This is a demonstration that Exp(i*Pi)=-1 (called Euler's formula, or Euler's identity). It uses the formula (1+z/N)^N --> Exp(z) (as N increases). The Nth power is displayed as a repeated multiplication in the complex plane. As N increases, you can see that the final result (the last point) approaches -1, the actual value of Exp(i*pi).
{{Information |Description=This is a demonstration that Exp(I*Pi)=-1 (called Euler's formula, or Euler's identity). It uses the formula (1+z/N)^N --> Exp(z) (as N increases). The Nth power is displayed as a repeated multiplication in the complex plane. As
{{Information |Description=This is a demonstration that Exp(I*Pi)=-1 (called Euler's formula, or Euler's identity). It uses the formula (1+z/N)^N --> Exp(z) (as N increases). The Nth power is displayed as a repeated multiplication in the complex plane. As
ไฟล, expipi, ไฟล, ประว, ไฟล, หน, าท, ภาพน, การใช, ไฟล, วนกลางไม, ภาพท, รายละเอ, ยดส, งกว, าน, expipi, 8206, กเซล, ขนาดไฟล, โลไบต, ชน, ดไมม, image, วนซ, เฟรม, นาท, ปภาพหร, อไฟล, เส, ยงน, นฉบ, บอย, คอมมอนส, รายละเอ, ยดด, านล, าง, เป, นข, อความท, แสดงผลจาก, ไฟล, . ifl prawtiifl hnathimiphaphni karichiflswnklangimmiphaphthimiraylaexiydsungkwani ExpIPi gif 8206 360 323 phikesl khnadifl 11 kiolibt chnidimm image gif wnsa 9 efrm 4 5 winathi rupphaphhruxiflesiyngni tnchbbxyuthi khxmmxns raylaexiyddanlang epnkhxkhwamthiaesdngphlcak ifltnchbbinkhxmmxns khxmmxnsepnewbistinokhrngkarsahrbekbrwbrwmsuxesri thi khunsamarthchwyid khwamyx khaxthibayExpIPi gif This is a demonstration that Exp i Pi 1 called Euler s formula or Euler s identity It uses the formula 1 z N N gt Exp z as N increases The Nth power is displayed as a repeated multiplication in the complex plane As N increases you can see that the final result the last point approaches 1 the actual value of Exp i pi wnthi 5 phvsphakhm ph s 2551 aehlngthima ngankhxngtw nbsp iflGIF phaphkrafiksewketxrni srangkhunodyich nbsp Mathematica phusrangsrrkh Sbyrnes321 karxnuyatichsiththi Public domain Public domain false false khapheca phuthuxlikhsiththiinnganni khxmxbnganihepnsatharnsmbti prakasnimiphlthwolkinbangpraeths karkrathadngklawxacimsamarththaidtamkdhmaykhaphecaxnuyatihthukkhnmisiththiinkarichiflniinthukehtuphlkarich odyimmimienguxnikh ewnaetkdhmayimxnuyatihthaechnnn Source code written in Mathematica 6 0 by Steve Byrnes 2008 I release this code into the public domain plot1 Table ListPlot Table Re 1 ImaginaryI Pi n m Im 1 ImaginaryI Pi n m m 0 n PlotJoined gt True PlotMarkers gt Automatic PlotRange gt 2 5 1 1 0 Pi 05 AxesOrigin gt 0 0 AxesLabel gt Real part Imaginary part PlotLabel gt N lt gt ToString n AspectRatio gt Automatic n 1 2 3 4 5 10 20 50 100 Export ExpIPi gif plot1 DisplayDurations gt 2 AnimationRepititions gt Infinity khabrryayodyyxithyephimkhabrryaythrrthdediywephuxkhyaykhwamwaiflnimixairixethmthiaesdngxyuiniflniprakxbdwyphusrangbangkhathiimmiixethmwikisnethsyuxaraexl https commons wikimedia org wiki user Sbyrnes321chuxphuichwikimiediy Sbyrnes321chuxphusrangsrrkh Sbyrnes321sthanalikhsiththicopyrighted dedicated to the public domain by copyright holder nbsp xngkvsmilikhsiththisyyaxnuyatreleased into the public domain by the copyright holder nbsp xngkvsthimakhxngiflkarsrangdngedimodyphuxpohldwnthisrang wnkxtng5 phvsphakhm 2008 prawtiifl khlikwnthi ewlaephuxduiflthipraktinkhnann wnthi ewlarupyxkhnadphuichkhwamehn pccubn02 46 26 minakhm 2553360 323 11 kiolibt Aiyizooptimized animation converted to 16 color mode 00 19 6 phvsphakhm 2551360 323 20 kiolibt Sbyrnes321 Information Description This is a demonstration that Exp I Pi 1 called Euler 039 s formula or Euler 039 s identity It uses the formula 1 z N N gt Exp z as N increases The Nth power is displayed as a repeated multiplication in the complex plane As 23 58 5 phvsphakhm 2551360 308 18 kiolibt Sbyrnes321 Information Description This is a demonstration that Exp I Pi 1 called Euler 039 s formula or Euler 039 s identity It uses the formula 1 z N N gt Exp z as N increases The Nth power is displayed as a repeated multiplication in the complex plane As hnathimiphaphni hnatxipni oyngmathiphaphni karykkalng exklksnkhxngxxyelxr karichiflswnklang wikixuntxipniichiflni karichbn ar wikipedia org رفع رياضيات karichbn ba wikipedia org Ejler tozhdestvoһy kompleksly analiz karichbn be wikipedia org Stupenyavanne karichbn bn wikipedia org অয ল র র অভ দ স চক করণ karichbn ca wikipedia org Identitat d Euler karichbn cs wikipedia org Iterace karichbn de wikipedia org Eulersche Formel karichbn el wikipedia org Dynamh ma8hmatika karichbn en wikipedia org Talk Euler s identity Archive 1 Euler s identity User Sbyrnes321 karichbn en wikiquote org Ludwig Wittgenstein George Polya Wikiquote Quote of the day April 2009 Wikiquote Quote of the day April 15 Benjamin Peirce Wikiquote Quote of the day Index Display User Kalki Restorations User Kalki images mathematics Euler s identity karichbn es wikipedia org Identidad de Euler karichbn fi wikipedia org Eulerin identiteetti Iterointi karichbn hy wikipedia org Աստիճան հանրահաշիվ Էյլերի նույնություն karichbn it wikipedia org Identita di Eulero karichbn ja wikipedia org オイラーの等式 karichbn ka wikipedia org ეილერის იგივეობა karichbn lmo wikipedia org Identita de Euler karichbn no wikipedia org Bruker Phidus sandkasse 20 karichbn pl wikipedia org Potegowanie Wzor Eulera karichbn pt wikipedia org Formula de Euler Identidade de Euler karichbn ru wikipedia org Tozhdestvo Ejlera kompleksnyj analiz karichbn ta wikipedia org ஆய லர ன ம ற ற ர ம karichbn tr wikipedia org Euler ozdesligi Portal Matematik Portal Matematik Haftanin maddesi karichbn tt wikipedia org Ejler berdәjlege karichbn zh wikipedia org 冪 ekhathungcak https th wikipedia org wiki ifl ExpIPi gif, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,
