MathPlotAI Logo MathPlotAI

Determine if a Number is a Square Number

Determine if a Number is a Square Number
Loading the math board and drawing, please wait…
2025-11-26 03:46
In collections Quadratzahlen und Quadratwurzeln
This example demonstrates how to determine if a number is a square number through geometric shapes. Key mathematical concepts include sequences and geometric construction. Using GeoGebra commands such as Sequence, Join, and Shuffle, the example dynamically shows the generation process of sequences and changes in geometric shapes. Suitable for middle school and above students to learn about square

GeoGebra Commands & Parameters

  1. Sequence(RandomElement[4…6], k, 1, 100) → NumberOfQ, {6, 5, 5, 5, 5, 6, 4, 5, 6, 5, 4, 5, 6, 4, 4, 4, 6, 6, 4, 4, 6, 4, 5, 4, 6, 4, 5, 5, 5, 4, 5, 4, 6, 6, 5, 4, 4, 5, 5, 6, 5, 6, 5, 5, 5, 6, 6, 6, 4, 4, 6, 5, 4, 6, 4, 5, 5, 4, 6, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4, 6, 5, 6, 4, 5, 5, 5, 4, 6, 5, 6, 4, 6, 4, 4, 4, 6, 5, 6, 6, 6, 5, 5, 5, 6, 5, 6, 4, 5, 6}
  2. Join({Sequence[1, k, 1, NumberOfQ(counter)], Sequence[2, k, 1, 10 - NumberOfQ(counter)]}) → ElementBox
  3. Sequence(ZuteilungListe(k) ≟ ElementBox(k), k, 1, 20) → CorrectList
  4. Shuffle(1…numberOfQuestions) → randomQuestions, {68, 25, 15, 70, 82, 18, 10, 37, 22, 61, 11, 34, 98, 27, 28, 23, 86, 78, 12, 83, 79, 41, 76, 17, 29, 39, 50, 100, 35, 19, 93, 80, 5, 91, 84, 74, 32, 49, 43, 2, 69, 20, 75, 66, 94, 47, 57, 62, 72, 85, 24, 31, 4, 7, 51, 40, 90, 26, 88, 58, 1, 71, 16, 3, 38, 6, 14, 89, 81, 99, 55, 64, 92, 87, 60, 46, 67, 45, 73, 36, 77, 97, 95, 48, 21, 65, 59, 42, 33, 44, 54, 63, 96, 13, 9, 30, 52, 53, 8, 56}
  5. Textfield(input) → inputBox
  6. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  7. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  8. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  9. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  10. Sequence(Sample[NumbersQ, NumberOfQ(k)], k, 1, 100) → SampleQList, {{144, 49, 121, 9, 4, 16}, {81, 1, 25, 100, 49}, {144, 9, 36, 100, 49}, {16, 1, 81, 144, 4}, {16, 4, 49, 64, 144}, {1, 100, 64, 121, 16, 81}, {81, 144, 4, 25}, {16, 4, 49, 81, 1}, {144, 100, 81, 1, 9, 121}, {100, 121, 36, 9, 25}, {36, 25, 100, 4}, {49, 36, 81, 4, 16}, {4, 9, 100, 25, 144, 49}, {121, 4, 25, 64}, {144, 9, 36, 81}, {64, 25, 49, 1}, {100, 144, 1, 64, 36, 121}, {64, 81, 9, 121, 25, 144}, {121, 9, 49, 1}, {16, 25, 9, 100}, {9, 25, 4, 81, 49, 36}, {36, 1, 100, 144}, {9, 4, 16, 121, 49}, {64, 100, 81, 144}, {36, 4, 64, 1, 16, 144}, {36, 4, 64, 144}, {25, 36, 121, 49, 144}, {100, 25, 81, 64, 144}, {81, 16, 25, 144, 49}, {144, 9, 25, 36}, {4, 25, 16, 1, 81}, {25, 64, 1, 4}, {1, 9, 36, 121, 4, 81}, {25, 49, 81, 121, 16, 64}, {9, 25, 121, 100, 1}, {36, 1, 4, 25}, {144, 1, 16, 121}, {49, 64, 4, 100, 16}, {81, 100, 36, 25, 16}, {81, 100, 25, 144, 1, 4}, {16, 121, 49, 144, 1}, {1, 25, 100, 121, 9, 49}, {81, 121, 49, 36, 4}, {144, 81, 121, 25, 9}, {4, 25, 81, 144, 49}, {49, 1, 9, 36, 64, 25}, {25, 144, 81, 9, 64, 100}, {81, 49, 1, 36, 144, 9}, {81, 144, 1, 9}, {64, 81, 1, 121}, {16, 1, 36, 64, 25, 4}, {121, 9, 4, 16, 