分数与小时或分割时间
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①本范例演示如何使用 GeoGebra 将时间分割成不同分数部分并可视化;②涉及核心数学概念包括分数运算、时间表示、几何图形(如圆、向量)的构造;③作图要点:运用了 Circle(圆)、Segment(线段)、Sequence(序列)、Rotate(旋转)、Vector(向量)等命令;④适合初中及以上学生学习分数、时间计算及几何作图。
GeoGebra 命令及参数
Circle(A, 1) → cElement(diviseurs60, b) → denominateurSegment(A, B) → dSequence(Segment[Rotate[A, (360° * i / denominateur), A], Rotate[E, (360° * i / denominateur), A]], i, 0, denominateur - 1) → listseg3, {0.8, 0.8, 0.8, 0.7999999999999998, 0.7999999999999999, 0.8000000000000003, 0.8, 0.8000000000000002, 0.8000000000000002, 0.8, 0.8, 0.8000000000000002, 0.8000000000000002, 0.8000000000000003, 0.8}Circle(A, E) → eRotate(E, (-360° * numerateur / denominateur), A) → E'CircleSector(A, E, E') → fRotate(F, (-360° * numerateur / denominateur), A) → F'Vector(A, F') → uCircle(A, E) → gCircle(A, B) → hElement(diviseur60_1, b) → denominateur_1Sequence(Text[(5 * i), Rotate[A, (-30° * i), I]], i, 1, 12) → lista4, {"5", "10", "15", "20", "25", "30", "35", "40", "45", "50", "55", "60"}Sequence(Rotate[B, (-i), A], i, 0, 6.28319, 0.5236) → liste1, {(2.1628706740563666, 2.104223490616733), (2.662871734418969, 1.9702482821996723), (3.0288973022399097, 1.6042213698892789), (3.1628706740496204, 1.10421981741163), (3.0288936290270168, 0.6042192491708196), (2.6628653722321087, 0.23819502584427066), (2.1628633276461597, 0.10422349064371805), (1.6628632515338881, 0.23820237227005703), (1.2968403727066695, 0.6042319735445402), (1.1628706741170824, 1.1042345102320428), (1.2968513923453489, 1.6042340942090298), (1.6628823380944695, 1.97025562853198), (2.1628853668767793, 2.1042234905087938)}Sequence(Rotate[B - (0, 0.2), (-i), A], i, 0, 6.28319, 0.5236) → liste2, {(2.1628706740563666, 1.9042234906167332), (2.562871522346449, 1.7970433238830843), (2.855691976603201, 1.5042217940347697), (2.9628706740509694, 1.1042205520526507), (2.8556890380328865, 0.7042200974600024), (2.5628664325969606, 0.41140071879876317), (2.162864796928201, 0.304223490638321), (1.7628647360383838, 0.4114065959393922), (1.470046432976609, 0.7042302769589788), (1.3628706741049395, 1.104232306308981), (1.4700552486875522, 1.5042319734905705), (1.7628800052868487, 1.7970492009489307), (2.162882428312697, 1.9042234905303816)}Sequence(Rotate[B - (0, 0.3), (-i), A], i, 0, 6.28319, 0.5236) → liste2b, {(2.1628706740563666, 1.8042234906167331), (2.5128714163101886, 1.7104408447247903), (2.7690893137848467, 1.454222006107515), (2.8628706740516443, 1.104220919373161), (2.7690867425358214, 0.7542205216045936), (2.5128669627793863, 0.4980035652760094), (2.162865531569222, 0.4042234906356227), (1.8128654782906315, 0.4980087077740599), (1.5566494631115786, 0.7542294286661981), (1.462870674098868, 1.10423120434745), (1.5566571768586541, 1.454230913131341), (1.8128788388830386, 1.710445987157406), (2.1628809590306557, 1.8042234905411756)}Sequence(Segment[Element[liste1, i], Element[liste2, i]], i, 1, Length[liste1]) → listseg2, {0.19999999999999996, 0.19999999999999993, 0.1999999999999999, 0.20000000000000026, 0.2000000000000002, 0.19999999999999984, 0.1999999999999999, 0.19999999999999996, 0.20000000000000007, 0.20000000000000018, 0.19999999999999987, 0.19999999999999993, 0.2}Sequence(Rotate[B, (-i), A], i, 0, 6.28319, 0.10472) → list60a, {(2.1628706740563666, 2.104223490616733), (2.267399380862877, 2.098745360388011), (2.3707828439323353, 2.0823709895234503), (2.4718883671163603, 