Construction of a Polygon from Rotations and their Centers

Given n points M1, M2, ..., Mn (n > 2) and angles a1, a2, ..., an, construct a polygon A1, A2, ..., An, An+1 = A1 such that triangles AiMiAi+1 are isosceles (AiMi = Ai+1Mi) with the apex angle ∠AiMiAi+1 = ai.

The applet has three modes. In the "Place points" mode, you define (by clicking) and move (by dragging) a sequence of points M. The order in which the points are created determines the order of traversal (orientation) of the sequence. The set of points may have two different orientations. The angles, on the other hand, are always measured in the positive direction of the coordinate system - left handed in the applet, which means that the angles are measured clockwise.

In the "Change angles" mode, angles are display next to the corresponding point and can be modified by clicking (slow) or dragging the cursor (fast) a little off their central line.

In the "Drag cursor" mode, the cursor position is rotated in order through the given angles around the given points. What is shown is a broken line whose starting and ending points are denoted by the same letter. There may be several such lines.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?


Related material

Various Geometric Constructions

  • How to Construct Tangents from a Point to a Circle
  • How to Construct a Radical Axis
  • Constructions Related To An Inaccessible Point
  • Inscribing a regular pentagon in a circle - and proving it
  • The Many Ways to Construct a Triangle and additional triangle facts
  • Easy Construction of Bicentric Quadrilateral
  • Easy Construction of Bicentric Quadrilateral II
  • Star Construction of Shapes of Constant Width
  • Four Construction Problems
  • Geometric Construction with the Compass Alone
  • Construction of n-gon from the midpoints of its sides
  • Short Construction of the Geometric Mean
  • Squares Inscribed In a Triangle I
  • Construction of a Cyclic Quadrilateral
  • Circle of Apollonius
  • Six Circles with Concurrent Pairwise Radical Axes
  • Trisect Segment: 2 Circles, 4 Lines
  • Tangent to Circle in Three Steps
  • Regular Pentagon Construction by K. Knop
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