lot of the Moinnesota ones like the Minnesota High School Math League. Also did the junior high one. I went to a few one time competitions too that were held at state universities.
rebecca
2002-01-20, 06:26 PM
that IS what that particular equation is used for. did you do AHSME? (american high school math exam)
harper
2002-01-20, 07:25 PM
Euler's equation identifies a single point on the complex plane in polar coordinates (r, theta) in this case r=1, theta=pi, or 180 degrees. In this notation, any point on the complex plane can be described by re^i*theta where r and theta are as given above. For example, the point (0,i) is e^(pi/2), (1,i) is (sqrt(2)/2)e^(pi/4) and on and on...The notation is particularaly useful early in functions of a complex variable in determining multiple roots of high order polynomials. It can be used to express the four values that would be the fourth root of (14+i18). Yes, there are 4 distinct numbers which, when raised to the 4th power equal 14+i18.
rebecca
2002-01-20, 08:19 PM
what does the notation itself mean? does this have anything to do w that sphere?
Gilby
2002-01-20, 08:37 PM
Originally posted by rebecca
that IS what that particular equation is used for. did you do AHSME? (american high school math exam)
For a second I thought the name sounded familiar, but then I remember what I was really thinking about ASME... the American Society of Mechanical Engineers. So I couldn't tell you. It was 5+ years for me on all that stuff. Mostly I did stuff with my high school math team and that's where we did competitions against other schools in our division. Then we went on to the state championships.
rebecca
2002-01-20, 09:06 PM
in college did you take the putnam exam (did you/do you go to college?) i'm looking forward to taking that nxt yr (assuming i finally get ACCEPTED somewhere (can you tell i'm a bit bitter abt my deferrals? ("bit bitter" sounds weird (wow, this is a ridiculous number of imbedded parentheses (i guess math is rubbing off on my typing)))))
Gilby
2002-01-20, 10:04 PM
Nope, I didn't take that. I am currently going to college and I graduate this spring (at least I think I am... aparently they don't have me on record as ever taking Calculus 1, but they have me down for calc 2-6, so I need to get in some document saying I took the AP test for that one).
rebecca
2002-01-20, 10:15 PM
i didnt know it went up to calc 6. where do you go to college, and is there an active unicycling club there? i don't think any of the schools i applied to have clubs, but i'd like to start one...there aren't any clubs listed in MD at all, but this yr i'm too stressed to try to start one, so 'twill have to wait until nxt yr
gauss
2002-02-14, 12:20 PM
I'm partial to my gaussian quadrature for all the solutions to your math inqueries or the bad action transforms from my buddy Laplace. Never give a closed form solution. That is what they want you to do. Pi=3. e=3. The Galerkin Gerkin will never let you down, even when Newton is left crying because the big bad ode with non constant coefficients and forcing functions took his lunch money.
erike
2002-02-14, 05:07 PM
For many years my licence plate in NH was
EIPI+9
This is because my favorite number is 8:cool:.
e^(i*pi)=-1 add 9 to get 8.
Also if you assign each letter it's numerical place:
E=5
I=9
P=16
I=9
9=9
===
total = 48
When you divide 48/8 you get 6, which is the first perfect number:).
A perfect number is a number that is the sum of its divisors. 6= 1 + 2 + 3
The next one is 28 = 1+2+4+7+14.
Ah, I live and die by e!
-Erik
darrell
2002-02-14, 06:29 PM
And that's not all!
Erik really wanted to get EIPI+1, but the plate was already taken in NH! So he went with EIPI+9.
If my memory serves me, Erik actually met the woman who had the plate at some math conference.
Months after hearing this story, I was driving up to the lakes region of NH and I saw a little red car bearing the plate EIPI+1!
Now you know the rest of the story. Sorry I can't ADD more to the converstation. I never studied calculus. I wish I kNEW TONs of stuff like you guys math whizzes, but I was an AVERAGE student. That about SUMS it up for me. :D Sorry for the bad puns. That was MEAN. ;)
-Darrell
erike
2002-02-14, 07:22 PM
I nearly forgot about that. Damn your memory is good (and your puns, too).
And don't anyone get on they 'we hate puns' high horse. Those are some damn good puns!:D
rebecca
2002-02-15, 04:08 AM
i have a screen name related to e^(i*pi). Ask me for it on my other name (rebeccaklambert or lyakr). Want to hear a mathematician joke?..
