Meetkunde 1: verschil tussen versies

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http://intimo-firmato-51.blogskine.net/2008/08/26/abbigliamento-firmato-offerta/ abbigliamento firmato offerta http://mariana-monteiro-29.blogskine.net/blog/entry/mariana-aguiar/ mariana aguiar http://sposa-59.alumblogs.net/2008/08/donna-sposate-it/ donna sposate it http://adesivi-camel-48.mygreatblogs.net/2008/08/camelot-cosenza/ camelot cosenza http://metropolitana-palermo-87.blogskine.net/node/agenzia-recapito-espresso-palermo/ agenzia recapito espresso palermo http://hooker-19.mygreatblogs.net/2008/08/27/ass-hooker/ ass hooker http://caccia-mongolia-51.blogskine.net/mongolia-online/ mongolia online http://domiciliazione-telefonica-45.mygreatblogs.net/wordpress/centraline-telefonica/ centraline telefonica http://claudio-lolli-83.blogskine.net/2008/08/15/claudio-bisio-sabrina-ferilli/ claudio bisio sabrina ferilli http://perverso-74.alumblogs.net/male-perverso/ male perverso http://analisi-aziendale-29.blogskine.net/capire-analisi-sangue/ capire analisi sangue http://kerri-hoskins-2.mygreatblogs.net/2008/09/11/kerrie-marie/ kerrie marie http://master-80.alumblogs.net/node/master-of-universe/ master of universe http://assunta-signorelli-15.alumblogs.net/blog/entry/assunta-menna/ assunta menna http://regia-caserta-22.alumblogs.net/2008/08/01/sconosciuta-regia/ sconosciuta regia http://schubert-concept-17.blogskine.net/wordpress/concept-car-porsche/ concept car porsche http://letterario-buscemi-63.blogskine.net/d-annunzio-percorso-letterario/ d annunzio percorso letterario http://sacro-monte-84.mygreatblogs.net/blog/entry/design-piemonte/ design piemonte http://australian-18.mygreatblogs.net/nazionalismo-australiano/ nazionalismo australiano http://nervi-frenici-84.blogskine.net/wordpress/nervi-corpo-umano/ nervi corpo umano http://rotoli-polipropilene-3.mygreatblogs.net/wordpress/rotoli-teflon/ rotoli teflon http://scuola-giudizio-29.alumblogs.net/educazione-musicale-scuola-secondaria/ educazione musicale scuola secondaria http://ceres-39.alumblogs.net ceres http://jovanotti-74.blogskine.net/wordpress/parodia-jovanotti/ parodia jovanotti http://maltese-33.mygreatblogs.net/wordpress/capra-razza-maltese/ capra razza maltese http://circolare-litio-48.blogskine.net circolare http://hentai-63.alumblogs.net/node/tokyo-mew-mew-hentai/ tokyo mew mew hentai http://ghiaccio-sintetico-41.mygreatblogs.net/courmayeur-palazzetto-it-ghiaccio/ courmayeur palazzetto it ghiaccio http://pennsylvania-shopping-9.alumblogs.net/node/mediashopping-com/ mediashopping com http://fideiussione-assicurativa-15.alumblogs.net/formazione-compagnia-assicurativa/ formazione compagnia assicurativa http://sistema-76.blogskine.net/2008/08/sistema-fissaggio-tubazioni/ sistema fissaggio tubazioni http://canile-savona-10.mygreatblogs.net/blog/entry/distanza-portofino-savona/ distanza portofino savona http://vendita-84.mygreatblogs.net/wordpress/vendita-licenza-applicativi/ vendita licenza applicativi http://orgoglio-bianconero-33.alumblogs.net orgoglio