2.05527977989507), (2.5696082119692614, 2.0177685498516658), (2.662871734418969, 1.9702482821996723), (2.750657115022346, 1.9132396213684921), (2.832002554285146, 1.8473671690945217), (2.9060168103877793, 1.7733526411218459), (2.9718889638628223, 1.6920069598965672), (3.0288973022399097, 1.6042213698892787), (3.0764172273155364, 1.5109576728885106), (3.1139280984136546, 1.4132376902498271), (3.1410189366605286, 1.3121320675549146), (3.157392927776314, 1.2087485443397312), (3.1628706740496204, 1.10421981741163), (3.157392159865556, 0.9996911307281208), (3.1410174092524414, 0.8963077278057825), (3.1139258282429205, 0.795202304134009), (3.0764142392547362, 0.6974825970682089), (3.0288936290270168, 0.6042192491708199), (2.9718846457425134, 0.5164340779725393), (2.906011894670505, 0.4350888806733165), (2.831997094828785, 0.3610748964417242), (2.7506511716421254, 0.2952030417664968), (2.6628653722321096, 0.2381950258442711), (2.5696015006815394, 0.19067544334565312), (2.471881380258392, 0.15316493119332653), (2.3707756580539567, 0.1260744643283246), (2.2673920746944427, 0.10970085296153398), (2.162863327646161, 0.10422349064371805), (2.058334661087063, 0.10970238878305083), (1.95495131831324, 0.12607751914449783), (1.8538459941550824, 0.15316947153479443), (1.7561264248777015, 0.19068141946725192), (1.6628632515338895, 0.23820237227005614), (1.5750782897418893, 0.2952116780071138), (1.4937333344073407, 0.36108472787627144), (1.4197196220477881, 0.4350997995860365), (1.353848066173265, 0.5164459647329807), (1.29684037270667, 0.6042319735445394), (1.2493211327857012, 0.6974960196436539), (1.2118109795796728, 0.795216277849947), (1.1847208840969083, 0.896322099562542), (1.1683476524793341, 0.9997057430649917), (1.1628706741170824, 1.1042345102320437), (1.16834995621161, 1.2087631566653203), (1.184725466321169, 1.3121464392892341), (1.211817790091876, 1.4132516639324124), (1.2493300969681016, 1.5109710954200557), (1.2968513923453502, 1.604234094209032), (1.3538610205341934, 1.6920188465935675), (1.4197343691996125, 1.7733635599623443), (1.4937497127764248, 1.8473770004488586), (1.5750961198825557, 1.9132482575217877), (1.6628823380944733, 1.9702556285319823), (1.7561465587408733, 2.0177745258746596), (1.8538669547289937, 2.0552843201338833), (1.9549728759483838, 2.0823740442340446), (2.058356579592374, 2.0987468961021807)}Sequence(Rotate[B - (0, 0.075), (-i), A], i, 0, 6.28319, 0.10472) → list60, {(2.1628706740563666, 2.029223490616733), (2.259559727852389, 2.024156220155165), (2.3551894311916377, 2.0090099271054465), (2.448712040136861, 1.9839505581991945), (2.5391028966257942, 1.9492526704090456), (2.625371654891774, 1.9052964228309515), (2.706573131949898, 1.85256341156211), (2.7818176632679874, 1.7916313932086876), (2.850280850162923, 1.7231679548339622), (2.911212592127338, 1.6479231997005797), (2.9639453051261437, 1.5667215289438376), (3.007901235821098, 1.4804526092181272), (3.0425987915868578, 1.390061625277345), (3.067657816965216, 1.296538924284551), (3.082803758747318, 1.2009091653105064), (3.087870674050126, 1.1042200929020127), (3.0828030484298665, 1.0075310577197667), (3.0676564041127357, 0.9119014100166037), (3.042596691678929, 0.8183788931202134), (3.0078984718648583, 0.7279881640843483), (2.9639419074042177, 0.6417195672792635), (2.911208597866052, 0.5605182839208539), (2.8502763031244447, 0.4852739764190729), (2.7818126132708536, 