A mathematician doing some hardcore research started to go a little crazy, so he ran around anouncing to everyone in sight, "I'm going to integrate you! I'm going to differentiate you!" Everyone got scared and ran away except one man. The mathematician approached this man and said "Aren't you going to run away in fear? I'm going to integrate you! I'm going to differentiate you!" The man said, "I'm not scared; I'm e to the x."
More corny mathematician jokes coming soon.
rebecca
2002-02-15, 04:10 AM
Originally posted by erike
Ah, I live and die by e!
-Erik
Hey! You can't have e factorial; only integers can be factorialed!
gauss
2002-02-15, 02:56 PM
That reminds me of another math joke: A polynomial and e^x are walking down the street when they spot a differential operator walking towards them. The polynomial gets scared and turns to run. "Why are you scared?" asks e^x. "that differential operator will differentiate me until there is nothing left. I'm getting out of here," says the polynomial. e^x replies, "I'm not afraid! I'm e^x." So he goes up to the operator and says, "Hi I'm e^x." And the operator says, "Hi, I'm d/dy."
harper
2002-02-15, 05:34 PM
And e^x was zero. I didn't know there were math jokes...I thought there were only mathematician jokes.
rebecca
2002-02-15, 10:18 PM
A mathematician, a physicist, and a biologist were watching all entrances and exits of a building they were certain was empty. They saw two people go in, and a while later, they saw three people go out.
"Data calculation error!" said the physicist.
"They've multiplied!" said the biologist.
And the mathematician said, "If one more person goes in, it will be empty again."
gauss
2002-02-15, 11:03 PM
three mathematicians and three engineers are going to a conference by train. The mathematicians go to the ticket window and buy three tickets. The engineers go to the window and collectively buy one. "how do you three plan to ride with one ticket!?" Asks the mathematicians. The engineers reply, "watch and see," and when everyone boards the train, the three engineers go cram into one bathroom. When the conductor gets to the bathroom, he knocks and says "ticket please." The door opens a crack and the ticket slides out. The watching mathematicians are quite impressed by this. On the return trip, the mathematicians go to the ticket window of the train station and buy one ticket. They werre quite proud of themselves until they saw that the engineers bought no tickets. "How will you ride with no tickets?" They asked. "Watch and see," reply the engineers. When they all board the train. the mathematicians go pack into one bathroom, and the engineers pack into the next one. A few minutes later, one engineer emerges, knocks on the mathematicians' bathroom door and says, "ticket please."
harper
2002-02-16, 01:43 AM
Do you know the story of Gauss (the older one) when he was nine years old or so and had to stay after class for misbehaving? The punishment for him and his classmates was to sum all of the integers from one to one hundred. Gauss did it in short order of course. That is the origin of the equation:
S=n(n+1)/2
for the sum of integers from one to n which he derived first and then solved for n=100.
rebecca
2002-02-16, 02:04 AM
i love that story!
A mathematician and an engineer went to a conference on high-level dimensions. When it was over, the mathematician said, "That was a great lecture!" The engineer said, "Are you kidding? It was horrible! How could you understand a word he said?" The mathematician responded, "I just visualized it." The engineer said, "How do you visualize something in eleven dimensions?" The mathematician said, "I visualized it in n dimensions and let n approach eleven."
gauss
2002-02-17, 06:20 PM
So there is this mathematician who wants to be a fire fighter because he realizes that the most exciting thing in his life is whether or not things will converge, so he goes to the firehouse and explains his situation. The fire chief doesn't really know what to do about him. "Well, I guess, if you can pass this test then we will see what we can do for you." So he takes the mathematician out back and says, "Suppose that dumpster is on fire. What would you do?" The mathematician thinks really hard for several minutes and says, "I would take that hose there and spray the dumpster until the fire went out." The fire chief commends him on his answer then asks, "now suppose we come out here and there is a cat stuck in that tree." The mathematician immediatly exclaims that he would light the dumpster on fire. "Why on earth would you do that?" Asks the fire chief. "Because then I've reduced the problem to one I've already solved!"