http://scartamento-ridotto-90.mygreatblogs.net/2008/08/ammortamento-ridotto/ ammortamento ridotto http://guest-rimini-88.mygreatblogs.net/wordpress/rimini-sant-arcangelo-romagna/ rimini sant arcangelo romagna http://boogie-elliot-1.alumblogs.net/wordpress/missy-elliot-lose-control/ missy elliot lose control http://contrassegno-ciclomotore-77.blogskine.net/node/polizza-temporanee-ciclomotore/ polizza temporanee ciclomotore http://fujitsu-60.alumblogs.net/2008/09/driver-xp-fujitsu-scaleo/ driver xp fujitsu scaleo http://progammi-televisione-60.mygreatblogs.net/2008/08/13/televisione-potente-mezzo-condizionamento/ televisione potente mezzo condizionamento http://nereo-capozza-94.alumblogs.net/2008/07/28/torneo-nereo-rocco/ torneo nereo rocco http://produrre-3.blogskine.net/blog/entry/produrre-karaoke/ produrre karaoke http://super-eagles-14.mygreatblogs.net/2008/07/progetto-accoglienza-istituto-superiori/ progetto accoglienza istituto superiori http://wooden-shutter-35.mygreatblogs.net/2008/08/03/nassau-green-shutters/ nassau green shutters http://napoli-senese-40.alumblogs.net/wordpress/napoli-galleria-umberto/ napoli galleria umberto http://tibia-99.blogskine.net/tibia-quests-walkthrough/ tibia quests walkthrough http://sweetheart-monica-5.blogskine.net/2008/09/11/monica-sweetheart-blow-job/ monica sweetheart blow job http://tavole-girevoli-42.blogskine.net/2008/08/seduta-girevoli-ufficio/ seduta girevoli ufficio http://picnic-benevento-37.alumblogs.net/vino-doc-benevento/ vino doc benevento http://upgrade-office-10.mygreatblogs.net/wordpress/loan-officer-what-is/ loan officer what is
http://intimo-firmato-51.blogskine.net/2008/08/26/abbigliamento-firmato-offerta/ abbigliamento firmato offerta http://mariana-monteiro-29.blogskine.net/blog/entry/mariana-aguiar/ mariana aguiar http://sposa-59.alumblogs.net/2008/08/donna-sposate-it/ donna sposate it http://adesivi-camel-48.mygreatblogs.net/2008/08/camelot-cosenza/ camelot cosenza http://metropolitana-palermo-87.blogskine.net/node/agenzia-recapito-espresso-palermo/ agenzia recapito espresso palermo http://hooker-19.mygreatblogs.net/2008/08/27/ass-hooker/ ass hooker http://caccia-mongolia-51.blogskine.net/mongolia-online/ mongolia online http://domiciliazione-telefonica-45.mygreatblogs.net/wordpress/centraline-telefonica/ centraline telefonica http://claudio-lolli-83.blogskine.net/2008/08/15/claudio-bisio-sabrina-ferilli/ claudio bisio sabrina ferilli http://perverso-74.alumblogs.net/male-perverso/ male perverso http://analisi-aziendale-29.blogskine.net/capire-analisi-sangue/ capire analisi sangue http://kerri-hoskins-2.mygreatblogs.net/2008/09/11/kerrie-marie/ kerrie marie http://master-80.alumblogs.net/node/master-of-universe/ master of universe http://assunta-signorelli-15.alumblogs.net/blog/entry/assunta-menna/ assunta menna http://regia-caserta-22.alumblogs.net/2008/08/01/sconosciuta-regia/ sconosciuta regia http://schubert-concept-17.blogskine.net/wordpress/concept-car-porsche/ concept car porsche http://letterario-buscemi-63.blogskine.net/d-annunzio-percorso-letterario/ d annunzio percorso letterario