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Fraction Clock

Fraction Clock
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2021-12-17 00:43
CircleAngleGeometric Construction
This example demonstrates the construction of a fraction clock. It involves core mathematical concepts such as fractions and angles. Using GeoGebra commands like Circle, Element, Segment, Sequence, etc., it dynamically shows the fraction value at each clock mark. Suitable for students at the junior high school level and above to learn about fractions and angles.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Element(diviseurs60, b) → denominateur
  3. Segment(A, B) → d
  4. Sequence(Segment[Rotate[A, (360° * i / denominateur), A], Rotate[E, (360° * i / denominateur), A]], i, 0, denominateur - 1) → listseg3, {0.6000000000000001, 0.6000000000000002, 0.6000000000000002, 0.6000000000000001, 0.6, 0.6, 0.6000000000000002, 0.6, 0.6, 0.6000000000000002, 0.6, 0.6000000000000001, 0.6000000000000001, 0.6000000000000002, 0.6000000000000002, 0.6000000000000001, 0.6000000000000002, 0.6000000000000002, 0.6000000000000001, 0.6, 0.6, 0.6000000000000002, 0.6, 0.6, 0.6000000000000001, 0.6, 0.6000000000000001, 0.6, 0.6000000000000001, 0.6000000000000001, 0.6000000000000001, 0.6000000000000001, 0.6000000000000001, 0.6000000000000001, 0.6000000000000002, 0.6000000000000002, 0.6000000000000002, 0.6000000000000002, 0.6, 0.6000000000000002, 0.6, 0.6, 0.6000000000000001, 0.6000000000000002, 0.6000000000000003, 0.6000000000000001, 0.6000000000000002, 0.6000000000000002, 0.6000000000000001, 0.6000000000000003, 0.6000000000000003, 0.6000000000000002, 0.6, 0.6, 0.6000000000000001, 0.6, 0.6, 0.6000000000000001, 0.6000000000000002, 0.6000000000000003}
  5. Circle(A, E) → e
  6. Rotate(E, (-360° * numerateur / denominateur), A) → E'
  7. CircleSector(A, E, E') → f
  8. Rotate(F, (-360° * numerateur / denominateur), A) → F'
  9. Vector(A, F') → u
  10. Circle(A, E) → g
  11. Circle(A, B) → h
  12. Element(diviseur60_1, b) → denominateur_1
  13. Sequence(Text[(5 * i), Rotate[A, (-30° * i), I]], i, 1, 12) → lista4, {"5", "10", "15", "20", "25", "30", "35", "40", "45", "50", "55", "60"}
  14. 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)}
  15. Sequence(Rotate[B - (0, 0.05), (-i), A], i, 0, 6.28319, 0.5236) → liste2, {(2.1628706740563666, 2.0542234906167334), (2.6378716814008394, 1.9269470426205255), (2.9855959708307327, 1.5792214759256518), (3.1128706740499577, 1.1042200010718852), (2.985592481278484, 0.6292194612431152), (2.637865637323322, 0.2814964490828936), (2.16286369496667, 0.15422349064236862), (1.6878636226600119, 0.2815034281873907), (1.3401418877741542, 0.6292315493981497), (1.2128706741140465, 1.1042339592512773), (1.3401523564308995, 1.579233564029415), (1.6878817548925642, 1.9269540216362178), (2.162884632235759, 2.054223490514191)}
  16. Sequence(Rotate[B - (0, 0.025), (-i), AA], i, 0, 6.28319, 0.5236) → liste2b, {(2.1628706740563666, 2.0792234906167333), (2.565371527648262, 1.9713734478409992), (2.860022109744119, 1.6767217834311325), (2.967870674050936, 1.274220533686625), (2.86001915280774, 0.8717200762527726), (2.5653664060878394, 0.5770705764749007), (2.1628647601961504, 0.4692234906384558), (1.7603646989257713, 0.5770764903476586), (1.4657162814698603, 0.8717303193736177), (1.3578706741052429, 1.2742323614070574), (1.4657251522789971, 1.6767320265085321), (1.7603800636070392, 1.971379361638507), (2.162882501776799, 2.079223490529842)}
