HU''''aNG DAN QUAN LI SU''''DUNG KHAM PHA DirCfNG CYCLOID VA HYPOCYCLOID V6l SIT TRO GIUP CUA PHAN MEM CABRI Dudng cycloid la dudng cong lien tuc dugc ve bdi mdt diem ndm ttdn dudng ttdn khi dudng ttdn lan[.]
HU'aNG DAN QUAN LI SU'DUNG KHAM PHA DirCfNG CYCLOID VA HYPOCYCLOID V6l SIT TRO GIUP CUA PHAN MEM CABRI Nguyen Ng^c Giang Dudng cycloid la dudng cong lien tuc dugc ve bdi mdt diem ndm ttdn dudng ttdn dudng ttdn lan dpc theo mpt dudng thang ttong cung mpt mat phang Cung gidng nhu dudng cycloid, mdt dudng ttdn Im ben ttong mdt dudng frdn cd dinh, quy tich cua mdt diem fren dudng ttdn lan dugc gpi la dudng hypocycloid Dudng cong cycloid a Ca sa todn cua duong cong cycloid Gia su rang dudng ttdn cd ban kinh a vd lan tten true Ox, bat dau tir vi tri md tam ciia hinh ttdn ddt tten tryc duong cua true Oy Duong cong Id quy tich cua diem P fren dudng ttdn tning vdi gde tpa tam C cua dudng frdn C nam fren true Oy Gde frong hinh ve la gde tao bdi ban kinh CP dudng frdn lan tdi vi tri radi Ndu x, y la tpa dp ciia P thi qud trinh lan cua dudng ttdn keo theo OB = arcBP aO, dd x = OB - OA = OB - PQ a9 - asinO = a(e - sinG) y = BC - QC = a - acosO ^ a(l - cos6) Vi vgy phuang trinh tham sd cua dudng cycloid la f x - a ( e - s i n e ) /QJ-, ly = a ( l - c o s e ) ^ -* Rd rdng frong hinh ve, y la ham sd cua x nhung rat khd cd the tim mdt cdng thiic don gian de cd ham sd Dudng cycloid Id rapt cac dudng cong raa phuang trinh tham sd don gidn vd de dang ldm viec ban phuang trinh tpa dp Dd-cac Tir phucmg frinh (1) chiing taco , _ dy _ asined6 _ sm9 ^ ~ dx ~ a(l - cose)de ~ - cosB Nhdn xet rang dao ham y ' khdng xdc dinh tai Lay diera A cd hoanh dp dm tren tryc hodnh Lay diera B Id diem ddi xiing ciia diem A qua goc toa ddO Ndi AB Lay diera T tren doan AB Ggi hoanh dp cua diem T i a t Khi T chuyen ddng thi gia trj tham sd t thay ddi • Tinh cdc gid tri x =f(t) vd y^g(t) Su dung niit lenh "Mdy tinh " de tinh cdc gid trj x = f(t) va y = g(t) Keo tha gia tri X, y chuyen vimg lam viec • Dung diem H co hodnh dox^f(t) tren true hodnh Sir dyng mit lenh "Chuyen sd do" —»• True O x ^ gid tti X = f(t) ta dupc diem mdi H fren true hodnh, dat ten la H (hodnh dd cua H chinh Id gia tri X = f(tj) • Dung diem K co hodnh dgy - g(t) tren true tung Sir dyng mit lfnh "Chuyen sd do" —> True Oy —> gia tri y = g(t) ta dugc diem mdi K tten tryc hodnh, dat ten Id K (tung dp ciia K chinh la gid tri y = g(t)) = 0,±27:,±4ji, Nhiing gia tri cua tuang iing vdi cdc diera tai dd dudng cycloid tiep xiic vdi Ox, cac diem dugc gpi Id diem liii Cac tiep tuyen ddi vdi ducmg cycloid thi vudng gde tai diem liii b.Ve duang cong cycloid tren phdn mem Cabri Ta dyng dd thi ham so cho bdi phuang trinh tham sd X - i(t) tj-gjj phan mem y = g(t) X = f(t) Cabri nhu sau • DungSemM(x;y):\ y = g(t) • Cdch tgo gid tri ciia tham so t Dudng vudng goc vdi Ox Hifn hf tryc vudng gde tai H va dudng vudng goc vdi Oxy Oy tai K cat tai M Ndi MH, M K ' • An di cdc doi tugng khong cdn thiit • Ve thi Tao vet cho diem M chuyen ddng diem T ta thu dupc vet ciia diem M Mudn cd thi ta sir dung mit Ngdy nhdn hdi 15/12/2012: Nea- TiDkP CHI THIET BI GIAO DUC-SO 91-03/2013 • 29 HUONG DAN QUAN LI SUDUNG lfnh Quy tich click vdo dilm M sau dd click vao diem T Ap dyng phuong phdp ndy cho ve dudng cong cycloid cd phuang trinh tham so j X = a(t - sin t) l y = a(l - c o s t ) ta dugc thi hen phan dudng cong