http://sacro-monte-84.mygreatblogs.net/blog/entry/design-piemonte/ design piemonte http://australian-18.mygreatblogs.net/nazionalismo-australiano/ nazionalismo australiano http://nervi-frenici-84.blogskine.net/wordpress/nervi-corpo-umano/ nervi corpo umano http://rotoli-polipropilene-3.mygreatblogs.net/wordpress/rotoli-teflon/ rotoli teflon http://scuola-giudizio-29.alumblogs.net/educazione-musicale-scuola-secondaria/ educazione musicale scuola secondaria http://ceres-39.alumblogs.net ceres http://jovanotti-74.blogskine.net/wordpress/parodia-jovanotti/ parodia jovanotti http://maltese-33.mygreatblogs.net/wordpress/capra-razza-maltese/ capra razza maltese http://circolare-litio-48.blogskine.net circolare http://hentai-63.alumblogs.net/node/tokyo-mew-mew-hentai/ tokyo mew mew hentai http://ghiaccio-sintetico-41.mygreatblogs.net/courmayeur-palazzetto-it-ghiaccio/ courmayeur palazzetto it ghiaccio http://pennsylvania-shopping-9.alumblogs.net/node/mediashopping-com/ mediashopping com http://fideiussione-assicurativa-15.alumblogs.net/formazione-compagnia-assicurativa/ formazione compagnia assicurativa http://sistema-76.blogskine.net/2008/08/sistema-fissaggio-tubazioni/ sistema fissaggio tubazioni http://canile-savona-10.mygreatblogs.net/blog/entry/distanza-portofino-savona/ distanza portofino savona http://vendita-84.mygreatblogs.net/wordpress/vendita-licenza-applicativi/ vendita licenza applicativi http://orgoglio-bianconero-33.alumblogs.net orgoglio http://scartamento-ridotto-90.mygreatblogs.net/2008/08/ammortamento-ridotto/ ammortamento ridotto http://guest-rimini-88.mygreatblogs.net/wordpress/rimini-sant-arcangelo-romagna/ rimini sant arcangelo romagna http://boogie-elliot-1.alumblogs.net/wordpress/missy-elliot-lose-control/ missy elliot lose control http://contrassegno-ciclomotore-77.blogskine.net/node/polizza-temporanee-ciclomotore/ polizza temporanee ciclomotore http://fujitsu-60.alumblogs.net/2008/09/driver-xp-fujitsu-scaleo/ driver xp fujitsu scaleo http://progammi-televisione-60.mygreatblogs.net/2008/08/13/televisione-potente-mezzo-condizionamento/ televisione potente mezzo condizionamento http://nereo-capozza-94.alumblogs.net/2008/07/28/torneo-nereo-rocco/ torneo nereo rocco http://produrre-3.blogskine.net/blog/entry/produrre-karaoke/ produrre karaoke http://super-eagles-14.mygreatblogs.net/2008/07/progetto-accoglienza-istituto-superiori/ progetto accoglienza istituto superiori http://wooden-shutter-35.mygreatblogs.net/2008/08/03/nassau-green-shutters/ nassau green shutters http://napoli-senese-40.alumblogs.net/wordpress/napoli-galleria-umberto/ napoli galleria umberto http://tibia-99.blogskine.net/tibia-quests-walkthrough/ tibia quests walkthrough http://sweetheart-monica-5.blogskine.net/2008/09/11/monica-sweetheart-blow-job/ monica sweetheart blow job http://tavole-girevoli-42.blogskine.net/2008/08/seduta-girevoli-ufficio/ seduta girevoli ufficio http://picnic-benevento-37.alumblogs.net/vino-doc-benevento/ vino doc benevento http://upgrade-office-10.mygreatblogs.net/wordpress/loan-officer-what-is/ loan officer what is


