Asked 7 years, 6 months ago Active 7 years, 6 months ago Viewed 780 times https://www.youtube.com/watch?v=Q9qAyt0G-jM        何度も云うよ          と 有る https://math.stackexchange.com/questions/662768/degree-of-the-dual-curve-to-xy2-z3 を         味読し  これに倣い ↓ の  dual-curve を求めて下さい; 27 X^4+616 X^3 Y+5232 X^2 Y^2-24 X^2 Y Z+19200 X Y^3-1056 X Y^2 Z-384 X Y Z^2+25600 Y^4-3840 Y^3 Z-1104 Y^2 Z^2+256 Y Z^3=0    獲た dual-curve を 非斉次化し   其の二重接線を 多様な発想で 求めてください;    二重接線は 高校数学で 履修済で もう卒業             と 云えますか ?

374995200015360000 x^24-2330452285009920000 y x^23+14706112899870720000 y^2 x^22+470203124428800000 x^22-52258509967656960000 y^3 x^21-3163335161057280000 y x^21+174520127252528640000 y^4 x^20-1417765645992960000 y^2 x^20+162942172560000000 x^20-447528306957456384000 y^5 x^19+17583115926435840000 y^3 x^19+1889719039468800000 y x^19+1054434307134868070400 y^6 x^18-78807100678606080000 y^4 x^18-10263758699859840000 y^2 x^18-6262197480000000 x^18-2195277891748568985600 y^7 x^17+171076572121593600000 y^5 x^17+29777939990415360000 y^3 x^17-563690729448000000 y x^17+3941341177035964838400 y^8 x^16-132514330351784832000 y^6 x^16-34734559215127680000 y^4 x^16-2872057858797600000 y^2 x^16+94569752448000000 x^16-6281105450287077273600 y^9 x^15-631116097338547814400 y^7 x^15+95857207014458880000 y^5 x^15+21369588682590720000 y^3 x^15-368383209984000000 y x^15+9360839525741703014400 y^10 x^14+2438205872374071360000 y^8 x^14-373219181707144320000 y^6 x^14-56029780685102400000 y^4 x^14+1166228922816000000 y^2 x^14-13979284560000000 x^14-12235622988408506081280 y^11 x^13-4873425379626404620800 y^9 x^13+846251127697746816000 y^7 x^13+59883533859441600000 y^5 x^13-1237124178777600000 y^3 x^13-183863907504000000 y x^13+13966311676564199476224 y^12 x^12+8028003034871111635200 y^10 x^12-1010445310781451043200 y^8 x^12+8846187265317600000 y^6 x^12+4703986859091840000 y^4 x^12+1010823045336000000 y^2 x^12+4111426392000000 x^12-15160077318017469763584 y^13 x^11-11339064033107783731200 y^11 x^11+354299507319919507200 y^9 x^11-190549958875309440000 y^7 x^11-17318230671479040000 y^5 x^11-2666654024832000000 y^3 x^11-3805816752000000 y x^11+16501423591073184293376 y^14 x^10+13600833595761606480000 y^12 x^10+1298911168379548944000 y^10 x^10+366130954320288696000 y^8 x^10+42043437053354880000 y^6 x^10+3955240641396000000 y^4 x^10+69485620248000000 y^2 x^10-3010467060000000 x^10-16241962151319001320960 y^15 x^9-12607135791724232668800 y^13 x^9-2899565767895088672000 y^11 x^9-351834659514751406400 y^9 x^9-69687083298412800000 y^7 x^9-4066867565529120000 y^5 x^9-116376836400000000 y^3 x^9+12156544476000000 y x^9+13777466841024303526560 y^16 x^8+7664015923228037102400 y^14 x^8+3430781516408675572800 y^12 x^8+109598819100462568800 y^10 x^8+87546296495956320000 y^8 x^8-682987728558960000 y^6 x^8+177384645108000000 y^4 x^8-34872207642000000 y^2 x^8+313680600000000 x^8-10657160260072644726144 y^17 x^7-1095825281028159052800 y^15 x^7-2970293020011359424000 y^13 x^7+271103825197281542400 y^11 x^7-77734385811054720000 y^9 x^7+7423918069201920000 y^7 x^7-172033671744000000 y^5 x^7+64146011184000000 y^3 x^7+423381600000000 y x^7+8291924161161688929024 y^18 x^6-3003745910286579876000 y^16 x^6+2060718673721004014400 y^14 x^6-484384676849735032800 y^12 x^6+61222082726772000000 y^10 x^6-13922436829708440000 y^8 x^6+180170600148000000 y^6 x^6-107645370498000000 y^4 x^6+530928000000000 y^2 x^6-24245500000000 x^6-6065897996086739591616 y^19 x^5+3656939332862094602400 y^17 x^5-1466297923714856193600 y^15 x^5+447964877186812893600 y^13 x^5-43994931342806880000 y^11 x^5+15305046962756760000 y^9 x^5-310972416084000000 y^7 x^5+114689004030000000 y^5 x^5-887067600000000 y^3 x^5-24311700000000 y x^5+3710431995991229195280 y^20 x^4-2685307848813071103600 y^18 x^4+1064711773649645734500 y^16 x^4-275389107443806474800 y^14 x^4+36674455822160040000 y^12 x^4-10650451002918540000 y^10 x^4+521355902710500000 y^8 x^4-117242344053000000 y^6 x^4+4743331900000000 y^4 x^4-62415750000000 y^2 x^4+13348125000000 x^4-1711356263752551435360 y^21 x^3+1473948369858595752000 y^19 x^3-584852649206134901400 y^17 x^3+109270847328667041600 y^15 x^3-28192110105713040000 y^13 x^3+5659479619980480000 y^11 x^3-586100867715000000 y^9 x^3+66726895716000000 y^7 x^3-6968178600000000 y^5 x^3+109872000000000 y^3 x^3-16908750000000 y x^3+574392004323313559616 y^22 x^2-594943128667495040400 y^20 x^2+212530497906325605300 y^18 x^2-48068200350130509450 y^16 x^2+14293117053302760000 y^14 x^2-1660152275230410000 y^12 x^2+488279444548500000 y^10 x^2-42509287275750000 y^8 x^2+7093353600000000 y^6 x^2-214924125000000 y^4 x^2+39740625000000 y^2 x^2-1139062500000 x^2-124154622565330008816 y^23 x+142650179779795300800 y^21 x-60594718845951450000 y^19 x+19317470768422284150 y^17 x-4083134280370560000 y^15 x+927812197248570000 y^13 x-208955660310000000 y^11 x+10104115871250000 y^9 x-4945144500000000 y^7 x+206858925000000 y^5 x-19642500000000 y^3 x+683437500000 y x+15762192873166337814 y^24-10243688070825518400 y^22+9848263255663564800 y^20-3020412127794986925 y^18+911914184092410000 y^16-277113259058805000 y^14+43898895015000000 y^12-8077921414875000 y^10+1668918937500000 y^8-88051112500000 y^6+22207500000000 y^4-1480781250000 y^2=0 低次とは云い難い 上の曲線 c の 特異点達を求め        其の名も明記願います; 双対曲線 c^★を 求め 其の二重接線達を求め        図示をも願います; https://context.reverso.net/%E7%BF%BB%E8%A8%B3/%E6%97%A5%E6%9C%AC%E8%AA%9E-%E8%8B%B1%E8%AA%9E/%E8%A8%80%E3%81%84%E9%9B%A3%E3%81%84 https://context.reverso.net/%E7%BF%BB%E8%A8%B3/%E6%97%A5%E6%9C%AC%E8%AA%9E-%E8%8B%B1%E8%AA%9E/%E4%BA%91%E3%81%84%E9%9B%A3%E3%81%84

