{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Cover","Minimum","Maximum"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Cover","index":0,"n_rows":21,"n_cols":3,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
[]
[]
[null,"Algorithmen"]
[null,"für Ingenieure"]
[]
[]
[null,"Kapitel",2]
[null,"Thema","Gleichungen höheren Grades"]
[]
[null,"Inhalt","Minimaler Materialverbrauch"]
[null,null,"Maximaler Inhalt"]
[]
[]
[]
[]
[null,"Version","1.0"]
[null,"Autor","Harald Nahrstedt"]
[null,"Datum","2025-06-15"]
[]
[]
[null,"Springer Vieweg Verlag"]

{"sheet":"Minimum","index":1,"n_rows":65,"n_cols":7,"rows_kept":65,"cut":false,"hidden":false,"merged":[]}
["Volumen V =",50,"cm³",null,"Oberfläche [cm^2]","O'(d)","O''(d)]"]
["Startwert d1 =",10,"mm",null,177.07963267948966,58.831853071795862,14.166370614359172]
["Startwert d2 =",100,"mm",null,201.57079632679489,-393.71681469282044,1612.5663706143591]
["Abschaltgrenze",0.01]
[]
[null,"d [cm]"]
[null,8.8299895340282735,null,null,145.12305486730355,50.350197690005054,14.890388233170764]
[null,7.9421921747208843,null,null,124.26530932561093,43.560951906735021,15.760105106179514]
[null,7.2506214557200614,null,null,110.16297961296966,37.948314547765435,16.763905237951128]
[null,6.701120157021287,null,null,100.38238332496243,33.196687944754615,17.883506590888835]
[null,6.2578024694360916,null,null,93.472629438319103,29.104451865785698,19.095487322849809]
[null,5.8958872324448102,null,null,88.52516630058895,25.53796418212686,20.373160260019713]
[null,5.5976652464786083,null,null,84.948288176079444,22.405423614080558,21.688562710525936]
[null,5.3501114557890688,null,null,82.344389966577921,19.641304299413868,23.014330442375243]
[null,5.1434096664355025,null,null,80.439598766419124,17.196788312627923,24.32526886506276]
[null,4.970007427120386,null,null,79.041587509366707,15.033784113661575,25.599504883437923]
[null,4.8239911649712077,null,null,78.013275476074284,13.121173991186737,26.819179817940771]
[null,4.7006613511093081,null,null,77.255861260623135,11.432480189815031,27.970710381341007]
[null,4.5962362956540659,null,null,76.697545771618309,9.9444409637482707,29.044690856801282]
[null,4.5076408235034089,null,null,76.285844361784427,8.6361656418507273,30.035532618379161]
[null,4.4323522867099294,null,null,75.982234014282525,7.4886496439418799,30.940939965453058]
[null,4.3682861509900572,null,null,75.758362372695061,6.484504464312316,31.761309931595481]
[null,4.3137094528692783,null,null,75.593326965196781,5.6078082519593089,32.499124859040606]
[null,4.2671742628342635,null,null,75.471702799039406,4.8440175280269777,33.158385610997584]
[null,4.2274657713899302,null,null,75.382101976845178,4.1799044345019425,33.744114063755326]
[null,4.1935612483277049,null,null,75.316116423981384,3.6034998065654946,34.261937953698904]
[null,4.1645972187509548,null,null,75.267539166101827,3.1040325550641263,34.717759849575415]
[null,4.1398429427122965,null,null,75.231789540715369,2.6718620333162946,35.117504694893512]
[null,4.1186787984221578,null,null,75.20548842558614,2.2984035272956973,35.46693629379584]
[null,4.1005785284804821,null,null,75.186144161819243,1.9760487002793994,35.771531442843951]
[null,4.085094564178525,null,null,75.171920306183353,1.6980834231137827,36.036400347481816]
[null,4.071845827312182,null,null,75.161463930795236,1.458605398123975,36.266242859345098]
[null,4.0605075439116334,null,null,75.153778736988883,1.2524436467645153,36.465331451616414]
[null,4.0508027044885324,null,null,75.148131334761018,1.0750814705488452,36.637513390644777]