hypocycloid N l u mpt dudng frdn ldn ben frong mpt dudng ttdn co djnh, quy tich cua mpt diem trdn dudng ttdn lan dugc gpi Id dudng hypocycloid Neu mpt dudng ttdn lan ben ngodi mpt dudng frdn CO djnh, quy tich cua mpt dudng ttdn nhp lan n ldn frong dudng ttdn cd djnh Phucmg trinh fliam s6 cda dudng hypocycloid cd dilm lui cd the viet dudi dang rat dem gidn nhd su dung cdc d|ic tinh lugng gidc Neu a = 4b thi phuong trinh (3) ttd thdnh X = 3bcos9 + bcos39, y = 3bsine - bsinSe Nhung cos39 = 4cos^9 - cos9 raera Cabri nhu hinh ve Dudng cong cycloid nhu da nghien cdu d fren dugc Galileo phdt hifn lan dau tien vao dau the ki 16 Tuy Galileo phat hifn dau tien nhtmg dng khdrig khdra phd them dugc gi vd nhiing tinh chat ciia nd Ong ben nhd cac ban be nghien ciiu ttong cd Merserme d Paris Merserme thdng tui cho Descartes va nhiing ngudi khac vdo nam 1638 Nhiing ket qua dupc tim thay xuat hifn khdng lau sau Descartes da tim thay sy kien thidt cho tiep tuyen Nam 1644, hgc ttd ciia Galileo Id ToriceUi cdng bd phdt hifn cua dng ve dien tich gidi han cua mdt cung Dp dai ciia mpt cung dugc nha kien true su ngudi Anh Christopher Wren phdt hien nam 1658 Duomg cong hypocycloid a Ca sa todn eua duang cong hypocycloid Bdy gid ta se kham phd 30 diem fren dudng trdn lan dugc gpi la epicycloid Chiing ta chi cdch bidu dien tham sd dudng hypocycloid Cho dudng frdn cd dinh cd ban kinh a va mdt dudng frdn lan ban kinh b vdi b < a Gia thiet tdm ciia dudng frdn cd dinh tning vdi gde tga dp (hinh ye) va dudng ttdn lan be hon bat dau chuyen ddng tai vi tri tiep xiic vdi dudng ttdn cd dinh tai A theo true duong ciia Ox Vdi ^ dugc chi frong hinh ve, qua trinh lan cua dudng ttdn nhd keo theo cung AB va cung BP Id bang : a9 = b p Tpa cua PId X - (a - b) cos9 + bcos9 (p - 9) x - ( a - b ) s i n + bcose((i)-9) Nhtmg p - = ^ - ^ nen phuang trinh tham sd ciia dudng hypocycloid la x = ( a - b)cose+ bcos a-b„ (3) a- b b Dp ddi cua cung dgc theo dudng frdn cd djnh giiia cdc diem liii ke tiep cua dudng hypocycloid la 27cb Neu 2jia la mpt bpi nguyen ciia 2jrb thi ãĐ-ld mpt sd nguyen n thi dudng hypocycloid cd n diem lui vd diem P quay lai diem A sau sin39 = 3sine - 4sin'e Vi vgy phuang trinh tham so Id: X = 4bcos^9 = acos^9, y = 4bsine = asin'9(4) Chuyen phuong trinh ndy sang tpa dp Dd-cdc tuong img Id x' + y* = a' Duong hypocycloid vdi diem liti thudng dugc gpi Id dudng asttoid b Ve duang cong astroid tren phdn mem Cabri Ta ye dudng asttoid tten phdn mem Cabri nhu sau: Dyng dogn thang cd dp dai a Dyng dudng trdn ( ; a) Hifn hf tryc vudng goc Oxy Dyng diem A ttdn Ox Dyng diem B ddi ximg vdi A qua O vd ndi AB Dyng dilm T(t ; 0) tren AB DyngdlniM(acos^asitft) Tgo vdt cho dilm M, chuyen dpng diera T ta thu dugc vet cua diem M la ducmg asttoid y = (a - b)sin9 - bsin • TAP CHI THIFT BI GIAO DUC - SO 91 - 03/2013 Xem tiep trang 33 HUONG DAN QUAN LI SU DUNG Cac nhdm lan lugt bao cao ket qud thi nghifm qua SDTD, GV tdng kit thdng qua SDTD da thiet kl sin Ien man chilu Kit lu^n GV su dyng SDTD day hpc se cung cap cho HS cd cai nhin tdng quat vl vdn dl dang hgc t£^ Thdng qua SDTD cdc em ty thilt kd cd the danh gid dugc iniic dp ty hoc tap, mure dp hieu biet va nam b^t van de d mdc dp nao, GV cd die nhanh chdng dieu chinh cho phu hgp Ngoai vifc diilt ke SDTD cho cac bai 1hi^ hanh, GV cdn cd the thilt ke cac Mi luyfn t ^ GV cd the hirdng ddn HS 1^ SDTD eho bai mdi, ghi chep