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How to Find a Square Root with a Compass?

How to Find a Square Root with a Compass?
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2020-12-09 17:10
VectorFunctionGeometric Construction
This example demonstrates how to find the square root of a number using a compass. Key mathematical concepts include the concept of roots and geometric construction. Through constructing circles, segments, midpoints, and intersections, the process is illustrated step by step. Commands used include Point, Segment, Ray, Midpoint, Circle, Intersect, etc. Suitable for students at the junior high school level and above to learn geometric construction and the concept of roots.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Segment(A, O) → f
  3. Point(yAxis) → C
  4. Ray(O, C) → g
  5. Midpoint(A, B) → D
  6. Circle(D, A) → c
  7. Intersect(c, g) → E,
  8. Sequence((i, 0), i, 0, 100) → l1
  9. Segment(E - (0.2, 0), E + (0.2, 0)) → h
  10. Semicircle(A, B) → d
  11. Sequence((0, sqrt(i)), i, 0, 100) → l3
  12. Sequence(Semicircle[A, Element[l1, i]], i, 1, 100) → l2
  13. Vector(G, F) → u
  14. Polygon(A, E, B) → t1, b, a, e
  15. Circle(H, 1) → k
  16. Point(k) → I
  17. Tangent(I, k) → i,
  18. Circle(H, sqrt(x(B))) → p
  19. Intersect(p, i) → J, K
  20. Line(H, i) → j
  21. OrthogonalLine(J, j) → l
  22. Intersect(j, l) → L
  23. Intersect(p, j) → M, N
  24. Line(L, l) → m
  25. Line(M, m) → n
  26. Intersect(n, i) → P
  27. Polygon(H, I, J, L) → q1, h_1, i_1, j_1, l_1
  28. Polygon(L, J, P, M) → q2, l_2, j_2, p_1, m_1
  29. Midpoint(H, I) → Q
  30. Segment(P, I) → s
  31. Segment(I, P) → t
  32. Segment((0, 0), E) → f_1
  33. Segment(H, J) → q
  34. CircleArc(H, J, M) → r

AI Drawing Prompt Reference

On a coordinate plane, place a point on the x-axis and connect it to the origin with a segment. Place a point on the y-axis and draw a ray from the origin through it. Find the midpoint of the x-axis segment and draw a circle centered there passing through the origin; this circle intersects the y-axis ray at a point. Construct a semicircle with the two x-axis points as endpoints, and add a series of equally spaced points along the axis. From the intersection point, draw a short horizontal segment. Then form a triangle using the origin, the intersection point, and the x-axis point. Next, draw a unit circle centered at a fixed point, pick a point on it, and draw a tangent line. Using that fixed point as center, draw a circle with radius equal to the square root of the x-coordinate of the original x-axis point; this circle intersects the tangent. Through perpendiculars and intersections, construct two quadrilaterals, and connect relevant points with segments and a circular arc.
The prompt above was compiled from the original drawing commands and is for reference only.