81}, {144, 4, 16, 36}, {25, 144, 81, 4, 121, 49}, {100, 81, 49, 64}, {36, 4, 16, 1, 49}, {144, 100, 25, 64, 16}, {9, 81, 100, 144}, {1, 100, 81, 144, 16, 25}, {64, 81, 25, 16, 100}, {16, 36, 64, 121, 144, 9}, {25, 16, 81, 4, 64, 9}, {64, 9, 4, 16, 144, 1}, {100, 16, 36, 144, 64, 81}, {25, 144, 49, 121, 16, 9}, {81, 4, 144, 64, 9, 25}, {25, 100, 9, 144, 64, 4}, {36, 4, 16, 144, 25, 64}, {64, 36, 49, 9}, {64, 81, 49, 144}, {64, 144, 25, 9, 1, 36}, {9, 25, 100, 1, 36}, {121, 49, 16, 1, 81, 4}, {9, 81, 49, 36}, {100, 121, 81, 1, 36}, {25, 9, 1, 121, 100}, {49, 4, 25, 1, 9}, {121, 49, 1, 144}, {25, 16, 9, 49, 81, 64}, {81, 100, 4, 121, 144}, {144, 36, 121, 64, 25, 49}, {4, 25, 81, 16}, {64, 100, 1, 144, 16, 36}, {64, 121, 81, 49}, {49, 25, 100, 36}, {25, 144, 49, 81}, {16, 49, 36, 81, 25, 121}, {4, 100, 9, 36, 81}, {16, 25, 64, 36, 144, 49}, {36, 144, 25, 81, 64, 121}, {144, 9, 16, 81, 36, 25}, {100, 4, 49, 9, 81}, {1, 4, 49, 25, 16}, {16, 49, 64, 144, 100}, {36, 16, 144, 81, 9, 1}, {144, 64, 121, 4, 36}, {36, 100, 64, 16, 4, 121}, {25, 9, 49, 1}, {81, 64, 16, 144, 100}, {16, 100, 121, 144, 9, 64}}
  11. Sequence(Sample[NoNumbersQ, 10 - NumberOfQ(k)], k, 1, 100) → SampleNoQList, {{128, 21, 28, 23}, {137, 6, 51, 34, 78}, {20, 87, 129, 79, 82}, {76, 31, 133, 62, 98}, {43, 108, 70, 99, 82}, {124, 59, 3, 74}, {28, 127, 23, 108, 97, 40}, {149, 120, 75, 78, 82}, {146, 55, 79, 34}, {93, 140, 130, 20, 150}, {135, 139, 76, 66, 10, 6}, {35, 139, 70, 5, 115}, {124, 73, 82, 38}, {37, 146, 27, 18, 12, 101}, {122, 61, 90, 20, 70, 19}, {42, 134, 132, 60, 131, 10}, {40, 19, 56, 51}, {83, 26, 18, 101}, {60, 24, 10, 82, 101, 17}, {133, 37, 3, 21, 96, 140}, {93, 137, 37, 43}, {17, 109, 12, 46, 117, 53}, {104, 137, 131, 143, 107}, {51, 62, 59, 133, 134, 24}, {101, 88, 18, 150}, {89, 86, 111, 63, 10, 104}, {146, 68, 53, 98, 70}, {125, 109, 31, 86, 137}, {42, 105, 68, 135, 11}, {133, 46, 115, 147, 91, 60}, {26, 58, 101, 15, 68}, {8, 50, 91, 104, 113, 34}, {117, 127, 119, 21}, {136, 84, 79, 103}, {48, 146, 83, 98, 92}, {72, 7, 24, 120, 10, 94}, {18, 7, 76, 69, 41, 86}, {42, 7, 150, 57, 73}, {23, 13, 60, 50, 75}, {51, 119, 108, 67}, {103, 72, 12, 123, 124}, {109, 137, 44, 8}, {140, 142, 122, 63, 139}, {56, 110, 76, 96, 61}, {105, 113, 72, 13, 22}, {21, 65, 117, 28}, {7, 52, 122, 134}, {107, 50, 58, 148}, {116, 6, 26, 31, 122, 109}, {63, 103, 104, 120, 45, 6}, {67, 99, 109, 107}, {130, 8, 106, 84, 62}, {65, 132, 46, 108, 126, 39}, {126, 20, 99, 110}, {71, 15, 77, 53, 90, 12}, {78, 35, 103, 148, 57}, {57, 113, 21, 73, 90}, {5, 70, 77, 66, 30, 18}, {61, 67, 30, 40}, {106, 98, 147, 114, 50}, {50, 46, 110, 33}, {79, 115, 148, 24}, {91, 70, 125, 27}, {122, 76, 3, 114}, {115, 123, 132, 92}, {122, 71, 127, 43}, {111, 72, 14, 6}, {119, 46, 111, 78}, {95, 59, 5, 114, 112, 44}, {43, 91, 37, 102, 54, 14}, {54, 102, 21, 106}, {22, 15, 48, 149, 123}, {77, 126, 107, 19}, {20, 42, 79, 65, 57, 111}, {80, 138, 118, 67, 20}, {15, 20, 24, 19, 107}, {110, 11, 14, 10, 119}, {103, 18, 48, 12, 85, 133}, {44, 133, 48, 23}, {56, 15, 111, 112, 19}, {33, 142, 146, 112}, {58, 24, 130, 91, 41, 90}, {146, 148, 23, 15}, {51, 39, 145, 147, 149, 129}, {51, 90, 50, 79, 66, 128}, {110, 101, 141, 140, 67, 12}, {110, 70, 134, 68}, {21, 18, 92, 23, 35}, {97, 2, 19, 5}, {20, 39, 74, 67}, {82, 92, 114, 136}, {12, 76, 103, 141, 91}, {21, 101, 73, 29, 20}, {10, 30, 115, 92, 135}, {73, 124, 129, 101}, {139, 93, 72, 20, 102}, {83, 41, 120, 125}, {70, 17, 6, 45, 105, 148}, {128, 39, 85, 56, 134}, {20, 53, 104, 136}}
