MathPlotAI Logo MathPlotAI

Cube of a Binomial by Gaetano Di Caprio

Cube of a Binomial by Gaetano Di Caprio
Loading the math board and drawing, please wait…
2018-01-15 01:33
PolygonFunctionSolid GeometryGeometric Construction
This example demonstrates the geometric construction and visualization of the cube of a binomial. It involves core mathematical concepts such as polygon construction, solid geometry, geometric transformations, and function graphing. Key GeoGebra commands and objects used in the construction include Polygon, Point, Prism, Translate, and Segment, as outlined in the construction summary. It is suitable for high school and above mathematics learners to understand the integration of algebra and geometry, as well as the construction of spatial figures.

GeoGebra Commands & Parameters

  1. Polygon(AA, BB, CC, DD) → q3, aa, bb, cc, dd
  2. Point(dd) → PP
  3. Polygon(E, F, G, H) → q2, c_1, e, f, g
  4. Prism(q2, b) → h, I, spigoloEI, spigoloFJ, spigoloGK, spigoloHL, spigoloIJ, spigoloJK, spigoloKL, spigoloIL, J, K, L, facciaEFJI, facciaFGKJ, facciaGHLK, facciaEHLI, facciaIJKL
  5. Polygon(A, B, C, D) → q1, a_1, b_1, c, d
  6. Prism(q1, a) → i, M, spigoloAM, spigoloBN, spigoloCO, spigoloDP, spigoloMN, spigoloNO, spigoloOP, spigoloMP, N, O, P, facciaABNM, facciaBCON, facciaCDPO, facciaADPM, facciaMNOP
  7. Prism(facciaBCON, b) → j, Q, spigoloBQ, spigoloCR, spigoloOS, spigoloNT, spigoloQR, spigoloRS, spigoloST, spigoloQT, R, S, T, facciaBCRQ, facciaCOSR, facciaNOST, facciaBNTQ, facciaQRST
  8. Prism(facciaMNOP, b) → k, U, spigoloMU, spigoloNV, spigoloOW, spigoloPZ, spigoloUV, spigoloVW, spigoloWZ, spigoloUZ, V, W, Z, facciaMNVU, facciaNOWV, facciaOPZW, facciaMPZU, facciaUVWZ
  9. Prism(facciaCDPO, b) → m, A_1, spigolo1, spigolo2, spigolo4, spigolo3, spigolo5, spigolo7, spigolo8, spigolo6, B_1, C_1, D_1, faccia1, faccia3, faccia4, faccia2, faccia5
  10. Prism(facciaEHLI, a) → n, E_1, spigolo10, spigolo9, spigolo11, spigolo12, spigolo13, spigolo15, spigolo16, spigolo14, F_1, G_1, H_1, faccia6, faccia7, faccia9, faccia8, faccia10
  11. Prism(facciaEFJI, a) → o, I_1, spigolo17, spigolo18, spigolo20, spigolo19, spigolo21, spigolo23, spigolo24, spigolo22, J_1, K_1, L_1, faccia11, faccia13, faccia14, faccia12, faccia15
  12. Prism(q2, (-a)) → p, M_1, spigolo25, spigolo26, spigolo27, spigolo28, spigolo29, spigolo31, spigolo32, spigolo30, N_1, O_1, P_1, faccia16, faccia18, faccia19, faccia17, faccia20
  13. Translate(h, Vector[(t_b * v)]) → b3
  14. Translate(i, Vector[(t_a * (-v))]) → a3
  15. Translate(j, Vector[(t_{a2b} * vv_1)]) → a2b1
  16. Translate(m, Vector[(t_{a2b} * vv_2)]) → a2b3
  17. Translate(k, Vector[(t_{a2b} * vv_3)]) → a2b2
  18. Translate(n, Vector[(t_{ab2} * (-vv_1))]) → ab21
  19. Translate(o, Vector[(t_{ab2} * (-vv_2))]) → ab22
  20. Translate(p, Vector[(t_{ab2} * (-vv_3))]) → ab23
  21. Prism(q3, l) → q, Q_1, spigolo33, spigolo34, spigolo35, spigolo36, spigolo37, spigolo39, spigolo40, spigolo38, R_1, S_1, T_1, faccia21, faccia23, faccia24, faccia22, faccia25
  22. Segment(U_1, V_1) → r
  23. Segment(V_1, W_1) → s
  24. Segment(W_1, Z_1) → t
  25. Segment(Z_1, U_1) → f_1
  26. Segment(AA, PP) → g_1
  27. Segment(PP, DD) → h_1