kien ihiic tren ldp, dn tap thi cir, ^ ke hoach ca n h ^ minh hga cac y tirdng cua ca nhan Sii dung SDTD ttong day hgc that Tony Buzan, Sa tu sy la ddi mdi phuong p h ^ day duy, NXB Tong hgp TP Hd Chi hgc, gdp phan nang cao hifu Minh, 2008 qud dgy hgc hda hgc ndi rieng va cac mdn hgc khac, gdp phan Summary nang cao nang lyc nhan thiic IMindMap huge role in cuaHS teaching chemistry, especially the exercises IMindMap in teaching chemistry to Tdi lifu tham khao Tran Dinh Chau, Dgng help lectures become more Thi Thu Thiiy Dgy lot - hgc intuitive, more scientific and tot cdc mdn hgc bdng bdn tu logic Instmctional practices duy, NXB Giao dye Vift Nam, to help students IMindMap to maximize the ability to think, 2011 Nguyen Xudn Trudng, to create, and stimulate the tdng chil bien, Sdch gido khoa imagination, inspire students Hoa hgc II, NXB Gido due to bring positive results in teaching chemistry In this 2007 PGS.TS Nguyin Thj Sim article we introduce you how to (Chu bien), TS Le Van Nam, build and use IMindMap from Phuang phdp dgy hgc hoa hgc, advanced exercise class taught NXB Khoa hoc va ky thuat, organic chemistry 11 2009 KHAM PHA DirdNG CYCLOID , Mpt s6 tinh chdt cua dvdng cycloid \k astroid Vi dv ^ Chi rang difn tich xdc dinh bdi mdt cung ciia dudng cycloid bang ba ldn difn tich cua dudng ttdn lan That vdy, mpt cung dugc xdc dinh dudng ttdn chuyen dpng dung mpt vdng trdn xoay Vi vgy sit dung tich phdn tinh dif n tich vdi tham sd la tham sd bifn lay tich phdn A=Jydx = J y | i = Ja(l-cos6) aO - cosewe = J a^a - cose)^de = a^ J a - 2cose + cos^ e)de 2Jt 1= = a^JO + cos^e>de = a^J"d6 + ° ° a^ J - (1 + cos 2e)de ^ 3jta^ Vi du Xet dudng thang tiep xuc vdi dudng asttoid tgi diem P ttong gde phan tu thii nhat Chi rang dogn thang dugc tgo bdi tiep tuyen cat bdi cdc true tga dp cd dp ddi khdng ddi, khdng phy thupc vao vi tri cua P That vdy, tu phuang trinh x = acos^G, y = asin^9, hf so gde cua tilp tuyen Id (liep trang 30) bdi cac tryc tga cd dp ddi la V^cos^ + a^sin^ ^ a la hang sd Tren day la mdt sd khdm phd xoay quanh cdc dudng cycloid vd hypocycloid Bdi viet ndy can trao ddi gi thera? Mong dugc su chia se ciia cdc ban Tai lifu tham khao George F Simmons, Gidi tich mgt bien so, Gido y' = -i- = = - tan6 trinh trudng Dai hpc Thiiy lpi Phgm Thanh Phuong, dx -3asinecos^ede Nen phuomg trinh ciia tilp Dgy vd hgc todn vai phdn mem Cabri, tdpl Hinh hoc tuyin Id y - asin^G = -tan9(xphang, NXBGD, 2006 acos^O) Summary Chiing ta tun giao vdi ttyc This article will explore Ox bdng each cho y = vatimX to the cycloid, hypocycloid x = acos'6 + asm^ecos9 = acos9 and some their Tuong ty, giao vditi-ycOy curves Id y = asinG Vi vay dogn tiidng properties by the aid of Cabri dugc tgo bdi tiep tuyen cat interactive software TAP CHI THIET BI GIAO DUC-SO 91-03/2013 • 3 ... Duomg cong hypocycloid a Ca sa todn eua duang cong hypocycloid Bdy gid ta se kham phd 30 diem fren dudng trdn lan dugc gpi la epicycloid Chiing ta chi cdch bidu dien tham sd dudng hypocycloid Cho... Id dudng hypocycloid Neu mpt dudng ttdn lan ben ngodi mpt dudng frdn CO djnh, quy tich cua mpt dudng ttdn nhp lan n ldn frong dudng ttdn cd djnh Phucmg trinh fliam s6 cda dudng hypocycloid cd... trinh tham sd ciia dudng hypocycloid la x = ( a - b)cose+ bcos a-b„ (3) a- b b Dp ddi cua cung dgc theo dudng frdn cd djnh giiia cdc diem liii ke tiep cua dudng hypocycloid la 27cb Neu 2jia la