serra´s torqued ellipses
a general understanding approach

- 2 ellipses 1; 2 with the axes 1,1.;2,2.

- are rotated 60° to each other about the common center*

- 2 is raised parallel to the common base

- a lateral surface of generatrices is drawn between the two ellipses in such a way that these lines connect parallel tangents of the two ellipses

- the resulting “torqued ellipse” is symmetrical in such a way that it consists of four (4) equal parts, whereby each of these parts again consists of two, which delimit the individual reference fields from each other

- 2 types of division make sense:
- the first is that of the common vanishing point x of the straight line
- the second is that of the point-symmetrically adjacent segments. There is one of 2 x 30° and one of 2 x 60°, if the strongest curvatures of the ellipses are chosen as reference tangents of a segmentation with straight lines

- the work consists of four identical conical segments

- in four places, the torqued ellipse swivels from the overhang on one side to the overhang on the other side

- in the side view, the surface appears vertical here.

- in fact, the boundary line between two segments is located exactly there

- the boundary lines as outer lines of all four segments are each part of both adjacent segments

- the torqued ellipse is inscribed in a cube

- the 4 boundary lines describe the diagonals of the vertical sides of the cube

- they describe a “tetrahedral zigzag”

- how do we determine whether the cone segments belong to a round or an ellipsoidal cone?

- the ellipse halfway up the sculpture has axes parallel to the outer edges of the cube

- it describes the only line that all four segments have in common

- since this does NOT have the diagonal as its longer axis to refer to the axis of the cone, the section around the cone axis is not round

- = the segments are part of an ellipsoidal cone

- to determine the round section planes, the ellipse at half the height of the sculpture helps

- all z-axes of the cones describe the spatial diagonals of the cube, which intersect at its center

- We select a cone and make an orthogonal section to its z-axis through this center point. The result is the ellipse of a base-parallel section that is characteristic of this cone

- If we rotate this ellipse in both directions around its longer axis until the shorter axis has the same length as itself, these two sections describe a circle

* I calculated this freely after a visit to Bilbao. Later I read Serra reports a 55° rotation.