Karl Menger, General Spaces and Cartesian Spaces, (1926) Communications to the Amsterdam Academy of Sciences. English translation reprinted in Classics on Fractals, Gerald A.Edgar, editor, Addison-Wesley (1993) ISBN 0-201-58701-7
Karl Menger, Dimensionstheorie, (1928) B.G Teubner Publishers, Leipzig.
Puzzle Hunt — Video explaining Zeno's paradoxes using Menger-Sierpinski sponge
Menger Sponge Animations — Menger Sponge Animations up to Level 9, discussion of optimization for 3d
กันยายน 29, 2021
ฟองน, ำเมงเงอร, งกฤษ, menger, sponge, อช, อเร, ยกของแฟร, กท, ลอย, างหน, งท, เป, นส, วนขยายในสามม, ของเซตค, นทอร, cantor, บพรมเซ, ยร, นสก, sierpinski, carpet, งบางตำราอาจเร, ยกว, เซ, ยร, นสก, หร, ฟองน, ำเซ, ยร, นสก, และหมายรวมไปถ, งแฟร, กท, ลหร, อกราฟท, เป, นซ,. fxngnaemngengxr xngkvs Menger sponge khuxchuxeriykkhxngaefrkthlxyanghnungthiepnswnkhyayinsammitikhxngestkhnthxr Cantor set kbphrmesiyrphinski Sierpinski carpet sungbangtaraxaceriykwa fxngnaemngengxr esiyrphinski hrux fxngnaesiyrphinski aelahmayrwmipthungaefrkthlhruxkrafthiepnsbestkhxngfxngnaemngengxrdwy ehtuthieriykwafxngnakhuxaefrkthlinsammitinimiruphrunthwthngwtthukhlayfxngna kharl emngengxr nkkhnitsastrchawxxsetriy epnphuxthibayokhrngsrangaelalksnakhxngaefrkthlchnidniepnkhrngaerkin kh s 1926fxngnaemngengxr enuxha 1 karsrangfxngnaemngengxr 2 niyamthwip 3 xangxing 4 duephim 5 aehlngkhxmulxunkarsrangfxngnaemngengxr aekikhkarsrangfxngnaemngengxrsamarthxthibayiddngni erimtncakthrnglukbask rupaerk epnfxngnaemngengxrradbsuny aebngyxyaetlahnaxxkepnrupsiehliymcturs 9 rup sungthaihthrnglukbaskthukaebngxxkepn 27 chinyxy khlaylukbaskkhxngrubikh nathrnglukbaskyxythixyutrngklangkhxngthukhnaxxk rwmthngchinthixyutrngklangphayin ehluxiwephiyng 20 chin epnfxngnaemngengxrradbhnung rupthisxng thasakhntxnthi 1 thung 3 kbthrnglukbaskyxythiehluxkarthasarxbsxngcaidfxngnaradbsxng rupthisam rxbsamcaidfxngnaradbsam rupthisi epnechnnitxiperuxy canwnchinkhxngthrnglukbaskcaephimthila 20 ethacakradbkxnhna hruxxthibayidcak 20 n displaystyle 20 n emux n khuxcanwnrxbkhxngkarthasa inkhxaerksungyngimmikarwnrxb camithrnglukbaskephiyngchinediyw 20 0 1 displaystyle 20 0 1 rxb canwn phlrwm0 1 11 20 212 400 4213 8 000 8 4214 160 000 168 4215 3 200 000 3 368 4216 64 000 000 67 368 421niyamthwip aekikhfxngnaemngengxrsamarthniyamidcak M n N M n displaystyle M bigcap n in mathbb N M n dd emux M 0 displaystyle M 0 khuxthrnglukbaskhnunghnwy aela M n 1 x y z R 3 i j k 0 1 2 3 x i 3 y j 3 z k M n and at most one of i j k is equal to 1 displaystyle M n 1 left begin matrix x y z in mathbb R 3 amp begin matrix exists i j k in 0 1 2 3x i 3y j 3z k in M n mbox and at most one of i j k mbox is equal to 1 end matrix end matrix right dd dngnnfxngnaemngengxrinradbxnnt cungmiphunthiphiwepnxnnt canwnhnaepnxnnt aelamiprimatrepnsunyxangxing aekikhKarl Menger General Spaces and Cartesian Spaces 1926 Communications to the Amsterdam Academy of Sciences English translation reprinted in Classics on Fractals Gerald A Edgar editor Addison Wesley 1993 ISBN 0 201 58701 7 Karl Menger Dimensionstheorie 1928 B G Teubner Publishers Leipzig duephim aekikhrupsamehliymesiyrphinski Sierpinski triangle thrngsihnaesiyrphinski Sierpinski tetrahedron aehlngkhxmulxun aekikhkhxmmxns miphaphaelasuxekiywkb fxngnaemngengxrAn interactive Menger sponge Fractal polyhedra Archived 2008 05 15 thi ewyaebkaemchchin VRML and interactive Java models Archived 2005 12 17 thi ewyaebkaemchchin Puzzle Hunt Video explaining Zeno s paradoxes using Menger Sierpinski sponge Menger Sponge Animations Menger Sponge Animations up to Level 9 discussion of optimization for 3dekhathungcak https th wikipedia org w index php title fxngnaemngengxr amp oldid 9654997, wikipedia, วิกิ หนังสือ, หนังสือ, ห้องสมุด,
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