Consider an isosceles right-angled triangle OXY. Project points P of the hypotenuse at P

[1] The circle (c) circumscribing the rectangle PP

[2] OFPF' is a rectangle, FF' is a diameter of (c), and is orthogonal to P

This property shows that Z lies on a parabola with focus F and directrix OF'. In addition shows that P

It is interesting to transfer the previous construction to an arbitrary triangle via an affinity mapping OXY to that triangle.

The figure above shows the image parabola under the affinity P'=A(P) transforming OXY to the arbitrary triangle O'X'Y'. The map respects parallelity but no metrical relations and orthogonality. P

Thus, the Artzt parabola, in the general case, is the envelope of diagonals of parallelograms constructed from points P' by drawing parallels to the sides O'X', O'Y'.

The focus and the directrix are not preserved in general. Thus, F

Artzt.html

Artzt2.html

Artzt_Generation.html

Artzt_Generation2.html

Parabola.html

ParabolaChords.html

ParabolaSkew.html

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