  12. Join({SampleQList(counter), SampleNoQList(counter)}) → TaskNumbers
  13. Text(txtElement1, PosP1 + (0, 0.05), false, true, 0, 0) → txtDD1
  14. Text(txtElement2, PosP2 + (0, 0.05), false, true, 0, 0) → txtDD2
  15. Text(txtElement3, PosP3 + (0, 0.05), false, true, 0, 0) → txtDD3
  16. Text(txtElement4, PosP4 + (0, 0.05), false, true, 0, 0) → txtDD4
  17. Text(txtElement5, PosP5 + (0, 0.05), false, true, 0, 0) → txtDD5
  18. Text(txtElement6, PosP6 + (0, 0.05), false, true, 0, 0) → txtDD6
  19. Text(txtElement7, PosP7 + (0, 0.05), false, true, 0, 0) → txtDD7
  20. Text(txtElement8, PosP8 + (0, 0.05), false, true, 0, 0) → txtDD8
  21. Text(txtElement9, PosP9 + (0, 0.05), false, true, 0, 0) → txtDD9
  22. Text(txtElement10, PosP10 + (0, 0.05), false, true, 0, 0) → txtDD10
  23. Text(txtElement11, PosP11 + (0, 0.05), false, true, 0, 0) → txtDD11
  24. Text(txtElement12, PosP12 + (0, 0.05), false, true, 0, 0) → txtDD12
  25. Text(txtElement13, PosP13 + (0, 0.05), false, true, 0, 0) → txtDD13
  26. Text(txtElement14, PosP14 + (0, 0.05), false, true, 0, 0) → txtDD14
  27. Text(txtElement15, PosP15 + (0, 0.05), false, true, 0, 0) → txtDD15
  28. Text(txtElement16, PosP16 + (0, 0.05), false, true, 0, 0) → txtDD16
  29. Text(txtElement17, PosP17 + (0, 0.05), false, true, 0, 0) → txtDD17
  30. Text(txtElement18, PosP18 + (0, 0.05), false, true, 0, 0) → txtDD18
  31. Text(txtElement19, PosP19 + (0, 0.05), false, true, 0, 0) → txtDD19
  32. Text(txtElement20, PosP20 + (0, 0.05), false, true, 0, 0) → txtDD20
  33. Take(OrderElements, 1, numberOfActiveElements) → ActiveElementList
  34. Take({box1(1), box2(1), box3(1), box4(1)}, 1, numberOfBoxes) → Boxes
  35. Sort(ZuteilungListe, Sequence[IndexOf[k, OrderElements], k, 1, 20]) → ZuteilungOrderListe
  36. Text("\textsf{\bold{← Zieh mich!\vphantom{Äg}}}", ParkP + (widthDD, 0.05), false, true, 1, 0) → CapZiehMich
  37. Text("\textsf{\bold{Box 3\vphantom{Äg}}}", PBox3 + (If[CapBoxOben, 1, -1] * (0, heightBox / 2)), false, true, 0, If[CapBoxOben, 1, -1]) → CapBox3
  38. Text("\textsf{\bold{Box 4\vphantom{Äg}}}", PBox4 + (If[CapBoxOben, 1, -1] * (0, heightBox / 2)), false, true, 0, If[CapBoxOben, 1, -1]) → CapBox4
  39. If(Defined[Unique[RemoveUndefined[Sequence[IndexOf[true, CorrectList, k], k, 1, 20]]]], Unique[RemoveUndefined[Sequence[IndexOf[true, CorrectList, k], k, 1, 20]]], {}) → CorrectZuteilung
  40. Text("\textsf{\bold{Quadratzahl\vphantom{Äg}}}", PBox1 + (If[CapBoxOben, 1, -1] * (0, heightBox / 2)), false, true, 0, If[CapBoxOben, 1, -1]) → CapBox1
  41. Text("\textsf{\bold{Keine Quadratzahl\vphantom{Äg}}}", PBox2 + (If[CapBoxOben, 1, -1] * (0, heightBox / 2)), false, true, 0, If[CapBoxOben, 1, -1]) → CapBox2
  42. Unique(KeepIf[a ≠ 0, a, ZuteilungListe]) → ZuteilungBoxen