rebecca
2002-02-17, 10:57 PM
Two mathematicians were in a bar having an argument: the first said that the average person doesn't know much about math, and the second that the average person does know a reasonable amount of math. When the first mathematician got up and left for a minute, the second called the waitress over and said, "When my friend gets back, I'm going to ask you a question, and I want you to answer "one third x cubed." " "wun thir- dex cue?" "close enough. A while later, the first returned, and the second said, "Well, let's ask that waitress over there a basic math question. If she's right, you pay for our drinks, and if she's wrong, I'll pay." So he called the waitress over and said, "What's the integral of x squared?" The waitress said, "One third x cubed." Then she started to leave, but suddenly she turned back and added, "Plus a constant!"
rebecca
2002-02-17, 10:58 PM
A mathematician was telling his child a bedtime story. "Once upon a time, there were three bears, B0, B1, and B2.
rebecca
2002-02-17, 11:02 PM
A mathematician, and engineer, and a physicist were captured and each locked up in a roofless prison cell with just a bed and sealed cans of beans. A year later, the captors returned to check on their prisoners. First they opened the engineer's cell and found that he had taken apart his bed and reassembled the pieces to make a can opener to eat the beans. Then, they opened the physicist's room. He had collected rainwater to corrode the cans and eat the beans. Then they went to the mathematician's room. He appeared to have been dead for a long time, and written on the floor in blood were the words, "Theorem: If I don't eat any beans, I will die. Proof: Assume the inverse and seek a contradiction."
gauss
2002-02-18, 12:00 AM
nice. I haven't heard the third one that way before. Alternate endings: The mathematician is pointing at the can of beans saying, "I define you to be open" Or they open his cell and he is stuffed inside the can and says, "oops, sign error!"
rebecca
2002-02-18, 12:31 AM
There were some dairy farmers who wanted to maximize the cows' milk production, so they called a vet to ask for advice. The vet recommended a certain diet for the cows and said this would increase their milk production by 5%. Not satisfied, tehy called another vet, who suggested a different fertilizer for the soil and said this would increase it by 10%. Still not satisfied, tehy called a mathematician, who said he could increase their milk production by 500%. "wow, how do you do that?" they asked. The mathematician said, "First you assume the cows to be spherical..."
rebecca
2002-02-18, 12:36 AM
A man and a woman were flying in a balloon, when suddenly their balloon crashed in the middle of the desert. They saw someone walk by and asked, "Where are we?" About an hour later, the person resonded, "You're in a balloon." As the person left, the man said to the woman, "thta must've been a mathematician." "how can you tell?" "The answer he gave was correct, it took a long time to answer, and it was completley useless."
gauss
2002-02-20, 03:48 AM
most of the jokes I have left are real stinkers. Today My advisor and I completed and rode a carbon fiber unicycle wheel. I was surprised at how strong it seems to be considering the simplicity of our design. It felt really stiff and survived the short off road riding and the small drops that we did. It is the first 20 inch unicycle I've ridden. I can't believe how much easier it is than my 26. I will post pictures soon in the other forum, but didn't want to steal any of Harper's thunder on that awesome ride he made. Good job with that!
harper
2002-02-20, 04:08 AM
The jokes both of you submit are great. I have not held my nose once.
Post your wheel experience NOW! Don't wait. Everyone wants to hear about cool stuff like this.
erike
2002-02-20, 01:40 PM
Today is a special day. Remember the last 'odd' day? Nov 19, 1999, written 19111999.
Well, today has a similar appeal.
20 Feb, 2002 is a palindrome:
20022002.
At 8:02pm tonight, it will be:
200220022002
Hard to get better than that (except for e, of course:D)!
-Erik
Brian MacKenzie
2006-03-06, 12:42 AM
10 - 8 = 2
U-Turn
2006-03-06, 02:51 AM
E to the x, dx, dx --
E to the x, dx.
Cosine, secant, tangent, sine,
3.14159.
Square root, cube root, log of pi --
Hit 'em, hit 'em, RPI!
erm, I was in the pep band for a little while.... :rolleyes:
Jerrick
2006-03-06, 05:19 AM
Pi times i! wee!
maestro8
2008-04-22, 06:43 PM
Bump for mathy goodness.
Mikefule
2008-04-22, 07:31 PM
Woooh! Back to the shaving thread for me.:confused:
vanpaun
2008-04-22, 10:07 PM
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