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Approximation of Pi

Approximation of Pi
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2013-04-27 18:59
CirclePolygonSequenceCoordinate GeometryGeometric Construction
This example demonstrates the approximation of pi as approximately 3.14 using geometric methods. It involves the properties of circles and the concept of approximating a circle with polygons. Commands used include Circle, Sequence, Polygon, Intersect, Segment, and are suitable for students in middle school and above to learn about geometry and limits.

GeoGebra Commands & Parameters

  1. Circle(S_2, T_2) → q_2
  2. Sequence(Rotate[T_2, (i * 360 / Sides)°, S_2], i, 1, Sides) → list1
  3. Polygon(list1) → poly2, , ,
  4. Sequence(Line[S_2, Element[list1, i]], i, 1, Sides) → list2
  5. Sequence(Tangent[Element[list1, i], q_2], i, 1, Sides) → list3
  6. Intersect(Element[list3, 1], Element[list3, 2]) → C_2
  7. Intersect(Element[list3, 2], Element[list3, 3]) → D_2
  8. Polygon(C_2, D_2, Sides) → poly4, n_2, q_3, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, r_3, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, s_3, t_3, a, b, c, d, e, f, p_2, g, h, i, j, k, l, m, p, q, r, i_3, s, a_1, b_1, c_1, d_1, e_1, f_1, g_1, h_1, i_1, j_3, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, k_3, a_2, b_2, c_2, d_2, e_2, f_2, g_2, h_2, i_2, j_2, l_3, k_2, F_2, R_2, U_2, V_2, W_2, Z_2, A_3, B_3, C_3, m_3, D_3, E_3, A, B, C, D, E, F, G, H, n_3, I, J, K, L, M, N, O, P, Q, R, p_3, S, T, U, V, W, Z, A_1, B_1, C_1, D_1
  9. Segment(S_2, T_2) → t

AI Drawing Prompt Reference

Draw a circle, then generate a polygon by rotating the circle around its center, gradually increasing the number of sides to observe how the polygon approximates the circle, ultimately forming a polygon that closely resembles a circle to estimate the value of pi. Start by drawing a circle, then rotate the circle around its center to create the vertices of the polygon, use these vertices to draw the polygon, and finally draw the sides of the polygon, using the intersections of the polygon's sides with the circle's tangents to approximate the circle's shape.
The prompt above was compiled from the original drawing commands and is for reference only.