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Math

Straightedge and compass

Choose the compass: click its center, then a point on the circle. For the straightedge, choose two points. Draw performs your move; the demonstration shows the requested move. Pause freezes either animation.

By Mykhailo Makarov

Straightedge and compass — Actual application image
Actual application image

What happens

Choose the compass: click its center, then a point on the circle. For the straightedge, choose two points. Draw performs your move; the demonstration shows the requested move. Pause freezes either animation. This is a guided construction, not a free drawing editor. Only named intersections of completed objects are selectable. Previews never create points. Undo removes the last move and dependent points. Move givens to start again. Right-drag rotates the instruments; the exact top view never rotates.

Equations used in the module
Equations
the two moves:  a circle about a point through another;  a line through two points;  every new point is an intersection - circle x circle, line x circle, line x line, all closed-form
bisector of AB:  arcs of radius |AB| about A and B meet at P, Q;  PQ passes through the midpoint (measured: distance 6e-17) at 90° (cos = 0)
bisector of angle BAC:  an arc about A meets the rays at D, E;  equal arcs about D and E meet at F;  the halves BAF, FAC are equal to 7e-15
regular hexagon:  the radius stepped round the circle six times lands on the first vertex (6e-17); six equal sides, six angles of 120°
square on AB:  the perpendicular at A by the bisector move on the doubled segment, D at |AB| up, C by two arcs;  diagonal/side = √2 = 1.4142135623730951
what the moves cannot do:  trisect a general angle, double the cube, square the circle - a number built by these moves lies in a tower of square roots (Wantzel 1837), and 2^(1/3), cos 20°, π do not

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