0.41681104100485), (2.7065676343231932, 0.3558795754302647), (2.625365769868929, 0.30314716070220593), (2.5390966886846513, 0.25919154689098434), (2.4487055772932402, 0.22449432315008222), (2.3551827842541373, 0.1994356412999554), (2.259552969646587, 0.18429005078567406), (2.1628638786269265, 0.1792234906416944), (2.066174862059761, 0.18429147142057722), (1.9705452699939745, 0.19943846700491563), (1.8770228451476787, 0.22449852296593997), (1.7866322435661015, 0.2591970748034632), (1.7003638082230754, 0.3031539561460571), (1.6191627185654753, 0.3558875639528354), (1.5439186348810179, 0.41682013508180615), (1.4754559509484317, 0.4852840764133389), (1.4145247617644978, 0.5605292791742622), (1.3617926453078975, 0.641731337324954), (1.3178373483810013, 0.7280005799666349), (1.283140456665425, 0.818391818807456), (1.258082118343868, 0.9119147038916064), (1.2429368790976119, 1.0075445741313724), (1.237870674112529, 1.1042336837608955), (1.2429390100499669, 1.2009226817116763), (1.258086356901309, 1.2965522181387965), (1.283146756389213, 1.3900745509337362), (1.3178456402497216, 1.4804650250598064), (1.3618028384736767, 1.5667332989396097), (1.4145367445483565, 1.6479341948953048), (1.4754695920638692, 1.7231780547614235), (1.5439337848724204, 1.7916404872114489), (1.6191792114455916, 1.8525714000039086), (1.7003814632916154, 1.9053032181883385), (1.7866508673895354, 1.9492581982303152), (1.8770422336785466, 1.9839547579200971), (1.9705652108064824, 2.0090127527127457), (2.0661951366771736, 2.0241576406907718)}Sequence(Segment[Element[list60a, i], Element[list60, i]], i, 1, Length[list60]) → listseg1, {0.07500000000000018, 0.07500000000000037, 0.07500000000000008, 0.07500000000000008, 0.07500000000000022, 0.07500000000000032, 0.07500000000000022, 0.07500000000000002, 0.07500000000000046, 0.07499999999999997, 0.07500000000000026, 0.0750000000000005, 0.07500000000000026, 0.0750000000000004, 0.07500000000000007, 0.07500000000000032, 0.07500000000000037, 0.07500000000000014, 0.07500000000000012, 0.07500000000000023, 0.07500000000000029, 0.07500000000000037, 0.07500000000000012, 0.07500000000000019, 0.07500000000000027, 0.0750000000000001, 0.07500000000000022, 0.07500000000000018, 0.0750000000000002, 0.07500000000000016, 0.07500000000000022, 0.07500000000000022, 0.07500000000000014, 0.07500000000000011, 0.0750000000000002, 0.07500000000000026, 0.07500000000000022, 0.07500000000000023, 0.07500000000000029, 0.0750000000000002, 0.07500000000000026, 0.07500000000000018, 0.0750000000000002, 0.07500000000000026, 0.07500000000000029, 0.07500000000000018, 0.07500000000000015, 0.07500000000000015, 0.07500000000000016, 0.07500000000000019, 0.07500000000000022, 0.07500000000000016, 0.07500000000000008, 0.07500000000000022, 0.07500000000000007, 0.07500000000000023, 0.07499999999999989, 0.0749999999999999, 0.07500000000000052, 0.0750000000000004}Sequence(Text[i, Element[liste2b, i + 1] - (0.065, 0.025)], i, 1, Length[liste2b] - 1) → liste3, {"1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12"}Circle(A, r + 0.02) → pCircle(A, r + 0.175) → qCircle(A, r + 0.255) → sCircle(A, r + 0.04) → kCircle(A, r + 0.05) → c_1Circle(A, r + 0.195) → tGCD(denominateur, numerateur) → aVector(A, F) → w
AI 绘图提示语参考
画一个圆,然后在这个圆上等分地画出60个扇形,每个扇形代表1分钟。接着,将圆分成若干个部分,每个部分代表1/2、1/3、1/4、1/5、1/6、1/10、1/12、1/15、1/20、1/30和1/60。每个部分用不同的颜色表示,并且在每个扇形的中心标注数字1到12。最后,画出一个稍大一些的同心圆,以及一个更大的同心圆,分别代表1/2和1/3的时间段。
以上提示语为根据原始绘图命令整理而来,仅供参考。