[null,4.0424948808230265,null,null,75.143982057758848,0.92258402323040656,36.786226062954945]
[null,4.0353821668442906,null,null,75.140933919698242,0.79153120800416588,36.914520768152727]
[null,4.0292920556001537,null,null,75.138694976192468,0.67895626158162159,37.025091442259992]
[null,4.0240770990494479,null,null,75.137050585985861,0.58229011259572516,37.120305723549372]
[null,4.0196112248614435,null,null,75.135842977874859,0.49931139955473469,37.20223652691115]
[null,4.0157866063159213,null,null,75.134956205883952,0.42810189326427661,37.272692876899413]
[null,4.0125109990417558,null,null,75.134305076246477,0.36700697860793241,37.333249191291067]
[null,4.0097054726562975,null,null,75.133827000564196,0.31460079957698994,37.385272533210625]
[null,4.00730247708041,null,null,75.133476003774192,0.26965564956472576,37.42994758496922]
[null,4.0052441929413884,null,null,75.133218318221196,0.23111518794286567,37.468299261562343]
[null,4.0034811234497525,null,null,75.133029144787145,0.19807107723621442,37.501212993422854]
[null,4.001970891765013,null,null,75.132890272456137,0.16974265772347863,37.529452780266482]
[null,4.0006772133998405,null,null,75.132788329121809,0.14545930421341424,37.553677161442906]
[null,3.9995690178491454,null,null,75.132713496454343,0.1246451403070914,37.574453271365584]
[null,3.9986196975280981,null,null,75.132658565845645,0.10680581670915501,37.592269157562626]
[null,3.9978064653878311,null,null,75.132618244994546,9.1517090770384613E-2,37.607544538294036]
[null,3.99710980535232,null,null,75.132588648642638,7.8414973577817904E-2,37.620640169897243]
[null,3.9965130020685535,null,null,75.132566924589824,6.718723804854676E-2,37.631865983485639]
[null,3.9960017384534794,null,null,75.132550979075972,5.7566106366710557E-2,37.641488138049809]
[null,3.9955637512121545,null,null,75.132539275140942,4.932195763961289E-2,37.649735123584904]
[null,3.9951885359391985,null,null,75.132530684578299,4.2257916863547962E-2,37.656803034385852]
[null,3.9948670946393103,null,null,75.13252437924335,3.6205204281813508E-2,37.6628601196293]
[null,3.9945917195450784,null,null,75.132519751257604,3.1019140131430589E-2,37.668050706111096]
[null,3.9943558079991512,null,null,75.132516354429697,2.6575713778683507E-2,37.672498576702537]
[null,3.9941537039261843,null,null,75.132513861252804,2.2768638514712336E-2,37.676309877802794]
[null,3.9939805620673816,null,null,75.132512031337725,1.9506823997105016E-2,37.679575619809569]
[null,3.9938322317034212,null,null,75.132510688240899,1.6712207652140876E-2,37.68237382637318]
[null,3.9937051570640687,null,null,75.132509702455337,1.4317894454698887E-2,37.684771380883532]
[null,3.9935962920266874,null,null,75.132508978925387,1.2266561524683084E-2,37.68682561219417]
[null,3.9935030270512399,null,null,75.132508447882429,1.0509090055005998E-2,37.688585655934233]
[null,3.9934231265947795,null,null,75.132508058118162,9.0033923349643885E-3,37.690093622819305]

{"sheet":"Maximum","index":2,"n_rows":10,"n_cols":7,"rows_kept":10,"cut":false,"hidden":false,"merged":[]}
["Kantenlänge a =",50,"cm",null,"Volumen [cm^3]","V'(x)","V''(x)]"]
["Startwert x =",2,"cm",null,4232,1748,-352]
["Abschaltgrenze",0.01]
[]
[]
[null,"x [cm]"]
[null,6.9659090909090908,null,null,9062.0468456517665,295.9230371900826,-232.81818181818181]
[null,8.2369568882893756,null,null,9258.326836604052,19.386750038703212,-202.313034681055]
[null,8.3327823998253283,null,null,9259.2592289058193,0.11019034393393667,-200.01322240419211]
[null,8.333333315122875,null,null,9259.2592592592591,3.6420915421331301E-6,-200.000000437051]