== Theorievragen ==
http://raggio-verde-3.alumblogs.net/blog/entry/certificato-verde/ certificato verde http://pedro-35.blogskine.net/arenas-de-san-pedro/ arenas de san pedro http://fatta-vedere-78.mygreatblogs.net/blog/entry/vedere-film-porno-gratis/ vedere film porno gratis http://porta-pacchi-30.alumblogs.net/wordpress/edil-portale/ edil portale http://clipart-religiose-42.alumblogs.net/2008/09/06/case-religiose/ case religiose http://insulina-basale-24.alumblogs.net/temperatura-basale-schema/ temperatura basale schema http://prezzo-iphone-30.alumblogs.net/node/prezzo-lenti-progressive/ prezzo lenti progressive http://vetrata-artistiche-46.alumblogs.net/blog/entry/vetrata-sacre/ vetrata sacre http://villa-corfu-6.blogskine.net villa http://forza-condivisione-50.blogskine.net/node/la-forza-dell-amore/ la forza dell amore http://bussiness-intelligence-20.alumblogs.net bussiness http://pensione-donoratico-66.mygreatblogs.net/pensione-cesenatico/ pensione cesenatico http://festivalbar-compilation-10.blogskine.net/wordpress/festivalbar-it/ festivalbar it http://vatican-crimes-43.mygreatblogs.net vatican http://prontuario-attuariale-35.mygreatblogs.net/2008/09/12/prontuario-farmaceutico-alfabetico/ prontuario farmaceutico alfabetico http://robbie-orifici-67.mygreatblogs.net/robbie-orifici/ robbie orifici http://rosarossa-7.alumblogs.net/node/rosarossa-transex/ rosarossa transex http://porte-telescopiche-53.mygreatblogs.net/blog/entry/porte-scorrevoli-sistema-interne/ porte scorrevoli sistema interne http://steve-41.mygreatblogs.net/wife-seekersteven-segal/ wife seekersteven segal http://steel-fittings-59.blogskine.net/stainless-steel-fittings/ stainless steel fittings http://black-inside-59.mygreatblogs.net/blog/entry/black-eied-peas/ black eied peas http://racer-40.mygreatblogs.net/node/adidas-adi-racer-low/ adidas adi racer low http://hotel-albuquerque-44.blogskine.net/nova-hotel-amsterdam/ nova hotel amsterdam http://bolaffi-33.blogskine.net/quotazioni-bolaffi/ quotazioni bolaffi http://letto-23.mygreatblogs.net/2008/09/02/letto-ferro-battuto-milano/ letto ferro battuto milano http://viene-32.blogskine.net/2008/09/avviene-inserimento-sociale/ avviene inserimento sociale http://emanuela-foliero-35.alumblogs.net/2008/09/08/emanuela-troisi/ emanuela troisi http://accumulo-energia-85.blogskine.net/node/tesi-energia-solare/ tesi energia solare http://speed-76.alumblogs.net/2008/09/19/portatarga-speed-triple/ portatarga speed triple http://brondi-bravo-10.alumblogs.net/wordpress/bravo-porno/ bravo porno http://window-69.blogskine.net/node/windows-workflow/ windows workflow http://cacciatore-appennini-11.mygreatblogs.net cacciatore http://severi-hotel-87.alumblogs.net/node/hotel-a-los-roques/ hotel a los roques http://cattaneo-francesco-38.alumblogs.net cattaneo http://giulio-rubinelli-16.mygreatblogs.net/node/giulio-giorgigiorgia-palmas/ giulio giorgigiorgia palmas http://barcellona-girona-34.blogskine.net/2008/09/rialto-barcellona/ rialto barcellona http://wingman-66.blogskine.net/wordpress/wingman-formula/ wingman formula http://spoleto-64.mygreatblogs.net/2008/09/b-amp-b-spoleto/ b amp b spoleto http://professor-gasparini-69.mygreatblogs.net/pasquali-g-pittore-professore/ pasquali g pittore professore http://bollettino-estrazione-76.blogskine.net/node/bollettino-liguria/ bollettino liguria http://confronto-banca-93.mygreatblogs.net/2008/09/banca-popolare-vicentina/ banca popolare vicentina http://mobil-24.blogskine.net/2008/09/13/kronos-immobiliare-piemonte/ kronos immobiliare piemonte http://north-sydney-45.mygreatblogs.net/2008/08/22/sydney-accommodation/ sydney accommodation http://patrizia-salviato-16.mygreatblogs.net/ottavia-patrizia/ ottavia patrizia http://informazione-35.alumblogs.net/wordpress/informazione-albergo-marsa-alam/ informazione albergo marsa alam http://alessia-poppea-45.alumblogs.net/2008/08/alessia-fabiani-nuda/ alessia fabiani nuda http://ground-38.mygreatblogs.net/wordpress/underground-tekno/ underground tekno http://codice-65.mygreatblogs.net/2008/09/codice-html-puntatore/ codice html puntatore http://stretto-74.alumblogs.net/node/stretto-torres/ stretto torres http://gyver-40.blogskine.net gyver
Een lijst met theorievragen die Professor Dillen reeds gesteld heeft, afkomstig uit de examenvragenbundel van Cudi.
 
