e = 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738132328627943490763233829880753195251019011573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069551702761838606261331384583000752044933826560297606737113200709328709127443747047230696977209310141692836819025515108657463772111252389784425056953696770785449969967946864454905987931636889230098793127736178215424999229576351482208269895193668033182528869398496465105820939239829488793320362509443117301238197068416140397019837679320683282376464804295311802328782509819455815301756717361332069811250996181881593041690351598888519345807273866738589422879228499892086805825749279610484198444363463244968487560233624827041978623209002160990235304369941849146314093431738143640546253152096183690888707016768396424378140592714563549061303107208510383750510115747704171898610687396965521267154688957035035402123407849819334321068170121005627880235193033224745015853904730419957777093503660416997329725088687696640355570716226844716256079882651787134195124665201030592123667719432527867539855894489697096409754591856956380236370162112047742722836489613422516445078182442352948636372141740238893441247963574370263755294448337998016125492278509257782562092622648326277933386566481627725164019105900491644998289315056604725802778631864155195653244258698294695930801915298721172556347546396447910145904090586298496791287406870504895858671747985466775757320568128845920541334053922000113786300945560688166740016984205580403363795376452030402432256613527836951177883863874439662532249850654995886234281899707733276171783928034946501434558897071942586398772754710962953741521115136835062752602326484728703920764310059584116612054529703023647254929666938115137322753645098889031360205724817658511806303644281231496550704751025446501172721155519486685080036853228183152196003735625279449515828418829478761085263981395599006737648292244375287184624578036192981971399147564488262603903381441823262515097482798777996437308997038886778227138360577297882412561190717663946507063304527954661855096666185664709711344474016070462621568071748187784437143698821855967095910259686200235371858874856965220005031173439207321139080329363447972735595527734907178379342163701205005451326383544000186323991490705479778056697853358048966906295119432473099587655236812859041383241160722602998330535370876138939639177957454016137223618789365260538155841587186925538606164779834025435128439612946035291332594279490433729908573158029095863138268329147711639633709240031689458636060645845925126994655724839186564209752685082307544254599376917041977780085362730941710163434907696423722294352366125572508814779223151974778060569672538017180776360346245927877846585065605078084421152969752189087401966090665180351650179250461950136658543663271254963990854914420001457476081930221206602433009641270489439039717719518069908699860663658323227870937650226014929101151717763594460202324930028040186772391028809786660565118326004368850881715723866984224220102495055188169480322100251542649463981287367765892768816359831247788652014117411091360116499507662907794364600585194199856016264790761532103872755712699251827568798930276176114616254935649590379804583818232336861201624373656984670378585330527583333793990752166069238053369887956513728559388349989470741618155012539706464817194670834819721448889879067650379590366967249499254527903372963616265897603949857674139735944102374432970935547798262961459144293645142861715858733974679189757121195618738578364475844842355558105002561149239151889309946342841393608038309166281881150371528496705974162562823609216807515017772538740256425347087908913729172282861151591568372524163077225440633787593105982676094420326192428531701878177296023541306067213604600038966109364709514141718577701418060644363681546444005331608778314317444081194942297559931401188868331483280270655383300469329011574414756313999722170380461709289457909627166226074071874997535921275608441473782330327033016823719364800217328573493594756433412994302485023573221459784328264142168487872167336701061509424345698440187331281010794512722373788612605816566805371439612788873252737389039289050686532413806279602593038772769778379286840932536588073398845721874602100531148335132385004782716937621800490479559795929059165547050577751430817511269898518840871856402603530558373783242292418562564425502267215598027401261797192804713960068916382866527700975276706977703643926022437284184088325184877047263844037953016690546593746161932384036389313136432713768884102681121989127522305625675625470172508634976536728860596675274086862740791285657699631378975303466061666980421826772456053066077389962421834085988207186468262321508028828635974683965435885668550377313129658797581050121491620765676995065971534476347032085321560367482860837865680307306265763346977429563464371670939719306087696349532884683361303882943104080029687386911706666614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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.
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.
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=C1e^2t + C2te^(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.
Well, I was more of wondering what that specific equation is used for, not similar ones.
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.
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.
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.
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)))))
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).
