Strophoid

The strophoid ( adjectival word of Greek art στροφή, Strofi - the verse, twist, bend, twist, bend ), more precisely the straight strophoid, is a special plane algebraic curve of 3rd order.

Equations of the straight strophoid

Following is a positive real number. In the graph of strophoid on the right side is called as. In Cartesian coordinates, the strophoid is defined by

A parametric representation of this curve is

Looking at the strophoid in polar coordinates so is their defining equation

Properties of the straight strophoid

In the following, each case that the coordinate axes are as shown in the sketch.

• The points of the straight strophoid are characterized by the following geometric properties: Let S of the apex of the curve and P, any point on the curve, which is different from S. If we denote the different of S and P intersection of the line with the SP curve as Q and the intersection with the y- axis than R, so R is far from P and Q and the origin O equal.

• Straight strophoid is axisymmetrical with respect to the x-axis. Exactly two points on the curve lying on the axis of symmetry, namely the origin and the vertex S of the coordinates.

• The origin of the coordinate system is a double point of the curve, ie it is traversed twice. The two bisectors of the quadrants of the coordinate system coincide with the two tangents in the origin.

• The ( dashed line in the diagram) straight line with the equation is the asymptote of the curve.

• The loop includes a straight strophoid area with the content.

• The area which is bounded by the curve and the asymptote and extends to infinity, the surface area has.

• The strophoid is also under the name of Ala, Focal, harmonious curve ( by value ), and Kukumaide Pteroides torricellana known.