c;768 x^3-384 x^2 y^2+960 x^2 y+360 x^2-384 x y^3+704 x y^2+360 x y-480 x-256 y^4+128 y^3+480 y^2-120 y-225=0   の 双対曲線 c^★ を多様な発想で 求めて下さい; c の common-tangent を多様な発想で 求めて下さい; https://mathoverflow.net/questions/110842/how-to-find-the-global-equation-of-a-dual-curve https://math.stackexchange.com/questions/662768/degree-of-the-dual-curve-to-xy2-z3 c^★ の common-tangent を多様な発想で 求めて下さい; c の common-tangent を多様な発想で 求めて下さい;   ●●「● 其の際 ↓達を味読し 模倣をも願います; https://math.stackexchange.com/questions/3436714/algorithm-to-find-common-tangent-to-any-two-conics https://math.stackexchange.com/questions/2428815/the-common-tangent-of-two-tilted-parabolas?rq=1 https://math.stackexchange.com/questions/1188704/equation-of-common-tangents-to-two-parabolas https://www.yu-hanami.com/entry/2019/05/22/170200

虚飾、捏造、歪曲されない真実を 後世に伝えて下さい

https://arxiv.org/pdf/2002.05681.pdf    に  双対を  論じている。        28 rational bitangent にも言及。          味読し        『思いの丈』を 激白し 虚飾、捏造、歪曲されない真実を 後世に伝えて下さい https://nrid.nii.ac.jp/nrid/1000000011627/ http://www.math.sci.hiroshima-u.ac.jp/branched/files/2016/shioda_j.pdf

https://math.stackexchange.com/questions/662768/degree-of-the-dual-curve-to-xy2-z3 を 味読し これに倣い ↓のdual-curve を求めて下さい; 16875 X^4+16000 X^3 Y+3300 X^2 Y^2+3750 X^2 Y Z+43140 X Y^3-142500 X Y^2 Z+120000 X Y Z^2+49232 Y^4-221700 Y^3 Z+328875 Y^2 Z^2-160000 Y Z^3=0    獲た dual-curve   を 非斉次化し   其の二重接線を 多様な発想で 求めてください; 二重接線は 高校数学で 履修済で もう卒業         と 云えますか ?

>Google、円周率計算31兆桁達成 世界記録更新 https://www.bbc.com/japanese/47552083 https://www.google.com/search?client=firefox-b-d&q=%E5%86%86%E5%91%A8%E7%8E%8762%E5%85%868000%E5%84%84%E6%A1%81%E8%A8%88%E7%AE%97%E3%80%81%E4%B8%96%E7%95%8C%E8%A8%98%E9%8C%B2%E6%9B%B4%E6%96%B0+%E3%82%B9%E3%82%A4%E3%82%B9%E7%A0%94%E7%A9%B6%E3%83%81%E3%83%BC%E3%83%A0 https://www.wakuwaku-catch.net/kouen201102/