=== Euclidische meetkunde ===
 
# Je mag zeker een vraag verwachten waarbij je ofwel de oriëntatiebewarende ofwel de oriëntatieomkerende isometrieën van <math>\mathbb{E}^2</math> of <math>\mathbb{E}^3</math> moet classificeren.
# Definieer rotatie in <math>\mathbb{E}^2</math> en <math>\mathbb{E}^3</math>.
# Definieer spiegeling en bewijs dat het een isometrie is.
#
#* Definieer schroefbeweging en rotatie in <math>\mathbb{E}^3</math> en geef uitgebreid commentaar.
#* Bewijs dan dat elke oriëntatiebewarende isometrie van <math>\mathbb{E}^3</math> een translatie of schroefbeweging is.
# Zij <math>F : \mathbb{E}^n \to \mathbb{E}^n</math> een willekeurige afbeelding. Bewijs dat F een isometrie is als en slechts als d(F(p), F(q)) = d(p,q) voor alle <math>p,q \in \mathbb{E}^n</math>.
# Bewijs de volgende stelling: Zij F een isometrie. Dan bestaat er juist één isometrie G en juist één translatie <math>t_b</math> zodat
#* <math>F = t_b \circ G</math>
#* <math>V(G) \neq \emptyset</math>
#* <math>G_* b = b</math>
#: Bovendien is dan ook <math>t_b \circ G =G \circ t_b</math> en V(G) is een affiene deelruimte in de richting van <math>\ker (F_* - I)</math>.
 
=== Krommen ===
 
# Geef het Frenetstelsel voor vlakke krommen en formuleer de congruentiestelling. Vergelijk het Frenetstelsel van congruente krommen met dat van booglengtegeparamatriseerde krommen.
# Bewijs dat een reguliere kromme in <math>\mathbb{E}^3</math> een vlakke kromme is als en slechts als de torsie 0 is.
#
#* In <math>\mathbb{E}^2</math>. Toon aan dat de kromming de kromme volledig bepaalt.
#* Definieer gesloten krommen en de rotatie-index en verklaar hoe de rotatie-index bepaald kan worden uit de kromming.
#
#* Definieer de cirkelschroeflijn en de cilinderschroeflijn en verklaar de naamgeving.
#* Geef de nodige en voldoende voorwaarden voor de kromming en torsie zodat een reguliere kromme een cilinderschroeflijn is.
#
#* Definieer het Frenet-referentiestelsel voor ruimtekrommen en bewijs de formules van Frenet.
#* Formuleer en bewijs de congruentiestelling voor ruimtekrommen.
# Formuleer en bewijs de congruentiestelling voor booglengtegeparametriseerde vlakke krommen.
# Rechten realiseren de kortste afstand tussen twee punten. Behandel uitvoerig.


== Tussentijdse toetsen ==
== Tussentijdse toetsen ==

Versie van 27 sep 2008 16:07

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Tussentijdse toetsen

2006-04-??

  1. Geef een basis voor de richting van de volgende affiene deelruimte van 𝔸4:
    x1−x3−x4=−1
    x1+x2−2x3=1
    x2−x3+x4=2
    x1+3x2−4x3+2x4=5
  2. Zij S een niet-lege deelverzameling van 𝔸n. Toon aan: S is een affiene deelruimte van 𝔸n als en slechts als voor elk tweetal punten p, q van S de verbindingsrechte pq tot S behoort.
  3. Zij b, c twee vaste punten in 𝔸2 en L een vaste rechte die bc snijdt in p. Toon aan dat de zwaartepunten van de driehoeken abc, waarbij a varieert op L \ {p}, steeds tot een vaste rechte behoren. Doe dit
    • analytisch;
    • synthetisch.
    (Voor het synthetisch bewijs mag je alle eigenschappen uit de cursus en de oefenzittingen gebruiken, maar zeg er wel bij welke eigenschap je gebruikt.)
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