Dynamic Geometry Demo for Parameter r in (-3, 3)
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ATC Cobwebs and Linear Difference Equations
This GeoGebra example demonstrates how a geometric configuration of points, segments, and intersections changes as the parameter r varies within the open interval -3 < r < 3. The core mathematical concept is the interplay between inequality constraints and dynamic geometry, emphasizing interval representation on the number line, point loci, and symmetry. The construction uses commands such as Point, Segment, and Intersect, with objects including r, C, f, A, b, c, and numerous labeled points (A1-A22, B1, C1) plus step markers (steps, D1-D7, E1-E2), indicating a multi-step interactive model. This is suitable for middle or high school students to explore how parameter ranges affect geometric shapes, reinforcing understanding of inequalities, coordinate geometry, and logical reasoning through visual manipulation.
GeoGebra Commands & Parameters
Point(yAxis) → CPoint(xAxis) → ASegment(A, (x(A), f(x(A)))) → cSegment((A1, A2), (A2, A2)) → B1Segment((A2, A2), (A2, A3)) → C1Segment((A2, A3), (A3, A3)) → B2Segment((A3, A3), (A3, A4)) → C2Segment((A3, A4), (A4, A4)) → B3Segment((A4, A4), (A4, A5)) → C3Segment((A4, A5), (A5, A5)) → B4Segment((A5, A5), (A5, A6)) → C4Segment((A5, A6), (A6, A6)) → B5Segment((A6, A6), (A6, A7)) → C5Segment((A6, A7), (A7, A7)) → B6Segment((A7, A7), (A7, A8)) → C6Segment((A7, A8), (A8, A8)) → B7Segment((A8, A8), (A8, A9)) → C7Segment((A8, A9), (A9, A9)) → B8Segment((A9, A9), (A9, A10)) → C8Segment((A9, A10), (A10, A10)) → B9Segment((A10, A10), (A10, A11)) → C9Segment((A10, A11), (A11, A11)) → B10Segment((A11, A11), (A11, A12)) → C10Segment((A11, A12), (A12, A12)) → B11Segment((A12, A12), (A12, A13)) → C11Segment((A12, A13), (A13, A13)) → B12Segment((A13, A13), (A13, A14)) → C12Segment((A13, A14), (A14, A14)) → B13Segment((A14, A14), (A14, A15)) → C13Segment((A14, A15), (A15, A15)) → B14Segment((A15, A15), (A15, A16)) → C14Segment((A15, A16), (A16, A16)) → B15Segment((A16, A16), (A16, A17)) → C15Segment((A16, A17), (A17, A17)) → B16Segment((A17, A17), (A17, A18)) → C16Segment((A17, A18), (A18, A18)) → B17Segment((A18, A18), (A18, A19)) → C17Segment((A18, A19), (A19, A19)) → B18Segment((A19, A19), (A19, A20)) → C18Segment((A19, A20), (A20, A20)) → B19Segment((A20, A20), (A20, A21)) → C19Segment((A20, A21), (A21, A21)) → B20Segment((A21, A21), (A21, A22)) → C20Segment((A21, A22), (A22, A22)) → B21Segment((A22, A22), (A22, A23)) → C21Segment((A22, A23), (A23, A23)) → B22Segment((A23, A23), (A23, A24)) → C22Segment((A23, A24), (A24, A24)) → B23Segment((A24, A24), (A24, A25)) → C23Segment((A24, A25), (A25, A25)) → B24Segment((A25, A25), (A25, A26)) → C24Segment((A25, A26), (A26, A26)) → B25Segment((A26, A26), (A26, A27)) → C25Segment((A26, A27), (A27, A27)) → B26Segment((A27, A27), (A27, A28)) → C26Segment((A27, A28), (A28, A28)) → B27Segment((A28, A28), (A28, A29)) → C27Segment((A28, A29), (A29, A29)) → B28Segment((A29, A29), (A29, A30)) → C28Segment((A29, A30), (A30, A30)) → B29Segment((A30, A30), (A30, A31)) → C29Segment((A30, A31), (A31, A31)) → B30Segment((A31, A31), (A31, A32)) → C30Segment((A31, A32), (A32, A32)) → B31Segment((A32, A32), (A32, A33)) → C31Segment((A32, A33), (A33, A33)) → B32Segment((A33, A33), (A33, A34)) → C32Segment((A33, A34), (A34, A34)) → B33Segment((A34, A34), (A34, A35)) → C33Segment((A34, A35), (A35, A35)) → B34Segment((A35, A35), (A35, A36)) → C34Segment((A35, A36), (A36, A36)) → B35Segment((A36, A36), (A36, A37)) → C35Segment((A36, A37), (A37, A37)) → B36Segment((A37, A37), (A37, A38)) → C36Segment((A37, A38), (A38, A38)) → B37Segment((A38, A38), (A38, A39)) → C37Segment((A38, A39), (A39, A39)) → B38Segment((A39, A39), (A39, A40)) → C38Intersect(f, b) → B