Construction of a Polygon from Rotations and their Centers

Given n points M₁, M₂, ..., M_n (n > 2) and angles a₁, a₂, ..., a_n, construct a polygon A₁, A₂, ..., A_n, A_n+1 = A₁ such that triangles A_iM_iA_i+1 are isosceles (A_iM_i = A_i+1M_i) with the apex angle ∠A_iM_iA_i+1 = a_i.

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.

Explanation

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