Lemniscate Curves and Polar Deflection Angle

Lemniscate curves are a type of curve with an interesting shape that resembles a figure-eight. These curves have some unique properties, including being symmetrical and having a constant distance between two points. One important property of lemniscate curves is their polar deflection angle, which is the angle between the tangent line and the radial line at a particular point on the curve.

Transitional Lemniscate Curves

A lemniscate curve is said to be transitional throughout if its polar deflection angle at the apex is equal to D/6, where D is the total deflection angle of the curve. This means that the curve smoothly transitions from one side to the other, without any sudden changes in direction or curvature.

The total deflection angle of a lemniscate curve is 360 degrees, which means that if its polar deflection angle at the apex is D/6, then the curve will be transitional throughout.

Answer Explanation

In this question, we are given that a lemniscate curve between the tangents will be transitional throughout if its polar deflection angle at the apex is D/6. Therefore, the correct answer is option D.

This means that the curve will have a smooth transition from one side to the other, without any sudden changes in direction or curvature. This property is important in many applications, such as road design, where smooth transitions are necessary for safe and efficient travel.

Conclusion

Lemniscate curves are an interesting type of curve with many unique properties. One important property is their polar deflection angle, which determines whether the curve is transitional throughout or not. In this question, we learned that a lemniscate curve will be transitional throughout if its polar deflection angle at the apex is D/6.

D/6