  17. Sequence(Segment[Element[liste1, i], Element[liste2, i]], i, 1, Length[liste1]) → listseg2, {0.04999999999999982, 0.049999999999999684, 0.0499999999999998, 0.050000000000000065, 0.050000000000000024, 0.04999999999999976, 0.04999999999999981, 0.0499999999999998, 0.04999999999999983, 0.04999999999999982, 0.049999999999999746, 0.04999999999999992, 0.04999999999999978}
  18. 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)}
  19. 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)}
  20. 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}
  21. 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"}
  22. Circle(A, r + 0.02) → p
  23. Circle(A, r + 0.175) → q
  24. Circle(A, r + 0.255) → s
  25. Circle(A, r + 0.04) → k
  26. Circle(A, r + 0.05) → c_1
  27. Circle(A, r + 0.195) → t
  28. GCD(denominateur, numerateur) → a
  29. Vector(A, F) → w
  30. Sequence(Text[If[i ≟ 0, "0", If[i ≟ m_{1}, "", "\frac{" + (i / GCD[i, m_{1}]) + ("}{" + (m_{1} / GCD[i, m_{1}]) + "}")]], Element[liste2b, i + 1] - (0.05, 0.015), true, true], i, 1, (2 * m_{1})) → l1, {"\frac{1}{12}", "\frac{1}{6}", "\frac{1}{4}", "\frac{1}{3}", "\frac{5}{12}", "\frac{1}{2}", "\frac{7}{12}", "\frac{2}{3}", "\frac{3}{4}", "\frac{5}{6}", "\frac{11}{12}", "", "", "", "", "", "", "", "", "", "", "", "", ""}
  31. Circle(A, E) → d_1
  32. CircleSector(A, F', E) → e_1
  33. Sequence(Rotate[B - (0, 0.35), (-i), A + (0, 0)], i, 0, 6.28319, 0.5236) → l2, {(2.1628706740563666, 1.754223490616733), (2.4878713632920584, 1.6671396051456435), (2.7257879823756697, 1.4292221121438877), (2.8128706740519815, 1.1042211030334161), (2.725785594787289, 0.7792207336768894), (2.487867227870599, 0.5413049885146326), (2.1628658988897325, 0.4542234906342735), (1.8378658494167555, 0.5413097636913937), (1.5999509781790637, 0.7792290045198078), (1.512870674095832, 1.1042306533666844), (1.5999581409442052, 1.4292303829517259), (1.8378782556811335, 1.6671443802616435), (2.162880224389635, 1.7542234905465723)}
  34. Sequence(Segment[Element[l2, i + 1], Element[l2, Length[l2] - i]], i, 1, Length[l2]) → l3, {0.6499931076284649, 1.1258298414618448, 1.29999999999123, 1.1258346166386057, 0.6500013784713836, 0, 0.6500013784713836, 1.1258346166386057, 1.29999999999123, 1.1258298414618448, 0.6499931076284649, 0.000009550333268473353, NaN}
  35. Segment(K, L) → i

AI Drawing Prompt Reference

Draw a circular “fraction clock” on a plane: use one main circle with a fixed center, mark several equal angle divisions around the circumference, and draw radial segments from the center to these division points to form wedge sectors. Use given integer numerator and denominator to determine how much rotation separates the key rays; construct the corresponding rotated rays and highlight the related circular sector. Add dynamic fraction text at each tick position by placing labels that show the reduced fraction value for that division. Near the circumference, include a thin set of concentric small circles (radius offsets) and short tick-like connections between neighboring points on the rings to create clear layered markings.
The prompt above was compiled from the original drawing commands and is for reference only.